Ultrafast processes in molecules visualized with femtosecond … · 2017-10-26 · structure during...

Ultrafast processes in molecules visualized

with femtosecond pump–probe

photoelectron spectroscopy

vorgelegt von

Dipl.-Phys.

Torsten Leitner

aus Kirchham

von der Fakultat II - Mathematik und Naturwissenschaftender Technischen Universitat Berlin

zur Erlangung des akademischen Grades

Doktor der Naturwissenschaften- Dr. rer. nat. -

genehmigte Dissertation

angefertigt am Helmholtz-Zentrum Berlin fur Materialien und EnergieInstitut fur Methoden und Instrumentierung der Forschung

mit Synchrotronstrahlung

Promotionsausschuss:

Vorsitzender: Prof. Dr. Mario Dahne

Gutachter: Prof. Dr. Dr. h.c. Wolfgang Eberhardt

Gutachter: Prof. Dr. Alexander Fohlisch

Tag der wissenschaftlichen Aussprache: 01. November 2012

Berlin 2012

D83

Zusammenfassung

Eine der großen Herausforderungen der modernen Wissenschaft ist es, die Chemieauf ihrer fundamentalen inter- und intra-molekularen Ebene zu verstehen. Das Elek-tron ist der Hauptakteur in chemischen Reaktionen und erfordert Untersuchungen auffundamentalen Langen- und Zeitskalen im Nanometer- bzw. Femto- bis Picosekun-denbereich. Photoanregung ist ein vielfach in der Natur vorkommender Ausloser furchemische Prozesse – ohne die Moglichkeit, das Sonnenlicht als Energiequelle zunutzen, ware Leben wie wir es kennen nicht moglich.Diese Arbeit untersucht Methoden zur Visualisierung der Interaktion von Licht mitder elektronischen Struktur von Molekulen sowie der Dynamik in der elektronsichenStruktur nach Photoanregung. Die Methode, um die Funktion des Elektrons zu un-tersuchen, war zeitaufgeloste Photoelektronenspektroskopie (TRPES – time-resolvedphotoelectron spectroscopy).Die Arbeit gliedert sich in zwei Hauptteile: Teil I “Methoden und Instrumente”, in demexperimentelle Aufbauten und Werkzeuge vorgestellt werden, die in der ultraschnellenPhotoelektronenspektroskopie zum Einsatz kommen, und Teil II “Experimente”, indem drei konkrete Experimente zur elektronischen Struktur von Molekulen vorgestelltund diskutiert werden.In Teil I wird die Implementierung und der Betrieb eines TRPES Aufbaus zur Unter-suchung ultraschneller Dynamik in elektronischen Strukturen detailliert dargestellt,der auf der Erzeugung Hoher Harmonischer eines Laser basiert. Desweiteren wirdeine Hochtemperatur-Molekul-Verdampfungsquelle vorgestellt, die im Rahmen dieserArbeit entwickelt wurde, und die TRPES Experimentieraufbauten werden erlautert,die fur diese Arbeit am Max-Born-Institut in Berlin und am Freie Elektronen LaserFLASH in Hamburg, verwendet wurden. Die Herausforderungen und Losungen zurDurchfuhrung eines TRPES Experiments bei FLASH werden detailliert geschildert,insbesondere wird ein Schema zur prazisen Bestimmung der Pump–Probe Zeitenvorgestellt, die bei FLASH von einer großen Schuss-zu-Schuss Schwankung der Licht-pulsankuftszeiten beinflusst sind.Teil II demonstriert die Verwendbarkeit von Photoelektronenspektroskopie zur Visu-alisierung der Dynamik der elektronischen Struktur von Molekulen. Die MoglichkeitSchlussfolgerungen uber die Symmetrieeigenschaften der Elektronendichteverteilungzu ziehen wird untersucht, indem die Polarisationsabhangigkeit eines zwei-Farbenzwei-Photonen Ionisierungsprozesses mit einem theoretischen Modell verglichen wird.Die Visualisierung koharenter Kern- und Elektronenwellenpaketoszillationen von NaIMolekulen im angeregten Zustand mittels TRPES mit sub 100 fs Zeitauflosung wirddemonstriert und zeigt quantenmechanische E↵ekte, wie z.B. koharente Uberlagerungvon Wellenpaketen, auf, die sich in der Koexistenz eines einzelnen Molekuls in ver-schiedenen intra-molekularen Abstanden widerspiegelt. Weiterhin wird ein Trans-fer des Wellenpakets zwischen verschiedenen intra-molekularen Potenzialen, folglichmolekularen Zustanden, visualisiert. Zuletzt wird ein Experiment zur O↵enlegung dertransienten elektronischen Struktur wahrend der schrittweisen Photo-Dissoziation von

iii

Fe(CO)5 Molekulen in der Gas-Phase vorgestellt, Der Schwerpunkt liegt hierbei aufder Entflechtung des komplexen TRPES Datensatzes bzw. der Trennung der uberlap-penden Photoelektronenspektren, die von den im Laufe des Photo-Dissoziations-Prozesses auftretenden verschiedenen molekularen Spezies stammen.

iv

Abstract

One of the grand challenges in modern science is understanding chemistry on a fun-damental inter- and intra-molecular scale. The principal player in chemical reactionsis the electron and therefore, the fundamental scales to address are the sub to fewnanometer length scale and the femto- to picosecond time scale. A widely occur-ring trigger for chemical reactions in nature is photo-excitation – without the abilityof harvesting sunlight and using it for further chemical processes life as we knowit would not be possible. Therefore, in order to contribute to understanding chem-istry on a fundamental level, methods for visualizing the interaction of light with theelectronic structure of molecules and the dynamics in the electronic structure afterphoto-excitation are investigated in this thesis. The method of choice to address thefunction of the electron was time-resolved photoelectron spectroscopy (TRPES).The thesis is divided into two major parts: Part I “Methods and Instruments” whereexperimental setups and tools used for ultrafast photoelectron spectroscopy are in-troduced and Part II “Experiments”, presenting and discussing three concrete exper-iments on electronic molecular structures.In Part I, the implementation and operation of a TRPES setup for investigatingultrafast electronic structure dynamics, based on laser high-harmonic generation, isdiscussed in detail. Furthermore, a high-temperature molecular evaporation sourcedeveloped within the framework of this thesis is introduced and the TRPES setupsused for this thesis at the Max-Born-Institute in Berlin and the free electron laserFLASH on the DESY site in Hamburg are detailed. The challenges and solutions forperforming TRPES at FLASH are addressed in detail, especially a scheme for accuratepump–probe timing, which at FLASH underlies a large shot-to-shot arrival-time jitter.Part II demonstrates the usability of photo-electron spectroscopy for visualizing thedynamics of the electronic structure in molecules. The possibility of drawing con-clusions on symmetry properties of the electron density distribution is explored bycomparing the polarization dependence of a two-color two-photon ionization processto an approximative theoretical model. The visualization of coherent nuclear and elec-tronic wave packet oscillations in excited state NaI molecules by means of TRPESwith sub 100 fs time resolution is demonstrated, revealing quantum mechanical e↵ectslike coherent superposition of wave packets reflected in the co-existence of a singlemolecule in several intra-molecular distances. Furthermore, a transfer of the molecularwave packet population between intra-molecular potentials, hence between molecu-lar states, is visualized. Lastly, an experiment on revealing the transient electronicstructure during the step-wise photo-dissociation of Fe(CO)5 molecules in gas-phaseis presented, with a focus on how to disentangle the complex TRPES data set andseparate the overlapping photoelectron spectra arising from the di↵erent molecularspecies occurring during the photo-dissociation process.

v

Contents

1 Introduction 1

I Methods and Intruments 3

2 High-order Harmonic Generation at HZB 52.1 HHG as a three step process . . . . . . . . . . . . . . . . . . . . . . 62.2 The HHG setup at HZB . . . . . . . . . . . . . . . . . . . . . . . . 9

3 High-Temperature Sample Source 27

4 Pump-Probe Setup at the Max-Born-Institute Berlin 31

5 Pump-Probe Setup at the Free Electron Laser in Hamburg 33

II Experiments 41

6 Polarization Control in Two-Color Above Threshold Ionization 436.1 Polarization dependence . . . . . . . . . . . . . . . . . . . . . . . . 446.2 Theoretical model . . . . . . . . . . . . . . . . . . . . . . . . . . . 466.3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.5 Conclusion for this chapter . . . . . . . . . . . . . . . . . . . . . . 54

7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI 577.1 How it works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.3 Ultrafast auto-ionizing dissociation . . . . . . . . . . . . . . . . . . 677.4 Coherent electronic and nuclear wave packet oscillations . . . . . . . 697.5 Conclusion for this chapter . . . . . . . . . . . . . . . . . . . . . . 83

vii

8 Transient Electronic Structures in Photo-Dissociation of Fe(CO)5 878.1 Rate model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 888.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 918.3 Decay of transient Fe(CO)4 and creation of free CO . . . . . . . . . 958.4 Transient photoelectron spectra . . . . . . . . . . . . . . . . . . . . 968.5 Conclusion for this chapter . . . . . . . . . . . . . . . . . . . . . . 99

9 Conclusion 103

Bibliography 105

Acknowledgment 113

viii

List of Figures

2.1 Exemplary HHG spectrum . . . . . . . . . . . . . . . . . . . . . . . 52.2 The three steps of HHG . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Pump-probe HHG setup at HZB . . . . . . . . . . . . . . . . . . . . 92.4 Experimental chamber at HZB . . . . . . . . . . . . . . . . . . . . 132.5 Time-of-flight electron spectrometer . . . . . . . . . . . . . . . . . . 142.6 Exemplary auto-correlation measurement . . . . . . . . . . . . . . . 192.7 Exemplary cross-correlation measurement . . . . . . . . . . . . . . . 202.8 Divergence of the HHG source . . . . . . . . . . . . . . . . . . . . . 222.9 Modified HHG setup for absolute photon number measurements and

GMD functional principle . . . . . . . . . . . . . . . . . . . . . . . 232.10 Shot-to-shot stability of the HHG source . . . . . . . . . . . . . . . 242.11 Purity of the GMD detection gas . . . . . . . . . . . . . . . . . . . 252.12 Reliability of a semiconductor diode vs. photon flux for several har-

monic photon enegies . . . . . . . . . . . . . . . . . . . . . . . . . 262.13 Reliability of a semiconductor diode vs. radiant power . . . . . . . . 26

3.1 High-temperature sample source . . . . . . . . . . . . . . . . . . . . 28

4.1 Experimental setup at MBI . . . . . . . . . . . . . . . . . . . . . . 31

5.1 Experimental setup at FLASH . . . . . . . . . . . . . . . . . . . . . 36

6.1 Two-color two-photon ATI principle . . . . . . . . . . . . . . . . . . 436.2 Sideband polarization dependence in Helium . . . . . . . . . . . . . 446.3 Idealized one-photon ionization PADs for motivating the sideband po-

larization dependence . . . . . . . . . . . . . . . . . . . . . . . . . 456.4 Typical sideband polarization dependence measurement in Argon . . 506.5 Photoelectron spectra for parallel and perpendicular polarization . . . 516.6 Polarization dependence: experiment vs. model . . . . . . . . . . . . 52

ix

7.1 Calculated intra-molecular potentials for the NaI molecule . . . . . . 597.2 Calculated electron binding energies versus intra-molecular distance

for photo-excited NaI molecules . . . . . . . . . . . . . . . . . . . . 607.3 Crossing, inner and outer turn visualized in the intra-molecular poten-

tials picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617.4 Simplified modeled photoelectron spectral evolution from photo-excited

NaI molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627.5 Ground state spectrum of NaI . . . . . . . . . . . . . . . . . . . . . 657.6 TRPES map from photo-excited NaI molecules . . . . . . . . . . . . 667.7 Photoelectron peak shift during dissociation to I� ions for negative

delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687.8 Distinguished features in the NaI TRPES maps . . . . . . . . . . . . 697.9 TRPES maps depicting the NaI wave packet dynamics: Plain and

normalized separately for each delay . . . . . . . . . . . . . . . . . . 707.10 Delay scans for wave packet dynamics in the A–X potential trap . . . 747.11 Delay scan map from photo-excited NaI molecules . . . . . . . . . . 777.12 Delay scans for wave packet dynamics in the B–X potential trap . . . 787.13 Simplified model versus experimental photoelectron spectra for se-

lected delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

8.1 Fe(CO)5 photo-dissociation sequence . . . . . . . . . . . . . . . . . 878.2 Rate model for Fe(CO)5 photo-dissociation . . . . . . . . . . . . . . 908.3 Fastest feature – time resolution and t0 . . . . . . . . . . . . . . . . 928.4 Comparison of valence photoelectron spectra for Fe(CO)5, pump–

probe di↵erences and CO molecules . . . . . . . . . . . . . . . . . . 938.5 Content of non-excited Fe(CO)5 in the TRPES data . . . . . . . . . 948.6 Creation of CO and decay of transient Fe(CO)4 . . . . . . . . . . . . 958.7 Scaled di↵erences at selected delays . . . . . . . . . . . . . . . . . . 968.8 Experimental valence spectra for Fe(CO)5, Fe(CO)4 and Fe(CO)3 . . 988.9 Calculated valence spectra for Fe(CO)5, Fe(CO)4 and Fe(CO)3 . . . 98

x

List of Tables

6.1 Electronic configurations for sideband formation from the HOMO forall investigated systems . . . . . . . . . . . . . . . . . . . . . . . . 49

6.2 Sideband modulation � and �2: experiment vs. literature . . . . . . 536.3 Asymmetry parameter �2 for the HOMO of N2 . . . . . . . . . . . . 54

7.1 NaI bound states and corresponding free fragments . . . . . . . . . . 607.2 NaI ground state valence orbitals . . . . . . . . . . . . . . . . . . . 64

8.1 Rate model for Fe(CO)5 photo-dissociation sequence . . . . . . . . . 89

xi

1 Introduction

One of the grand challenges in modern science is understanding chemistry on anfundamental inter- and intra-molecular scale [1]. Understanding chemistry on thisfundamental level means elucidating the complex dynamics of the correlated andcoupled motion of nuclei and electrons, which build the basis for chemical processes.As the nuclei rearrange, intra-molecular bonds break and new bonds are formed withinthe natural molecular time scales of femto- to picoseconds and on length scales fromsub- to few nanometers. Ultimately, understanding chemistry leads to the dream ofgaining control over chemical reactions, enabling new ways of designing materials,driving them along the desired reaction path and corresponding transient states tothe desired products. Gaining insight into photochemical reactions, as photosynthesisor photovoltaic processes or clarifying combustion processes in fuels, for example,can lead to new and optimized solutions for e�cient light harvesting and fuel design,respectively. Therefore, understanding chemistry on the fundamental level can providethe knowledge to master one of the biggest challenges for humanity: “How to satisfythe world’s increasing demand of energy and at the same time account for the world-wide climate change and reduce the exhaustion of climate gases?”.The (valence) electrons are the ’glue inside molecules’, as transferring and sharingelectrons between atoms means breaking and formation of molecular bonds. The elec-trons are hence the principal player in chemical reactions. Therefore, understandingchemistry requires us to address the function and dynamics of the evolution of theelectronic structure during a reaction. Another important aspect of chemical reactionsis that in general they start from molecules in an excited state, where the excitationprovides the necessary energy to trigger the reaction. Photo-excitation, hence theabsorption of one or more photons, is one of the most important ways for triggeringchemical reactions in nature. Life as we know it would not be possible without theability of using the earth’s primary energy source, sunlight.

Time-resolved pump–probe photoelectron spectroscopy (TRPES) techniques can serveas a powerful tool to investigate the properties of the electronic structure of moleculesand the dynamics therein. A pump laser pulse of desired photon energy excites thesample and triggers a photochemical reaction. A delayed probe pulse photo-ionizesthe dynamically evolved sample, creating ions and photoelectrons. Measuring theproperties of these photoelectrons, for example their kinetic energy or their ejectionangular distribution, enables to directly map the properties of the electronic structureof the system under investigation. Varying the delay between pump and probe pulsesthus enables recording a ’molecular movie’ of the dynamics in the molecular electronic

1

1 Introduction

structure during photochemical reactions. Photo-ionization is capable of accessing allstates within the energy of the ionizing probe photons, hence there are no invisibledark states [2]. Furthermore, TRPES enables us to visualize nature’s restlessness onthe fundamental level of quantum mechanics, where the description of the physicalreality falls apart to probability densities and interfering complex wave packets, incontrast to the intuitive description of the macroscopic world, based on the idea ofassemblies of robust particles. Photoelectron spectra can be determined from atomsand molecules in the ground state as well as from highly complex, quantum mechan-ically entangled or superposed molecular states, arising from the interaction of twoatoms to a few thousands or even millions of atoms, in macromolecules like DNA orbiological viruses. The desired ultrafast femtosecond time resolution is provided bystate-of-the-art laser and accelerator based light sources.

This thesis deals with the implementation and operation of a laser high-harmonicgeneration based TRPES setup for experiments on matter in the gas-phase and fur-thermore with the interpretation of TRPES datasets, acquired in three di↵erent cam-paigns at three di↵erent light sources and experimental setups, moving us anothersmall step towards understanding chemistry on its fundamental level.

The thesis is divided into two major parts: Part I “Methods and Instruments” (chapters2–5) and Part II “Experiments” (chapters 6–8).Chapter 2 describes a high-order harmonic generation based femtosecond pump–probe photoelectron spectroscopy setup for investigation of ultrafast processes in theelectronic structure of molecules in the gas-phase, as implemented at HZB and theday-to-day operation of this setup. For enabling experiments with a larger numberof samples, a high-temperature sample source for evaporating molecular or atomicsamples, which are in solid or liquid phase under vacuum conditions and room temper-ature was developed within the framework of this thesis and is introduced in chapter3. Chapters 4 and 5 describe the pump–probe photoelectron spectroscopy setups usedin measurement campaigns at the Max-Born-Institute Berlin and at the free-electronlaser FLASH in Hamburg, respectively. An experiment on polarization control of two-color two-photon ionization of small molecules and atoms, where the influence ofthe symmetry of the electronic structure on a two-photon ionization process is in-vestigated is detailed in chapter 6. Based on the ground-breaking femtosecond spec-troscopy experiments by A. Zewail and coworkers [3, 4], the coherent electronic andnuclear dynamics in photo-excited NaI molecules are revisited in chapter 7, by meansof time-resolved pump–probe photoelectron spectroscopy, disclosing deeper insightsinto the coherent molecular wave packet dynamics. In chapter 8 an experiment onrevealing the transient electronic structure during the step-wise photo-dissociation ofFe(CO)5 molecules in gas-phase is presented. The thesis is concluded in chapter 9.

2

Part I

Methods and Intruments

3

2 High-order Harmonic Generationat HZB

High-order harmonic generation (HHG) has emerged as a widely used tool to producebright femto- and attosecond vacuum-ultraviolet (VUV) and soft x-ray pulses [5–9]. These pulses can be used to study ultrafast atomic, molecular and magnetismdynamics [10–14] and are bright enough to perform coherent x-ray di↵ractive imagingfor investigations on the nanoscale [15]. Furthermore, the HHG process itself canprovide insight into the electronic structure of the generating molecule [16–21].HHG occurs when an intense laser field interacts with an atomic gas target. Whenrare gas atoms are irradiated by short laser pulses with peak powers of the order of1014 to 1016 W /cm2, the gas medium responds in a highly non-linear way, generatingradiation with higher frequencies co-propagating with the fundamental laser beam.In general, the obtained spectra consist of the fundamental frequency !0 plus its oddmultiples !

q

= q!0, q 2 (2N + 1) up to the cut-o↵ frequency, where the spectrumends abruptly. A typical HHG spectrum is depicted in figure 2.1.

Figure 2.1: Typical HHG spectrum measured at a previous version of the HZB HHG setup(reprinted with permission from [22]).

In the first section of this chapter the high-order harmonic generation process and asimplified semi-classical three-step model to allow for understanding the major aspectsof HHG is presented. The second section introduces the existing HHG source basedpump–probe setup at HZB: the experimental arrangement, instruments and methodsfor operation and optimization, typical characteristics and a publication on the shot-

5

2 High-order Harmonic Generation at HZB

to-shot variation of the absolute flux of the HZB HHG source and the validity of astandard average photon flux detector - a photodiode - are presented.

2.1 HHG as a three step process

HHG can be understood in an intuitive semi-classical view as a three step process[23–26]. This often is called Simple Man Model and is valid in the tunnel regime,where the frequency !0 of the fundamental generating laser is characterized by:

~!0 ⌧ Ip

⌧ Up

, (2.1)

with the ionization potential of the atom Ip

and the ponderomotive potentialUp

= e2E 2/(4m!20) of a free electron, oscillating in the electric field of the laser.

Typically, IR laser sources with photon energies of ~!0 1.6 eV (800 nm) and raregases are used for generating high harmonics. The ponderomotive potential can beapproximated from the laser peak intensity as U

p

(eV) ⇡ 6 ⇥ Ipeak(W /cm2) for 800nm lasers [25]. Hence, peak intensities around 3 ⇥ 1014 W /cm2 for Xe, Kr and Ar(Ip

=12.1, 14.1 and 15.8 eV), 4 ⇥ 1014 W /cm2 for Ne (Ip

=21.6 eV) and 5 ⇥ 1014

W /cm2 for He (Ip

=24.6 eV) or even higher peak intensities are necessary in order towell fulfill the tunnel regime constraints for typical femtosecond high power 800 nmTi:Sapphire lasers.

(1) tunnel ionization

energ

y !

(2) acceleration (3) radiative recombination

Figure 2.2: The three steps of HHG: (1) The outer electron wave packet (Gaussian shape)of an atom is trapped in the coulomb potential of the ionic core (gray line). Astrong laser electric field (thin straight line) superposes with the core potential,creating a finite potential barrier (black line), which enables tunnel ionizationof the system. (2) The free electron is accelerated in the strong electric field,gaining kinetic energy, and driven back to the parent ion, when the laser fieldchanges its sign. (3) The electron recombines with the parent nucleus and itsexcess energy, the gained kinetic energy E

kin

of the electron plus the ionizationpotential I

p

is emitted via a high harmonic photon (purple) of the frequency!q

= (Ekin

+ Ip

)/~.

6

2.1 HHG as a three step process

The three steps of HHG are depicted and described in figure 2.2. In the first step,where the atom ionizes, the electron has to tunnel through a coulombic barrier. Theheight of this barrier is characterized by the ionization potential I

p

, therefore thecondition ~!0 ⌧ I

p

implies that the absorption of many photons is necessary toionize the atom, making HHG a highly non-linear multiphoton process. The tunnelingprocess is not described quantitatively in this picture as this model serves only for aqualitative understanding of HHG. However, the highest frequency occurring in theHHG spectra can be determined quantitatively by considering the classical motionof an electron in the laser field. After ionization, when the electron appears in thecontinuum, it will immediately be accelerated in the strong laser field. Neglecting thecore attraction, thus considering a free electron and assuming a linear polarized laserfield in x-direction, the classical electron motion is described by:

m@2x

@t2= eE (t) . (2.2)

Solving this di↵erential equation within the slowly varying envelope approximation(i.e. E (t) ⇡ E cos(!0t)) and assuming zero initial velocity leads to a time dependentelectron velocity of

v(t) =eE

me

!0(sin(!0t)� sin(!0ti)) , (2.3)

and the ponderomotive potential of the electron in the fundamental laser field ofwavelength � as its classical mean kinetic energy,

Up

=⌦12m

e

v 2↵=

e2E 2

4me

!20

=e2

16⇡2me

c2E 2�2 . (2.4)

A numerical investigation of the maximum velocity of the electrons at their first returnto the parent ion results in an estimate for the maximum photon energy present inthe HHG spectrum, the cut-o↵ law :

~!c

= Ip

+ 3.17Up

/ E 2�2. (2.5)

The cut-o↵ law clarifies, that the maximum harmonic frequency achievable from theHHG process is strongly linked to the ponderomotive potential U

p

and thus to thefield amplitude and the wavelength of the fundamental laser light. The maximumapplicable field amplitude is limited, because for very high intensities of the drivinglaser well above ⇠ 1016 W/cm2, the magnetic component of the laser field becomesstrong enough to induce a lateral acceleration, hence deflecting the electron, reducingthe overlap between the electronic and the nuclear wave packet and thus preventinge�cient harmonic generation. However, the cut-o↵ law states, that the maximumharmonic frequency in the HHG spectra will increase for longer wavelengths of thedriving laser field. A shift of the cut-o↵ frequency towards the water window, or even

7


the keV range of photon energy, by using driving lasers in the few µm range wasdemonstrated very recently at experimentally relevant harmonic flux in [9, 27].Note that not only the cut-o↵ law, but also some other interesting limits on theHHG process are explained by the Simple Man Model. For instance, HHG will onlyoccur if the driving laser field is linearly polarized. Electrons in an elliptically polarizedlaser field fly in spirals and therefore miss the parent nucleus. In terms of quantummechanics, the overlap of the nuclear and the electron wave packet is reduced uponreturn. This has been observed in experiments, where the intensity of harmonics hasdecreased rapidly with increasing ellipticity [28]. However, it is possible to generateelliptically polarized harmonics with linearly polarized driving laser fields by usingaligned molecules as non-linear medium for harmonic generation, for example laseraligned N2 molecules as demonstrated in [29].

Coherence and Phase Matching

Within the Simple Man Model conclusions on the coherence properties of the HHGradiation can be drawn. The electron has to be considered as a quantum mechanicalwave packet, which undergoes a transition from a bound state to a continuum stateat a certain time t

i

, evolves in the laser field and finally descends to the bound stateagain under radiation of the kinetic energy gained while propagating through thecontinuum. This quantum wave packet oscillates with its own frequency, however thetotal phase of the electron at recombination and therefore the phase of the occurringXUV radiation is strongly linked to the time of ionization and to the strength of thefundamental laser. Thus the phase of the electronic wave packet at recombinationand therefore the phase of the XUV light are locked to the phase and amplitude ofthe fundamental laser beam. This influences the collective behavior in the spatiallydomain, since spatial coherence properties of the irradiating laser are transfered tothe harmonic emission, hence forth HHG is a spatially coherent process.The total emitted field in a macroscopic medium is given by a sum over the emissionsfrom many atoms. Thus not only the single atom response, but also collective e↵ectsas phase matching or re-absorption of the XUV light determine the intensity of thegenerated harmonics. Phase matching is given, if the radiation generated by di↵erentatoms at di↵erent positions in the medium interferes constructively at the exit of themedium. For a perfect match of phases, this condition reads as

�K = kq � q k0 = 0 , (2.6)

where �K denotes the mismatch between the wave vectors kq of harmonic q andk0 of the fundamental. Approximate phase matching is achieved for

�K Lmed < ⇡ , (2.7)

where the vector Lmed describes length and direction of the medium. The dependenceof the harmonic phase '

q

on the laser intensity at the position of emission can be

8

2.2 The HHG setup at HZB

written as 'q

= ↵q

I , where ↵q

is linked to the q-th Fourier component of the atomicpolarization and proportional to the atomic dipole moment and density. An additionalwave vector kI = �r'

q

enters the phase mismatch, leading to a generalized phasematching condition for HHG [25, 30]:

�K = kq + kI � qk0 . (2.8)

This emphasizes, that transversal intensity profile and wavefront shape do play animportant role for optimizing the HHG yield.


In this section, the high-order harmonic experiment at HZB is presented in detail. Itis based on an existing setup [22], which was further developed within the frameworkof this thesis. The experiment on two-color two-photon ionization of small moleculesdescribed in chapter 6 and measurements on the reliability of semiconductor photo-diodes [31] introduced at the end of this section were carried out at this setup.

polarizer

power & polarization control

Ti:Sapphire

f=500 mm

gas celltoroidal grating

Al foils

slit

CCD

removeablemirror

diode

toroidalmirror

delay

BBO

magnet &ion TOF

camera

electronspectrometer

785 nm1.5 mJ50 fs3 kHz

slit

0.3 mJ

1.2

mJ BS 80/20

f=400 mm

ap1 ap2

ap3

waveplate

waveplates

IR filter

ap5

ap4

dichroic mirror

dichroic mirrorSHG

IR

available for experiments IR 785 nm, < 230 µJ

SHG 393 nm, < 50 µJ HHG 30-70 nm, < 40 pJ

HHG

gas inlet with hand valve

vacuum chamber

~ 10 m

Figure 2.3: The pump-probe setup at HZB (see text for details).

Figure 2.3 shows a schematic sketch of the femtosecond pump-probe HHG setup atthe HZB lab. The whole setup is driven by a Ti:Sapphire laser at a central wavelengthof 785 nm, which delivers 50 fs pulses with a pulse energy of 1.5 mJ at a repetitionrate of 3 kHz. A beam splitter (T=0.2, R=0.8) in the very beginning of the setupsplits the incoming pulses into a 0.3 mJ pump pulse and an intense 1.2 mJ pulse forharmonic generation. The laser is situated in di↵erent hutch than the the HHG setupand the beam is transported via several mirrors to the beam splitter. The distancebetween laser and beam splitter is roughly 10 m, leading to an amplification of possible

9


pointing instabilities of the laser, which is transfered to the pointing stability of pumpand probe and to the shot-to-shot intensity stability of the harmonic yield. In orderto minimize these e↵ects, the laser hutch is equipped with a climate control system,ensuring well defined and stable humidity and temperature.After individual manipulation, the pump and probe pulses are overlapped again. Arectangular in-vacuum mirror reflects the pump pulses into the interaction region,whereas the HHG probe pulses travel curtly above this mirror. This way, the pumpand the probe beam are almost collinear in the experimental chamber at the end of thesetup with a spreading angle well below 1�, thus preventing broadening of the time-resolution due to non-collinear in-coupling. The experimental chamber is equippedwith a photoelectron spectrometer, a molecular source and tools for aligning thesetup.On the next pages, the two optical pathways and the experimental chamber aredescribed in detail, as well as typical characteristics of the setup and tuning andoptimization procedures.

2.2.1 High-Harmonic Generation Path

The part of the laser reflected by the beam splitter consists of typically 1.2 mJ pulsesand is used for harmonic generation (see figure 2.3, lower optical path). The pulsesfirst pass a �/2-wave-plate to control the polarization direction of the fundamentallaser pulse which is directly transfered to the later generated harmonics. The wave-plate is tuned such, that the polarization is aligned along the groves of the gratingfurther down the optical path to achieve optimum transmission of the grating. Twoapertures (ap1 & ap2) are used for aligning the laser and tweaking the HHG output.The laser is focused by a f=500 mm lens into a 5.5 mm long stainless steel gas cellinside the vacuum chamber for high-harmonic generation, resulting in a focal spot sizeof ⇠60 µm and an approximated peak intensity in the order of 3–4⇥1014 W/cm2.The entrance and the exit of the gas cell along the laser path are sealed with a0.1mm thin copper foil in which the laser itself drills optimum sized holes of a fewtens of µm for propagating through. The cell is connected to a gas reservoir via ahand valve which allows to control the flow into the cell and therefore control thequasi-static pressure which builds up inside the cell. The cell is operated with eitherXe or Ar as non-linear medium for harmonic generation at pressures in the gas inlettube of 0.46mbar for Xe or 3.2 mbar for Ar and a background pressure outside thecell of 8 ⇥ 10�3 mbar or 1.1 ⇥ 10�2 mbar, respectively. This configuration enablescut-o↵ frequencies around the 21st harmonic, corresponding to 33.2 eV photon energyfor Xe (I

p

=12.2 eV) as non-linear medium and around the 23rd harmonic (36.3 eV)for Ar (I

p

=15.8 eV). However, mostly Xe was used in every day operation as theharmonic yield is one order of magnitude higher than for Ar. In order to tune thephase matching condition, the cell is mounted on a manipulator which allows foroptimizing its position along the laser path and therefore change its relative positionwith respect to the laser focus. Additionally, the apertures ap1 & ap2 before the

10


vacuum chamber can be tuned to achieve maximum HHG output. When tuning theapertures, the maximum intensity in the focal spot is optimized by cutting o↵ partof the laser beam, as well as the wavefront is manipulated due to di↵raction at theaperture (for details see below).After generation, the light passes through a monochromator equipped with an en-trance and an exit slit of 0.5 mm width. Dispersion is achieved by a 550 lines/mm goldcoated toroidal grating operated at a constant deviation angle of 142�. The calculatede�ciency of the grating is 4 - 5 % at 20 eV and 6 - 8 % at 30 eV. Two aluminumfoils (150 nm thick) one before the grating and one after the exit slit can be movedinto the beam to block the IR light and ensure that no fundamental IR photons passthrough to the experimental chamber and influence ongoing experiments when themonochromator is used in zero order and e↵ectively acts as mirror. The transmissionof each of these foils amounts to ⇠70% [32]. The monochromatized VUV pulseshave a duration of 110 ± 10 fs at full width half maximum (FWHM) determined byVUV-IR cross correlation with photo-ionization sidebands of Ar, explained in detailon page 19 later in this chapter. The bandwidth of the pulses is ⇠140 meV as shownin earlier work [22]. For experiments usually the 15th or 17th harmonic of the laserare selected, corresponding to a photon energy of 23.7 eV or 26.9 eV.In the next chamber along the beam, a removable piezoelectric driven 2 inch mirrormount is installed giving the possibility to reflect the VUV pulses on a CCD camerato inspect their spatial profile. Within the framework of a diploma thesis this mirrormount was equipped with a reflective zone plate to explore new monochromatizationschemes [33]. Such a zone plate monochromatizes and focuses the beam at oncemaking a more compact setup feasible. Additionally, a lower temporal stretch of thepulses than for standard grating monochromatization can be expected.Next along the beam path, a GaAsP semiconductor photodiode (Hamamatsu modelg112704) is mounted on a translational stage which allows for measuring absoluteaverage photon numbers of our HHG setup [31].Finally, the VUV pulses are focused into the interaction region of the experimentalchamber by a gold coated toroidal mirror at a grazing angle of 6� and a calculatedreflectivity of 0.83 in the range of 20 - 30 eV of photon energy. The focal spot size isof approximately 100 µm horizontally and slightly less vertically [22].

2.2.2 Pump Path

The part of the laser transmitted through the beam splitter consists of 0.3 mJ pulseswhich serve as pump in time-resolved experiments. In the following, the preparationof the pump pulses is described element by element along the optical setup (seefigure 2.3, upper optical path).First the light travels through a high-precision delay stage for varying the di↵erencein length of the two optical paths and therefore varying the di↵erence in the time ofarrival of pump and probe at the experiment. The delay stage’s reproducible posi-tioning accuracy is 1 µm. Thus, as the laser travels the delayed path back and forth,

11


the minimum variation of the optical path is 2 µm and hence the minimum repro-ducible step size in time delay in this setup amounts to 7 fs. Note however, that whilescanning the delay range, it is possible to use smaller steps, but reproducibility is notguaranteed.After passing an aperture (ap3) which is used for aligning and reduction of the beamdiameter, if necessary, the laser enters a stage for power and polarization control.This stage consists of a �/2-wave-plate — polarizer — �/2-wave-plate sequentialarrangement. The polarizer is set to a fixed position, therefore by controlling thepolarization of the incoming laser beam with the first �/2-wave plate, one e↵ectivelycontrols the transmission through the polarizer and thus the power of the of theoutgoing beam. The additional �/2-wave-plate after the polarizer enables to adjustthe direction of the polarization of the pump beam to any desired angle. The overallthroughput of this stage is variable in the range from 20% to 85% of initial laserpower.Next along the beam path, a BBO crystal is installed for frequency doubling, oftencalled second harmonic generation (SHG). The BBO is fixed in a rotatable kineticmirror mount which enables tweaking the BBO to highest available e�ciency. Notethat the polarization of the SHG pulses is perpendicular to that of the fundamentalIR pulses.After another aligning aperture (ap4), the two color beam (fundamental & SHG) issplit by a dichroic mirror reflecting the blue and transmitting the IR light. After shortindividual pathways, both beams are recombined by another dichroic mirror. The pathfor the blue light is equipped with an additional IR filter, to ensure monochromaticity.This assembly enables easy pump color selection by simply placing a beam stop inthe optical path of the undesired color, without touching any optical elements, andhence, without influencing the optical alignment. However, the optical path lengthsare di↵erent, mainly due to the additional IR filter in the blue path. Measurementshave shown, that pulses from the blue path arrive 19.7 ± 0.1 ps later than the redpulses.After recombination, both colors pass through a last aperture (ap5) which enablesblocking of possibly occurring stray light. The last optical element outside vacuumis a f=400 mm focusing lens. The lens is mounted on a 3-way translation stagefor exact positioning in both transverse directions and along the beam path. Hence,the position of the focus in the experimental chamber can be controlled in all threedirections, enabling optimization of the focal position with respect to the detectorand tweaking the spatial overlap between pump and probe pulses.Lastly, the beam enters the experimental chamber through a fused silica view port andis reflected by an in-vacuum mirror towards the interaction region of the experimentalchamber. The size of the focus of the pump pulse amounts to approximately 200 - 400µm [22].

12


2.2.3 The Experimental Chamber

IR filter

gas inlet

evaporation source

magnet &ion TOF

camera

electronspectrometer

top viewside view

auto-correlator

YAG:Ce screen

BBOdiode

Figure 2.4: The experimental chamber. Either the camera depicted in the left sketch orthe auto-correlator setup shown in the right sketch can be mounted behind thechamber.

The last assembly of the HZB HHG setup shown in figure 2.3 is our experimentalchamber, in which both light beams are collinearly coupled in and focused. A moredetailed side and top view of the assembly is given in figure 2.4. The chamber isequipped with a variety of tools for aligning and setting up a pump-probe experimentand of course the main detector, a magnetic bottle photoelectron time-of-flight spec-trometer (MBPES), which is described in detail in the next section. The interactionzone for experiments is in the very center of the chamber, indicated in the picture bythe foci of the pump and probe beams.Besides the detector, a main part of the chamber is the evaporation source for bringingthe sample into the interaction zone. In the left part of figure 2.4 the high-temperaturesample source developed within this thesis is depicted, see chapter 3 for a detaileddescription. Instead of the high-temperature source, it is possible to mount a simplemetal tube with a hand-operated fine valve, which allows for connecting varioussamples which are gaseous at least under the vacuum conditions in the chamber(well below 10�5 mbar). For example, the experiments on above-threshold ionizationdescribed in chapter 6 were carried out with this metal tube. For using samples,which are liquid under normal conditions, they were filled into a glass dome whichwas connected to the tube, enabling measurements, for example, on H2O. Eitherevaporation source is mounted on a 3-way manipulator for optimal positioning of thesource underneath the interaction volume.From top, a combination of a YAG:Ce scintillation crystal screen holder and anothergas inlet are mounted to the chamber on a translational stage. The YAG:Ce screen isused for visualizing the light pulses at the interaction point and thus the transversespatial overlap. Setting up the spatial overlap is described in detail on page 21 in thischapter. The gas inlet, equipped with a hand-operated fine valve, is used for inserting

13


test gas (in our case mostly Ar) to the interaction point for cross-correlating thepump and probe pulses and therefore determining their temporal overlap (in detail onpage 17).Our setup provides the possibility to mount a magnifying video camera system behindthe view port at end of the experimental chamber for imaging the YAG:Ce screen andthus observing the transverse positions of the pump and probe beam.If required, the camera system can be replaced by an intensity auto-correlator setup,as shown in the top view on the right in figure 2.4. The functionality and operationof the auto-correlator is described in detail on page 17.Inside the experimental chamber, there are high vacuum conditions with pressures wellbelow 10�7 mbar, when HHG is in operation, but all other inlets are closed. Duringoperation of the gas inlet or the evaporation source, pressures of up to 10�5 mbarare acceptable in the chamber.

2.2.4 The Time-of-Flight Photoelectron Spectrometer

magnet meshesMCP

phosphorscreen

drift tube with solenoid

PMT

Uret +kV

interactionvolume

mesh

Figure 2.5: Schematic diagram of the time-of-flight electron spectrometer installed at theHHG setup at HZB.

The core of the experimental chamber is a magnetic bottle photoelectron time-of-flight spectrometer (MBPES) for measuring kinetic energies of photoelectrons. Thedesign is based on work by Eland et al. [34] and is nearly identical to a device developedby Michael Meyer (XFEL) operated at FLASH in Hamburg [35].An overview of the assembly is given in figure 2.5. All Electrons ejected from photo-ionization in the interaction volume are directed by a strong permanent magnet(0.5 T) towards a drift tube. The tube is approximately 80 cm long and equippedwith metal meshes for electron retardation at the entrance and another mesh at theexit on the same potential as the entrance mesh, to ensure electric field free spaceinside. A solenoid produces a weak magnetic field inside the drift tube, guiding al-most all the electrons to a stacked micro channel plate detector (MCP). The electronshower created in the MCP stack is accelerated by a high voltage in the kilovolt rangetowards a phosphor screen and converted into visible light. A photomultiplier tube(PMT), which is mounted outside vacuum behind a view port detects the light fromthe screen. The phosphor screen – PMT combination is used for electron detection

14


instead of a metal anode to allow for visual inspection of the electron distribution onthe MCP stack and thus for detection of misalignment. The collection e�ciency is50–100% and the energy resolution without retardation amounts to 2% of the kineticphotoelectron energy, determined in commissioning measurements [22].The signals from the PMT are recorded by a computer equipped with a triggered4096 bit analog-digital converter card with 1 ns wide time slots, yielding a total de-tection window of 4096 ns. The trigger signal is obtained from a diode measuringthe leakage of the laser through a mirror. The photoelectron spectra are typicallyrecorded for flight times of 300 ns–1500 ns.The resolution for the photoelectron spectrum under investigation can be furtherincreased by tuning the retardation voltage. Already small retardation voltages are apowerful tool to reflect slow photoelectrons arising from multiphoton ionization bythe pump laser only.

2.2.5 Tuning HHG

High-harmonic generation is a sensitive process depending on carefully handling awhole set of parameters, to achieve good phase-matching and therefore high radia-tion yield. As described in section 2.1, the cut-o↵ frequency in the harmonic spectrumdepends on the wavelength and the peak intensity of the fundamental laser, thus onthe focusing strength and the pulse duration. However, the harmonic yield or con-version e�ciency strongly depends on phase matching inside the generation medium,strongly influenced by the generation gas density, the transverse intensity profile, theshape of the wavefront of the laser and the length of the generating medium. Themedium length is given by the length of our gas cell and fixed in our setup. Weexperimented with several cell lengths and found the 55 mm cell is optimal for oursource. The other parameters transfers to the following knobs, used for tweaking theHHG yield from our source.

• position of gas cell with respect to laser focus

• flow/pressure of generation gas

• beam diameter / aperture width

• chirp & pulse duration of the laser

For tuning, these parameters are optimized until the HHG yield converges to a stableoptimum. Usually it is enough to optimize the laser chirp and the gas cell position onlyonce, while the aperture width and the flow through the gas cell have to be optimizedin an iterative cycle. The optimum chirp of the laser corresponds to the shortestavailable pulses (45 - 65 fs), which was checked with an auto-correlator installeddirectly at the laser.The pressure inside the gas inlet tube is set with a hand valve to 0.46 mbar for Xenonor 3.2 mbar for Argon as generation gas, then the generation is optimized by slightly

15


tweaking the hand valve. Unfortunately, it is not possible to measure the optimumpressure with higher accuracy.Tuning the width of the aperture in front of the vacuum chamber cuts the laserbeam and adjusts the beam diameter and hence, the peak intensity in the focus. Toohigh peak intensities would lead to a breakdown of the harmonic generation, as themagnetic component of the laser field becomes high enough to induce a non-negligiblelateral shift to the electron trajectory in the laser field (see figure 2.2). Hence, theelectron will miss the parent nucleus, thus radiative recombination is prevented andthe gas medium is ionized instead.Cutting the laser beam also influences its wave front and thus the phase matchingin the HHG process. As our setup is not equipped with a wave front sensor, measur-ing and quantifying the exact influence of the wave front distortion is not possible.Hence, when tuning the opening of the aperture, it cannot be distinguished, in whichproportion the optimization of the HHG yield arises from wavefront distortion or frompeak intensity optimization. The width of the aperture is a very sensitive number aschanging it by less than 0.5 mm can already change the harmonic output by morethan a factor of 2. However, the width set after completing the tweaking procedurevaries a lot from day to day due to varying performance of the fundamental laserbetween two start-ups, which a↵ects for example its transverse intensity profile.Typically, the pulse energy e↵ectively used for HHG after cutting the beam amountsto 0.7–1.2 mJ. Assuming a pulse duration of ⇠ 60 fs of the laser inside the gascell and a focal spot size of ⇠ 60 µm, the laser peak intensity available for high-harmonic generation is in the order of 3–4⇥1014 W/cm2. The cut-o↵ in the harmonicspectrum for Xe as generation medium should therefore be around the 21st harmonic(corresponding to 33.2 eV photon energy), well above the 15th (23.7 eV) or 17th(26.9 eV) harmonic, which are usually used for experiments.

16


2.2.6 Temporal Overlap – Cross- & Auto-Correlation

One of the most important parameters in time-resolved pump-probe measurements isT0 and the time resolution. T0, i.e. full temporal overlap, is given at the delay stageposition where both pulses arrive simultaneously at the experiment. Assuming a delaystep size well below the pulse durations, the time-resolution is dominated by the cross-correlation function of pump and probe. In this setup, T0 and the time resolution aredetermined in a two stage approach. First, an approximate value of T0 is estimatedwith an optical intensity auto-correlator setup, mounted behind the experimentalchamber, then T0 and the time resolution are determined most accurately at theinteraction point with an intensity cross-correlation experiment using two-color photo-ionization.Intensity auto- & cross-correlation is a widely used technique to determine temporalcharacteristics of signals. In optics this technique serves as a tool for measuring theduration of light pulses and their temporal overlap. From the mathematical point ofview, the intensity cross-correlation function X (⌧) of two light pulses E1 and E2 fordelay ⌧ is defined as the convolution of the two pulses:

X (⌧) = |E1 ⇤ E2|2 =

Z +1

�1|E ⇤

1 (t)E2(t � ⌧)|2 dt

=

Z +1

�1I1(t) I2(t � ⌧) dt

= I1 ⇤ I2 . (2.9)

Let’s assume Gaussian shaped intensity distributions of height A and width �:

I (t) = A exp⇣� t

2

2�2

⌘. (2.10)

Then the cross-correlation becomes:

Xg

(⌧) = I1 ⇤ I2 =Z +1

�1A1A2 exp

⇣� t

2

2�21� (t�⌧)2

2�22

⌘dt

= exp⇣� t

2

2(�21+�2

2)

⌘⇥p2⇡ �1�2

�21+�2

2A1A2

= exp⇣� t

2

2�2X

⌘⇥ A

X

. (2.11)

Xg

(⌧) is of Gaussian shape and the relation between the width of the cross-correlationmeasurement and the initial pulse durations is given by:

�2X

= �21 + �2

2 . (2.12)

Hence, if one knows the duration of one of the pulses, the duration of the secondpulse can be determined from the cross-correlation width �

X

. Furthermore, �X

gives

17


an estimate of the time resolution available for experiments. Equation (2.12) alsostates, that the cross-correlation width is an upper limit for the pulse durations. Foran auto-correlation, where �2 = �1, the pulse duration reads as:

�1 = �X

/p2 . (2.13)

In these considerations a zero centered relative delay axis ⌧ is assumed. In praxis,a delay stage position z in length units is often recorded. The maximum of X (z)determines z0 the point of maximal temporal overlap, thus T0. The transformationbetween delay stage position z and relative time-delay ⌧ is:

⌧ = (z � z0)/c , (2.14)

where c denotes the speed of light.Next, the implementation of auto- & cross-correlation at the HZB HHG setup ispresented. A sketch of the auto-correlator setup is shown on the right side in figure 2.4.It consists of a sequential arrangement of a BBO SHG crystal, an IR filter and aphotodiode, forming an intensity auto-correlator. Such auto-correlation schemes area widely used technique in laser labs and well described in textbooks, for example [36].To run the auto-correlation, the monochromator in the HHG path is set to zero orderand all Aluminum filters are moved out letting the IR pulses pass through the vacuumsystem to the auto-correlator. In the pump path, IR is selected and the focusing lens istuned to overlap both light beams in the BBO crystal for second harmonic generation(SHG). After filtering out the IR, the on-axis SHG signal, which is proportional toE (t)E (t � ⌧) is detected by a photodiode. The diode is an intensity detector and itstime constant is large compared to the pulse durations, hence it integrates over timet. The recorded signal is

ID

(⌧) /Z +1

�1|E (t)E (t � ⌧)|2 dt =

Z +1

�1I (t)I (t � ⌧) dt (2.15)

and corresponds to an intensity auto-correlation as described above.Figure 2.6 shows an exemplary auto-correlation taken with our setup. The FWHM

of the correlation is 121 ± 2 fs, therefore the duration of the laser pulse here is86 ± 2 fs. However, the group velocity dispersion in the exit window of the vacuumchamber prolongs the highly chirped pulses, therefore the pulse duration deducedfrom auto-correlation behind the chamber does not correspond to the duration insideat the interaction point. In order to estimate the pulse length inside, we simulated thissituation by placing a fused silica view port of same type as the laser in-coupling viewports in front of a SPIDER commercial auto-correlator and measured the duration ofthe laser pulses before entering the vacuum. The simulation suggests a pulse durationin the vacuum chamber of 45 - 65 fs.

18


!500 0 500

0.5

0.6

0.7

0.8

0.9FWHM = 121 ± 2 fs

delay (fs)

rel.

inte

nsi

ty (

a.u

.)

fitdata

Figure 2.6: Auto-correlation function measured with the arrangement of BBO crystal andphotodiode behind the experimental chamber.

Note that overlapping the pulses in the BBO crystal slightly changes the di↵erenceof pump and probe path, therefore T0 gained in this auto-correlation is only accuratewithin ±300 fs with respect to the interaction zone.

For precise determination of T0 at the interaction volume in front of the photoelectronspectrometer and for cross-correlating pump and HHG probe pulses, sidebands aremeasured. The occurrence of sidebands in the photoelectron spectra from ionizationwith a VUV/XUV pulse in presence of a long wavelength electromagnetic dressing fieldwas first discovered and described by Glover et al. in 1996 [37]. Sidebands arise fromtwo-color multiphoton absorption, when the electron in a single ionization processinteracts simultaneously with the ionizing VUV/XUV photon and one or more photonsfrom the dressing field. Their formation is described in detail in chapter 6, where anexperiment on polarization dependence of sidebands is introduced. The height of thesidebands depends on the intensity of the dressing field at ionization and thus on therelative time delay ⌧ . Assuming Gaussian shaped pulses, a delay scan of the sidebandheight corresponds to a cross-correlation as introduced in equation (2.11).For carrying out a sideband intensity delay scan with our setup, a gas jet is broughtinto the interaction volume by the gas inlet tube mounted to the chamber togetherwith the YAG:Ce screen holder, see figure 2.4. After ensuring spatial overlap in theinteraction region, the delay dependence of the intensity of one of the sidebands inthe photoelectron spectrum of the detection gas is measured.We used mostly Ar as gas for sideband generation, because it shows an intensepeak at 15.8 eV binding energy with a high sideband generation cross-section for ourVUV radiation, hence enabling high contrast cross-correlation measurements, but,in principle, any other gaseous sample with electronic states accesible by the VUVradiation is suitable.

19


!500 0 500

50

100

150

200FWHM = 72 ± 2 fs

delay (fs)

rel.

inte

nsi

ty (

a.u

.)

fitdata

(a) unmonochromatized VUV beam

!500 0 500

0

200

400

600

800

1000FWHM = 123 ± 2 fs

delay (fs)

rel.

inte

nsi

ty (

a.u

.)

fitdata

(b) 17th harmonic, 26.9 eV

Figure 2.7: Cross-correlation functions deduced from two-color two photon ionization side-bands in the interaction volume of the experimental chamber.

In figure 2.7 exemplary cross-correlation measurements with fitted Gaussian curvesobtained from our setup are shown for (a) the unmonochromatized VUV beam and(b) the 17th harmonic at a photon energy of 26.9 eV.T0, determined from these measurements is accurate within ±5 fs, as estimated fromrepeating the measurements several times. Note that T0 for the unmonochromatizedbeam di↵ers by approximately 10–20 fs from T0 for the harmonics, due to a slightchange of the optical path length, when tuning the monochromator. An estimate forthe time resolution given by the FWHMs of the cross-correlation functions is 72 ± 2fs for the unmonochromatized beam and 123 ± 2 fs for the monochromatized 17thharmonic. These numbers are typical for our setup, however on a day to day basis,they vary by ±10 fs. In a pump-probe experiment, actual time resolutions better thanstated above may be achieved by increased data statistics.With the FWHMs from cross-correlations and assuming 45-65 fs pump pulses, thepulse duration of the HHG signal can be determined by applying equation (2.12).Taking into account the day to day variation of the pulse widths and the uncertaintyin pump pulse duration, the average HHG pulse duration is 47 ± 19 fs for the un-monochromatized light and 110 ± 12 fs for the 17th harmonic, which should wellapply for the other high-harmonics in the spectrum. Thus, the temporal stretching ofthe probe pulses induced by the grating in our monochromator amounts to 63±22 fs.Note that the line density of our grating, 550 lines/mm is not optimal, the stretchingcould well be reduced by installing a grating with fewer lines/mm and still keepingthe dispersion high enough to ensure separation of the individual harmonics.

20


2.2.7 Spatial Overlap

Another crucial parameter in pump-probe experiments is good spatial overlap of bothlight beams. In order to image the transversal sections of the light beams, hencetheir spatial overlap, a 24-fold magnifying video camera system is mounted to theexperimental chamber and focused on the YAG:Ce scintillation crystal, positioned atthe point of interaction (see figure 2.4). The crystal converts VUV radiation intovisible light by photoluminescence and di↵usively di↵racts the optical pump pulses,ensuring that both beams are imaged at same depth. The HHG focal spot of ⇠ 60 µmdiameter is magnified 24-fold to a spot of ⇠ 1.4 mm diameter on the 12.7⇥12.7 mm2

CCD chip in the camera, hence to roughly 10% of the image size. The camera imageis displayed on a monitor and by tuning the position of the lens in the pump path bothlight spots are centrally overlapped. The pump beam is usually 2 - 4 times bigger insize than the VUV. This procedure is accurate enough to measure a two-color photo-ionization signal, thus enabling cross-correlation and temporal overlap measurements.After assuring temporal overlap, the lens position, hence the spatial overlap can befurther optimized by maximizing the two-color sideband photo-ionization yield.

2.2.8 Divergence of the VUV Beam

In order to estimate the divergence of our VUV source, an X-ray CCD camera (AndoriKon-L 936) was mounted directly to the exit of the monochromator in a dedicatedexperiment for measuring the spot sizes on the CCD and thus the divergence of thebeam. The additional chamber after the monochromator in figure 2.3, equipped witha removable mirror and a CCD camera was installed later, in consequence of thisexperiment.The harmonic yield was varied by tuning the gas pressure inside the gas cell, the cell’sposition along the laser beam and the width of the apertures in front of the vacuumchamber (ap1 & ap2 in figure 2.3).Figure 2.8 shows exemplary measurements of the divergence of the 17th harmonic(26.9 eV) generated in Xe for four di↵erent flux levels with intensity profiles andGaussian fits for vertical (Y) and horizontal (X) direction. The measurements yieldedan average divergence of the VUV pulses from our source of div(Y) = 3.7±0.6 mradvertically and div(X) = 2.6 ± 0.4 mrad horizontally, which should well translate toother harmonics from our source.

21


div X (mrad)

div

Y (

mra

d)

6.8!108 ph/s

!4 !2 0 2 4

!4

!2

0

2

4

(a) 2.6⇥4.4 mrad2

div X (mrad)

div

Y (

mra

d)

5.2!108 ph/s

!4 !2 0 2 4

!4

!2

0

2

4

(b) 2.4⇥3.6 mrad2

div X (mrad)

div

Y (

mra

d)

4.6!108 ph/s

!4 !2 0 2 4

!4

!2

0

2

4

(c) 3.1⇥3.7 mrad2

div X (mrad)

div

Y (

mra

d)

2.8!108 ph/s

!4 !2 0 2 4

!4

!2

0

2

4

(d) 2.2⇥3.2 mrad2

Figure 2.8: Divergences for the 17th harmonic of our HHG source generated in Xe forseveral values of the photon flux (indicated in white). Normalized intensityprofiles (green) with Gaussian fits (red) are plotted on top for the divergencein horizontal direction (X) and aside for vertical divergence (Y). The subtitles(a-d) give the corresponding widths (FWHM) of the fits as div(X)⇥div(Y).

22


2.2.9 Absolute Photon Flux & Shot-to-Shot Stability

A separate experiment on the reliability of semiconductor photodiodes under radiationwith ultrashort pulses was carried out and published in [31], where the photon numbersmeasured with a diode are compared against calibrated absolute photon numbersobtained from a Gas Monitor Detector (GMD). In the following, the main parts ofthis publication are reproduced and summarized.Semiconductor photodiodes are calibrated a synchrotron light sources, at high rep-etition rates under quasi-cw irradition, whereas a femtosecond photon source likeour HHG setup produces short intense pulses with peak intensities exceeding thoseduring calibration by several orders of magnitude. This brings up the question, if thecalibration is still reliable under these extreme conditions.

Figure 2.9: The HHG setup as modified for the measurements on the shot-to-shot stabilityand absolute photon flux from our source and on the reliability of semicon-ductor photodiodes. Inset: (principal) sketch of the assembly inside the GMDillustrating its basic functional principle. (reprinted from [31])

For cross-calibration measurements, we mounted a GMD to our setup directly be-hind the monochromator and the semiconductor photodiode behind the GMD, seefigure 2.9. The GMD is based on the photo-ionization of a (rare) gas and was de-veloped for on-line measurement of the radiant power of VUV and soft X-ray FELs[38–41]. Measurements of absolute average photon fluxes as well as shot-to-shotphoton numbers with an accuracy below 5% are feasible with this device.The inset of figure 2.9 illustrates the functional principle of this detector. The VUVradiation ionizes the target gas (either Xe or Ar in our experiment) and the gen-erated ions and electrons are extracted and accelerated in opposite directions by ahomogeneous static electric field. The extraction field of 333 V/cm (correspondingto an extraction voltage of 1000 V) is chosen to be high enough to ensure completecollection of the charged particles created in the interaction volume accepted by the

23


respective particle detector. In our experiment the ion signal was measured only. Afirst simple metal plate detection electrode allows for measuring a slow averagingcurrent I

AV

by a calibrated Keithley 617 electrometer with a time constant of a fewseconds, which is not a↵ected by any individual intra-pulse time structure or shot-to-shot variations of the radiation. Moreover, a fraction of the ions enters a drift sectionthrough a small aperture in the detection electrode and is detected by an open elec-tron multiplier (ETP 14880) operated in a linear regime. The multiplier delivers asingle shot current I

SS

, which can be utilized for pulse resolved (shot-to-shot) relativeflux measurements. Knowing the averaged absolute photon number N

AV

, single shotabsolute photon numbers, determined from the peak value of the multiplier signal I

SS

read as:

NSS

= NAV

⇥ ISS

IAV

(2.16)

Figure 2.10: Shot-to-shot stability of the fundamental IR laser (top) and the generatedharmonic VUV output (bottom). (adapted from [31])

Figure 2.10 depicts the shot-to-shot stability of the fundamental laser, deduced fromleakage through a mirror and stability of the HHG source measured with the GMD at3 kHz repetition rate. The intensity of the fundamental laser is stable within ±2.3%FWHM, in contrast, the flux of the HHG source varies by ±26.6%. This points out thehighly non-linear nature of the HHG process. Note that the source was not optimizedfor minimal shot-to-shot fluctuations.Additionally, the multiplier can be used for ion time-of-flight spectrum measurements(see figure 2.11) which enables checking the purity of the target gas and rulingout multiple ionization. Both e↵ects would perturb the ion-current signal by adding

24


currents from other ions than singly ionized target gas particles and therefore theabsolute calibration of the GMD would no longer be valid [31].

Figure 2.11: Two exemplary GMD ion time-of-flight spectra (averaged over ⇠ 5000 shots)illustrating the purity of the target gas. The spectrum of Xe target gas andresidual air is shown in (a), while (b) shows the spectrum of pure singly ionizedXe target gas as used for the flux measurements. (adapted from [31])

In figure 2.12 the relative deviation (in percent) between the average photon fluxderived from the diode signal and that from the GMD is plotted against the absoluteaverage flux measured with the GMD. Four data sets (connected with lines) are shownfor four di↵erent photon energies corresponding to di↵erent harmonics of our source.To vary the harmonic yield and therefore the fluxes, the width of an aperture in thegenerating laser beam was tuned.In a next step we calculated the resulting power (product of photon energy and flux)of the VUV radiation. Figure 2.13 depicts the deviation (in percent) between theaverage photon flux calculated from the response of the diode and that of the GMDversus the absolute average power given by the GMD signal.The error bars in both graphs are deduced by taking into account the 5% accuracyof the GMD and the accuracy of the measurement of the photo current from thediode. The photo current was measured with a Keithley 6485 electrometer in slowaveraging mode. The accuracy of the photo current values were approximated forevery measurement by carefully observing the variation of the photo current signaland amounted to be in the range of 3% to 10%.The graphs show, that the diode systematically underrated the photon flux by up to�15%. This points to saturation e↵ects in the diode due to the high peak power emit-ted from our HHG source. However, our results proof, that a calibrated photodiodeis still a good and easy-to-use tool for measuring the flux of femtosecond VUV HHGphoton sources within, as in our case, an accuracy of around 15%. Depending on the

25


day-to-day laser performance, 106–107 photons/pulse/harmonic, corresponding to aflux of 109–1010 photons/s/harmonic could be measured at our HHG source with thediode.

Figure 2.12: Relative deviation of the photon numbers estimated from our semiconductorphotodiode and the GMD versus the photon flux for several VUV harmonics:⌥ H11 (17.4 eV), • H13 (20.5 eV), ⌅ H15 (23.7 eV), H H17 (26.9 eV).(adapted from [31])

Figure 2.13: Relative deviation of the photon numbers estimated from our semiconductorphotodiode and the GMD versus the average power of the VUV radiation.(adapted from [31])

26

3 High-Temperature SampleSource

In order to enable gas-phase measurements on samples which are solid or liquidin vacuum at room temperature, a high-temperature sample source with an ovenwas developed within the framework of this thesis. The oven was planned and usedfor measurements on NaI (chapter 7), but will in future serve as source for varioussubstances, where temperatures of up to 1000 �C are needed for evaporation.

High-temperature in-vacuum ovens have long since been used as molecular sources formany experiments on atoms, clusters and molecules or as sources for sputtering andlayer deposition of materials. Various concepts of molecular ovens have been realizedso far, meeting the demands of the individual applications. A summary on ovens formetal atom beam sources by Ross and Sonntag [42] has inspired the development ofour molecular source.Our oven had to meet several constraints: it had to be dimensioned to fit our existingexperimental chamber (p.13↵), the maximum reachable temperature had to be wellabove 600 �C to evaporate NaI at a su�cient rate and the exit nozzle of the ovenhad to be positionable very close underneath the interaction point without touchingthe magnet of our magnetic bottle, thus the nozzle has to be of small outer diameter.Following these constraints, we developed, designed and built the molecular oven ina close in-house collaboration with K. Kalus and T. Noll from the HZB engineeringdepartment and A. Drescher and his co-workers from the scientific workshop at HZB.A sketch of the resulting molecular oven is depicted in figure 3.1.The smaller picture on the left shows a complete view of the oven mounted on top ofthe main rod, which is fixed to a CF63 flange. Water tubes and an electric feedthroughare built into the flange to feed electric power and cooling water to the oven assembly.The large drawing on the right shows the oven assembly in more detail. A watercooled cup, housing the oven is mounted to the main rod. Cooling is achieved bya meandering water circuit just underneath the surface of the cup and e↵ectivelyshelters the surrounding, i.e. the experimental chamber, from heat. The oven itselfis mounted in this cup. It consists of a heated main body, where a separate stainlesssteel crucible, later containing the sample, is put in, and a copper nozzle with a 2mm inner diameter tip is plugged into the crucible. For filling in sample material,only the copper nozzle has to be removed. A resistively heated wire is wrapped inspiral carvings around the main body and clamped by a thin metal cylinder. Theinconel alloy sheathed, 987 mm long, 28 ⌦ resistance heating wire is well-suited for

27

3 High-Temperature Sample Source

copper nozzle

cylindricwire clamp

inductive heating wire

cooling cupwith integrated

water circuit

heat shelter

main oven body

melting pot

water intaketubes

water intake tubes

electric feedthrough

main rod and mounting assembly

main rod

CF 63 flange

molecular evaporation source mountedin water cooled cup

Figure 3.1: The high-temperature sample source designed and constructed at HZB, suitablefor temperatures of up to 1000 �C.

temperatures of up to 1000 �C. Such heating elements are commercially availablefrom the companies Thermsys or Thermocoax. We tried wires from both suppliersand could see no di↵erence in operation. According to the technical specificationsof the wires, voltages of up to 110 V can be applied, corresponding to a currentof 3.9 A and an electric heating power of 430 W. However, we never ran the ovenabove 250 W (3 A). When starting up the oven, the current must be ramped up notfaster than 1.5 A per 30 min, to ensure a slow thermal stretching of the wire andthat all humidity possibly in the wire has evaporated before applying high currentsthus preventing electrical or mechanical destruction of the heating element. Duringan experiment, the current for operation is set and optimized using the molecularsignal from the experiment itself, as no thermocouples or other devices allowing formeasuring the temperature are installed to the oven assembly. In the case of NaI, forexample, first signals from NaI molecules are usually visible around a current of 1.7 A.However, to achieve a good signal-to-noise ratio, currents between 2.0 A and 2.7 Aare necessary. Private communications with the engineers from the manufacturingcompanies suggest, that such currents correspond to temperatures of 500 - 700 �C.

28

Under these conditions, the oven has to be refilled with fresh NaI sample every 10-14 hours.By now, the oven was used only with NaI as sample, but there is no principal con-straint in using any other liquid or solid sample, which is non-corrosive to copperand stainless steel. After operation with NaI, left overs in the oven show glass-likestructure, supporting the conclusion that during operation, the whole sample is atleast liquefied or even completely gasified. For a constant heating current, this leadsto a constant gas pressure inside the pot–nozzle assembly and therefore to a constantflow through the tip of the nozzle. The copper nozzle is in tight contact with thecrucible and hence indirect heating prevents plugging of the 2 mm diameter channelin the tip of the nozzle.

The oven was used in three di↵erent setups so far: for test measurements at the HZBHHG setup, at the MBI laser pump–probe setup (see chapter 4) and at FLASH inHamburg, by a group from Lund University to whom we lent the oven.The experimental results obtained at MBI are presented in chapter 7.

29

4 Pump-Probe Setup at theMax-Born-Institute Berlin

For the measurements on NaI in chapter 7, a collaboration between the Max-Born-Institute Berlin (MBI) and HZB was formed and the experiment was carried out at thelaser laboratory at MBI in April 2011. The general setup is described in detail in [43],except that for our purpose the original liquid jet was replaced by our high-temperaturemolecular oven (see chapter 3) and the magnetic bottle electron spectrometer wasreplaced by a velocity map imaging spectrometer (VMI). The pump-probe setup asused for the NaI experiments is briefly described here. A principal sketch is given infigure 4.1.

310-410 nm<100 fs3-7 µJ

delay

BBO

TOPASlight conversion

focusing mirror

Ti:Sapphire

800 nm3 mJ40 fs1 kHz

BBO

BBO

200 nm<100 fs2-3 µJ3 hv

4 hv molecular oven

VMI spectrometer

BBO

2 hv

Figure 4.1: Schematic diagram of the experimental setup at the Max-Born-Institute.

A titanium sapphire laser delivering short and intense 40 fs, 2 mJ pulses at a centralwavelength of 800 nm and a repetition rate of 1 kHz serves as primary light source.The pulses are split in order to generate two beams of di↵erent photon energy whichlater serve as pump and probe.One part of the laser drives a commercial TOPAS light conversion stage, equippedwith a frequency doubling BBO crystal at its exit. In combination with the bandwidthof the mirrors, this assembly delivers pulses with wavelengths between 310 nm and410 nm (corresponding to 4.0 - 3.0 eV photon energy) with a bandwidth of 0.06eV (FWHM), pulse durations well below 100 fs and pulse energies of 3-7 µJ to theexperiment.The second part of the primary laser travels through a delay stage, before entering afourth harmonic generation setup. In a sequence of three BBOs, the fourth harmonicof the laser wave is generated stepwise by first frequency doubling in the first BBO

31

4 Pump-Probe Setup at the Max-Born-Institute Berlin

and then wave mixing of the fundamental and the harmonic output from the previousBBO in two more stages. Thereafter, two narrow band wavelength filtering dielectricmirrors ensure clean 200 nm (6.2 eV) pulses shorter than 100 fs and with an energyof 2-3 µJ and a bandwidth in the order of 0.06 eV.After recombination, both colors are focused into the interaction volume in the vac-uum chamber by a spherical focusing mirror. The vacuum chamber is equipped withan VMI spectrometer for measuring the kinetic energy and the angular velocity dis-tribution of photoelectrons. The detection scheme is described, for example in [44].The molecular oven used for evaporating NaI in this experiment is mounted on a 3Dmanipulator for exact alignment of the molecular jet. The oven was developed andconstructed at HZB and is introduced in detail in chapter 3.

32

5 Pump-Probe Setup at the FreeElectron Laser in Hamburg

The measurements on photo-induced dissociation of Fe(CO)5 described in chapter 8were carried out in a collaboration between DESY Hamburg, XFEL Hamburg andHZB within the framework of two measurement campaigns at the Free electron LASerin Hamburg (FLASH) [45–47] (4 shifts, 21-25 April and 8 shifts, 27 Mai - 6 June2011). This section describes the experimental setup used at FLASH and the technicalchallenges to be dealt with when performing a time-resolved pump-probe experimentat a free electron laser (FEL).

5.1 FEL principle

A free electron laser is an accelerator based, highly brillant and coherent light source.Electron bunches are accelerated to energies in the GeV range and sent throughan undulator, a periodic alternating assembly of magnets, in which the electrons areforced on a sinusoidal trajectory and emit spontaneous synchrotron radiation. The ra-diation moves faster than the electrons and slips over the electrons further up in thebunch, imprinting an energy modulation at the period of the fundamental resonantwavelength of the undulator. Coherent oscillation of the electrons in this well-definedperiodicity leads to an exponentially enhanced emission of coherent, high power ra-diation at the resonant wavelength. This process is called self-amplified spontaneousemission (SASE) and takes place during one single pass of the electrons through theundulator without the use of any optical resonator. SASE starts from spontaneous,stochastically distributed emission, therefore the spectral distribution and the intensityof the yielded radiation vary from shot to shot in a SASE FEL. At Flash, the electronbunches are accelerated in a super conducting linear accelerator to an energy of about1 GeV and sent through a 30 m long undulator. The fundamental wavelength avail-able at FLASH is in the range from 47 nm to 6.9 nm, corresponding to 26 - 180 eVphoton energy and the inherent spectral bandwidth of FLASH amounts to ⇠1% [47].Other FELs are designed for even higher photon energies in the hard x-ray range,for example the Linac Coherent Light Source (LCLS) in Stanford (USA) can go upto 10 keV [48], the SPring-8 Angstrom Compact Free Electron Laser (SACLA) atthe RIKEN Harima Insitute (Japan) recently lased at 12 keV [49] and the EuropeanX-ray Free Electron Laser (XFEL), currently built in Hamburg (Germany) is designedto reach photon energies of more than 12 keV [50].

33

5 Pump-Probe Setup at the Free Electron Laser in Hamburg

5.2 Monochromator beamline

In many spectroscopic experiments, it is crucial to exactly know and control theincoming photon energy with an accuracy better than the inherent 1% bandwidth ofFLASH, therefore the FLASH facility o↵ers monochromatic beamlines behind a planegrating monochromator unit, PG1 and PG2 [47]. The design of the monochromatorunit is described in [51, 52]. A variable slit at its entrance allows for controlling thenumber of grooves illuminated on the Carbon coated grating and thus for controllingthe temporal stretch induced upon monochromatization. Illuminating fewer groovesdecreases the prolongation of the light pulses, on the cost of transmission e�ciencyand energy resolution. A second variable slit after the grating is used for limiting andadjusting the spectral bandwidth of the di↵racted, spatially energy dispersed photonbeam.The transmission through the monochromator for open slits and in zero order is 64%for a 200 lines/mm grating [47] and about 12% for the monochromatized first orderbeam for 2 mm exit slit width, 88.3 eV photon energy and a constant fixed focus(c↵) value of 1.5 [51]. In [35], first order transmission of 4% for the complete PG2beamline is reported at 114.9 eV photon energy, a c↵ value of 1.5 and 300 µm exitslit width.The smallest focal spot available for experiments at the PG2 beamline is in the orderof ⇠50 µm depending on photon energy and monochromator settings [47]. However,in our experiment at the PG2 beamline, the focal spot size was about 280 µm inhorizontal and 400 µm in vertical direction, for 123 eV photon energy, c↵=1.5 andthe exit slit width set to 2 µm, corresponding to 0.1 eV bandpass.

5.3 Timing in pump–probe experiments

The FLASH facility provides a high power femtosecond optical laser system for pump-probe experiments, transported to the experimental stations by a separate laser beam-line system and synchronized to the electron accelerator via an RF source. However,due to a number of reasons mainly arising from electron acceleration, the pulses fromthe FEL itself show shot-to-shot jitter, short term and long term drifts with respectto the RF source, and hence with respect to the optical laser.Electron bunch arrival monitors (BAMs) are installed at FLASH and used as feed-back for jitter reduction and drift compensation. It has been demonstrated that thisfeedback can reduce the stochastic shot-to-shot jitter to 40 fs RMS

However, due to a vast number of reasons originating from size and complexity of themachine, in praxis, pump–probe experiments su↵er significantly larger shot-to-shotjitter between FEL and optical laser pulses in the order of 250 fs RMS, correspondingto 600 fs FWHM [53]. Furthermore, the BAM system is not directly correlated to theoptical laser and drifts of the FEL pulses with respect to the laser in the order ofpicoseconds per hour are still remaining [47]. Hence, for performing precise pump–

34

probe experiments, it is crucial to monitor the actual timing between FEL and opticallaser.In an FEL, the arrival time of the electrons at the undulator is directly linked tothe arrival time of the photons at the experiment by a constant o↵set. Thus, if theelectron arrival time can be correlated with the optical laser, accurate pump–probetiming is feasible by sorting the data in time domain during post processing. At FLASHtwo di↵erent timing tools are installed, directly linking the optical laser and electronarrival: a streak camera system, cross-correlating optical laser and dipole radiationfrom the electron dump, and timing by electro-optical sampling (TEO).TEO is based on the Pockels e↵ect in an electro-optical crystal [54–56]. The electricfield of an electron bunch flying near by (⇠1 mm) induces a birefringence whichrotates the polarization of a laser pulse traveling through the crystal. At FLASH,the crystal is mounted perpendicular to the propagation direction of the electrons.A pulse split from the optical pump laser and widened to large diameters, is shinedon the crystal at an incident angle of 45�. This geometry correlates the transversecoordinate of the laser profile and the time coordinate along the electron path. Onlythe polarization of that part of the laser interacting with the crystal at the sametime as the electrons pass by is rotated, thus the arrival time of the electron bunchis encoded in the transverse polarization profile. The polarization profile is measuredwith a CCD camera behind an optical analyzer for shot-to-shot determination of therelative arrival time of electron bunch and optical laser. Time sorting of the data withrespect to the arrival times during post processing enables a reduction of the jitterand thus an increase of the time resolution to 90 fs RMS (210 fs FWHM) and better[56].The streak camera (Hamamatsu C5680) correlates the optical laser pulses and dipoleradiation produced by a bending magnet after a undulator for directing the electronsto a beam dump. The nominal streak camera resolution is only about ⇠2 ps FWHM,hence precise shot-to-shot jitter measurements are not feasible. But for determinationof the relative arrival time only the position of the correlation maximum on the streakcamera has to be analyzed, which is feasible with an accuracy of 400 fs [35]. Furtheraveraging can provide for estimation of short and long term drifts within about 100 fsaccuracy [47], but admittedly this gives only an estimate for the central time valuearound which the FEL jitters.Another promising method for direct x-ray/optical shot-to-shot correlation has re-cently been reported [53, 57], where the x-ray pulses induce transient reflectivitychanges in a GaAs substrate and intensity changes in reflected optical pulses areused for deducing relative arrival times. In contrast to measurements of the electrontiming, this technique monitors the pump–probe delay directly at the experiment,taking into account all possible jitter sources in the electron and in the photon beam-lines of FLASH and providing for an accuracy in the order of about 100 fs FWHM

[53]. However, this method is rather photon hungry and can not be utilized for themonochromatized first order beam of FLASH so far and hence was not an option forour experiments at PG2.

35


5.4 Experimental setup at FLASH

Figure 5.1 shows a principal sketch of the setup, which previously has been describedin [35].

267 nm< 80 fs, < 50 µJ

3 hv

2 hvTi:Sapphire

delay

magnet

electronspectrometer800 nm

< 1 mJ50 fs10 Hz

10 nmnJ - µJ

200-300 fs10 Hz

FLASH PG2

focusing mirror with pinhole

vacuumchamber

streak camera

BBO

BBO

telescope

dielectric mirrors

Figure 5.1: Schematic diagram of the pump-probe setup at FLASH.

From the Ti:Sapphire laser system, 50 fs, 1 mJ, 800 nm pulses are delivered tothe experiment at the 10 Hz repetition rate of FLASH, after a minor portion ofthe laser power was directed to the streak camera system. The laser first passes adelay stage, allowing for a variable delay over a total range of 3 ns, before drivinga third harmonic generation (THG) setup. THG is achived in a two BBO frequencyconversion crystal sequential arrangement and yields 267 nm pump pulses, shorterthan 80 fs FWHM and of up to 50 µJ pulse energy. A set of three dielectric narrowband mirrors directly behind the THG stage is used for filtering out the fundamentaland the second harmonic beams.A Galilean telescope in front of the experimental chamber allows for adjusting thefocal position of the laser along the beam path by ±1 mm. Changing the distance ofthe telescope lenses to a value o↵ the nominal telescope distance alters the divergenceof the beam and controls the focusing of the spherical mirror inside the chamber andthus the longitudinal position of the pump laser focus.The monochromatized pulses from the PG2 beamline pass through a pinhole in thespherical mirror, hence both, the pump and the probe beam can be overlapped in acollinear geometry in the interaction region. For our experiment, FLASH was tunedto 123 eV photon energy (10.1 nm) and a pulse energy of approximately 30 µJ,resulting in monochromatized pulses fluctuating in the range from approximately afew tens of nJ to µJ pulses. The intrinsic shot-to-shot fluctuations in pulse energyarising from the SASE process are even increased by monochromatization, becauseshot-to-shot instabilities in the spectral distribution of the FEL light translate tointensity fluctuations, when only a limited bandwidth of the spectrum is selected bya monochromator. The pulse duration available after the monochromator was in therange of 200 - 400 fs FWHM, depending on the appointed monochromator slit widths.

36

In the experimental chamber, a simple thin metal tube just underneath the interactionvolume (not shown figure 5.1) serves as sample gas inlet. The tube is mounted ona 3-way translation stage for exact positioning and connected to an electronic leakvalve for regulating the sample gas flow.For detecting photoelectrons, a magnetic bottle time-of-flight electron spectrometeris installed, o↵ering an energy resolution of 1–2% of the kinetic energy of the photo-electrons. The photoelectron time-of-flight distributions are determined from a microchannel plate (MCP) in current mode. The signals are either analyzed and storedvia a digital oscilloscope or directly stored to the FLASH data storage system viaa network connected 10 bit digitizer system provided by FLASH (see next section).This spectrometer is described in detail in [35] and served as model for ours at theHZB HHG setup (see p.13↵).

5.5 Post processing and time sorting

FLASH is equipped with a facility-wide data acquisition (DAQ) system, which storesall properties and monitored parameters from FLASH — from the accelerator tothe experimental endstations — to a central server at the DESY site and labelsthe datasets for every single shot with a unique electron bunch ID number [58].The experimental data can either be stored locally at the experiment by the usersthemselves or, as in our case, fed into the DAQ system via an Acqiris 10 bit digitizersystem provided at FLASH.The amount of data produced in time-resolved experiments at FLASH is enormous,because for enabling sorting of the data in time domain during post processing, eachmeasured photoelectron distribution has to be stored separately for each shot. In ourcampaign, for example, data in the order of 1600 GB were produced in 80 hours oftotal acquisition time, corresponding to a rate of 20 GB/h or 5.7 MB/s.In order to handle this huge flux of data, a fast network reserved for DAQ tra�conly and a state of the art file server and storage system including a dedicated binarydata container file format designed and implemented by DESY are part of the DAQsystem. DESY provides a software library for Linux/Unix systems for later access tothe datasets in the binary containers. Based on this library, we developed a set ofapplications for extracting the relevant data from the DAQ system and for sortingthe datasets with respect to pump-probe delay times, taking into account the positionof the delay stage and jitter measurements available from the streak camera system.We tried to include the timing signal from the BAM system into our post processingprocedure for an estimate and reduction of the shot-to-shot jitter, but could notachieve an improvement of time resolution, as the BAM is not directly linked to theoptical laser, and as it is not clear how the di↵erent timing signals depend on eachother. Hence, it was not clear how to account for and disentangle contributions tothe arrival jitters measured by di↵erent timing tools. Unfortunately, the TEO system,which could have served as stand-alone timing tool for shot-to-shot jitter and drift

37


deduction with 200 fs accuracy and better was not functional during our campaign.

As mentioned before, for sorting the datasets in the time domain, the arrival timesdeduced from the streak camera system have to be averaged over several shots fora reliable compensation of short and long term drifts in post processing. Accord-ing to FLASH sta↵, the most reliable drift correction for dataset n is obtained byexponentially weighted averaging:

< tcam >n

= w tcamn

+ (1� w) < tcam >n�1 , (5.1)

with the actual value from the streak camera tcamn

, the averaged value < tcam > andthe exponential weight w = 1� e�q ; q = 0.05 was found to be a good exponent intests by H. Redlin from FLASH. The time allocated to dataset n reads as:

tn

= tstagen

+ < tcam >n

, (5.2)

where tstage is derived from the delay stage position. The time tn

di↵ers from the realdi↵erence between pump and probe pulse by a constant o↵set t0, which has to beassigned by the pump-probe experiment itself. Knowing this o↵set, the pump-probedelay for the nth recorded spectrum is given by:

�tn

= tn

� t0 . (5.3)

Post processing is performed in a two stage approach: first the relevant datasets areextracted from the raw data stored in the DAQ system and second a time sorting anderror detection script is applied to the raw data, creating final datasets for furtherscientific analysis.For extraction, a C++ application was developed, which catches the experimen-tal data, the photoelectron spectrum, streak camera time, delay stage position,monochromator settings, relative pump intensity, GMD and BAM signals from theDAQ raw data containers for each shot. The photoelectron spectrum is stored in atemporary binary container file and all the other meta data is stored to a separatemat file. The mat file format is the native binary format from Matlab, a widely usedhigh-level programming language and scientific software package developed by Math-works. This format is supported by most scientific data analysis programs, hence stillleaving the freedom of choosing one’s favorite software package for further analysisof the data.In a second step, sorting in time-domain and basic error analysis is performed by aMatlab script. The meta data mat file is read and for error analysis, the GMD signal,monitoring the intensity of the FEL shots, is analyzed and shots, where the intensityis below a given threshold are marked as false shots, where FLASH was deliveringonly very few or no photons, thus not running optimal. In order to prevent unknownperturbations to our measurements, these shots are omitted upon time-sorting. Fur-thermore, the live signals from streak camera, delay stage, BAM, monochromator

38

energy setting and relative pump intensity are checked for steadiness and an errormessage is printed, when huge jumps are found. In this case, detailed, manually per-formed consistency checks of the data are required. Fortunately, this was not necessaryfor the datasets from our campaign at FLASH.For time-sorting, the arrival time is computed for each shot according to equa-tion (5.2), and the photoelectron spectrum is read from the temporary containerfile and added up to the corresponding time slot. The number of datasets sorted intoeach slot is counted in a separate variable. The width of the time slots (in our case50 fs) is chosen well below the jitter of the FEL and further binning in time is left tolater analysis. This ensures that the maximum available time resolution is transferedto the post processed data. In case, the monochromator energy setting was variedduring the experiment, the data is additionally sorted with respect to the incidentphoton energy from FLASH.Finally, the resulting sorted dataset with all meta data is saved to one single mat file,containing all information relevant for the detailed scientific analysis. The amountof hard disk space occupied by the post processed dataset is reduced by a factor of50 - 1000 with respect to the initial raw DAQ data, depending on several factors asfor example scanned delay range, acquisition time and photon energy range.

39

Part II

Experiments

41

6 Polarization Control in Two-ColorAbove Threshold Ionization

The occurrence of satellite peaks in the photoelectron spectra from ionization with aVUV/XUV pulse in presence of an IR dressing field was first discovered and describedby Glover et al. in 1996 [37]. These satellite peaks, also called sidebands, arise frommultiphoton two-color above-threshold ionization (ATI), occurring when the dressingfield photon density is high enough to enable simultaneous absorption or emission ofone ore more additional IR photons by the photoelectron created by the XUV/VUVpulse. The sidebands show up in the photoelectron kinetic energy distribution left andright of the main peaks from single photon ionization at integer multiples of the IRphoton energy.

12 14 16 18 200

0.2

0.4

0.6

0.8

1

electron energy (eV)

norm

aliz

ed in

tensi

ty

IR off

IR on

Figure 6.1: The process of two-color two-photon sideband formation shown here for pho-toionization of the 3p shell in Ar (left) and corresponding idealized photoelec-tron spectra (right) for single photon ionization (blue line) and for two-colortwo-photon ionization in presence of a dressing IR field (red line). The bindingenergy of Ar 3p6 is 15.8 eV (see table 6.1).

Figure 6.1 illustrates the process of sideband formation for two-color two-photon ATIof the outer shell of Ar 3p6, creating Ar+ 3p5 (left) and shows idealized calculatedphotoelectron spectra with the IR field present or absent (right). Note that spin-orbitsplitting of the Argon 2P peak at 15.8 eV into 2P3/2 (15.76 eV) and 2P1/2 (15.94 eV)[59] is not plotted.

43

6 Polarization Control in Two-Color Above Threshold Ionization

A VUV photon lifts an electron from the outer shell into the continuum above theionization threshold. The electron can simultaneously interact with the dressing IRfield by either absorbing or emitting an IR photon, hence gaining or loosing kineticenergy of the equivalent of the energy of one IR photon. In the photoelectron spectra,the main peak is depleted with respect to single photon ionization without the IR fieldpresent by the amount of electrons undergoing interaction with the IR field and theseelectrons form satellite peaks to the main peak, the sidebands. For higher IR photondensities, the electron can interact with several IR photons and thus a whole seriesof higher-order sidebands can occur in the photoelectron spectrum (not visualized infigure 6.1). The probability for sideband formation depends on the intensity of thedressing field, therefore following the sideband intensity versus the time delay betweenthe two light pulses enabled the first direct measurement of the pulse duration of fem-tosecond high-order harmonic radiation by intensity cross-correlation [37]. Nowadays,this technique has evolved as standard tool for characterizing ultra-short XUV/VUVpulses, for example at the HZB HHG source (see subsection 2.2.6).

6.1 Polarization dependence

Recent experiments on sideband formation in atoms confirmed that the intensityof sidebands depends on the relative angle between the polarization vectors of theionizing and the dressing light fields. This was demonstrated with HHG VUV lightfor Argon [60] and with XUV light from FLASH for Helium [61, 62]. An exemplarymeasurement from [62] is reprinted in figure 6.2, where the relative sideband intensityis plotted versus the relative angle ✓ between the polarization vectors of IR and XUVpulses.

Figure 6.2: Polarization dependence of two-color two-photon sideband formation in He-lium. (reprinted with permission from [62])

44

6.1 Polarization dependence

This polarization dependence is linked to the geometry and especially to the symme-try of the electronic structure of the system under investigation. Interaction with anelectromagnetic field prepares a principal direction in the electronic distribution of thesystem along the polarization of the field, and if the electromagnetic field ionizes thesystem, a characteristic photoelectron angular distribution (PAD) will be measuredby an angular resolved photoelectron detector. In the case of one-photon ionizationof isotropically oriented gas-phase atoms or molecules, the PAD is cylindrically sym-metric around the polarization vector of the ionizing light field and characterizedby a dimensionless asymmetry parameter �2 2 [�1, 2], which is a measure for theasymmetry in perpendicular and parallel dimensions of the PAD with respect to thepolarization vector. Two exemplary PADs are plotted in figure 6.3 for di↵erent degreesof asymmetry, hence di↵erent �2 (see equation 6.2, introduced in the next section foran analytical expression).Let’s assume in a gedankenexperiment that a dressing IR field, with a polarizationangle ✓, relative to the ionizing VUV pulses, interacts with the angularly directedPADs and that the length of the overlap of PAD and IR polarization vector is ameasure for the sideband formation cross-section (yellow line in figure 6.3). Withinthese assumptions, it follows from figure 6.3, that the higher the asymmetry of theone-photon PAD, the smaller the sideband intensity modulation for varying relativepolarizations of VUV and IR light. This links the amplitude of the sideband intensitymodulation to the geometry of the electronic state.

θ

(a) (b) VUVIR

VUVIR

θ

Figure 6.3: Idealized one-photon ionization PADs for a high (a) and a medium (b) degreeof asymmetry, �2=1.5 and �2=0.5, respectively. The polarization vectors of theionizing VUV and the dressing IR light fields and the overlap of PAD and IRpolarization vector (yellow) are indicated for an exemplary relative polarizationangle ✓.

However, in the gedankenexperiment, interaction with isotropically oriented atoms ormolecules by the VUV pulse is assumed and the IR light is thought to interact with theresulting 2-dimensional PAD, which represents the averaged outcome of many repeti-tions of the interaction. In reality the two light fields interact with the 3-dimensionalelectron density distribution of the system. A 2-dimensional PAD depends on thesymmetry properties of this electron distribution, but does not completely reflect its

45


geometry or shape. In terms of sequential one-photon ionization, the outgoing electronwave has to perform an angular momentum transition (l = l ± 1), thus a geometryand symmetry transition, for each photon taking part in the ionization process. Notethat in quantum mechanics the succession of the interaction with the two photons isnot decidable. But, as in the gedankenexperiment, a principal direction in the electrondistribution is prepared by each pulse and therefore the relative polarization of thepulses should influence the e�ciency of the two-color two-photon ionization processof sideband formation and link the initial electronic distribution geometry with thesideband polarization dependence. This link can enable an alternative way of testingthe symmetry of the angular distributions of photoelectrons from atoms and moleculesby determination of the sideband polarization dependence, without the need of anangularly resolved photoelectron detector.In order to see the influence of the molecular electronic structure on the polarizationdependence and in order to test, if symmetry properties of the electronic geometryof the system under investigation can be estimated from the process of sidebandformation, we performed measurements on the polarization dependence of two-colortwo-photon ionization intensity of several atoms and small molecules, in our case Ar,H2O, O2 and N2, and compared the experimental results to a theoretical approximativemodel.

6.2 Theoretical model

Two-color sideband formation is related to photoelectron angular distributions (PADs)formed by multiphoton ionization. The general theoretical form of a PAD for absorp-tion of m photons from an excitation pulse and n photons from an ionization pulseof arbitrary polarization can be expressed as [63]:

I (✓,') /2n+2mX

L=0

+LX

M=�L

BLM

YLM

(✓,') , (6.1)

where YLM

(✓,') denotes spherical harmonics and L must be even for parity reasons.The B

LM

coe�cients depend on the molecular alignment prepared by the excitingpulse and thus on the geometry of the molecular electronic structure, on the pho-toionization dynamics and on the relative polarization of the exciting and the ionizingpulse. In order to obtain the sideband intensities, as measured by the angularly in-tegrating magnetic bottle electron spectrometer of our HHG setup (p.14), the PADhas to be integrated over both angles.Note that for the case of one-photon ionization with linear polarized light, the aboveequation simplifies to:

I (✓) / 12(1 + �2 P2(cos ✓)) , (6.2)

46

6.2 Theoretical model

with the second order Legendre polynomial P2 and the asymmetry parameter �2,well known in photoelectron spectroscopy. The PAD for single photon ionization hascylindrical symmetry, hence equation (6.2) is independent of '.

In a two-color two-photon process, like the formation of first-order sidebands, as con-sidered in this chapter, it is n = m = 1, hence the first sum over L in equation (6.1)runs only to 4, but still leaves 9 complex terms to compute. However, the relativedecrease in sideband intensity for the extremal cases of perpendicular and parallelrelative polarization can serve as a characteristic property of their polarization depen-dence. Reference [63] provides the form of the PADs for these two special cases ofrelative polarization:

parallel (cylindrical symmetric ) ' independent)

I (✓,' = 0) / B00Y00(✓, 0) + B20Y20(✓, 0) + B40Y40(✓, 0) , (6.3)

and perpendicular

I (✓,') / B00Y00(✓,')

+X

L=2,4

BL�2YL�2(✓,') + B

L0YL0(✓,') + BL+2YL+2(✓,') , (6.4)

where the Z axis is defined by the polarization of the ionizing pulse. If the detector ismounted in the plane spanned by the two polarization vectors, the PAD for perpendic-ular relative polarization becomes cylindrical symmetric as well and thus independentof '. Equation (6.4) than simplifies to:

I (✓,' = 0) / B0

00Y00(✓, 0) + B0

20Y20(✓, 0) + B0

40Y40(✓, 0) . (6.5)

Equation (6.5) has now a form similar to equation (6.3), but the factors B0LM

dependon the factors B

LM

from equation (6.3) for parallel polarization plus B22 and B42 (seeref. [63] for detailed formulas), thus the problem is reduced to calculating a total of5 factors B

LM

. As mentioned above, the coe�cients BLM

depend on the molecularelectronic structure of the molecule and the molecular orbital under investigation andare of high complexity, hence hard to compute already for well defined polarizationgeometries, therefore a simplifying easy-to-compute approximative model is desired.Such an approximation, tracing back the polarization dependence in two-color two-photon ionization to the asymmetry parameter �2, known from one-photon ionization,is given in [60]. The model was developed to be valid for two-color two photonionization starting from atomic p-states and describes the modulation of the relativesideband intensity as:

ISB(✓) / 1� 3 �25 + 2 �2

sin2 ✓ , (6.6)

47


with the angle ✓ between the two polarization vectors and assuming the soft-photonlimit, where the IR photon energy is assumed considerably less than the kinetic energyof the observed photoelectrons and small compared to the ionizing VUV/XUV photonenergy. For deriving equation (6.6), the authors of [60] express sideband formationin terms of transition amplitudes for ground state to continuum transitions via anintermediate continuum state. The polarization dependence arises from polarizationdependent coupling of this intermediate state to the final state. In each transition,the selection rules for the angular momentum have to be fulfilled: �l = ±1, hencestarting from a p-state, the intermediate continuum state is either ✏s or ✏d , leadingto two possible final continuum states, ✏p or ✏f .Although, the above statement suggests that by varying the relative polarization, oneprobes the coupling between intermediate and final states, the polarization of thephoton preparing the intermediate state still introduces a principal direction, thus thesecond photon probes the symmetry of the initial state as well. Note that this modelis derived under the assumption of an initial p-state and is explicitly not valid forother initial angular electron momenta.

The model equation (6.6) clearly links the symmetry of the initial state with thestrength of the sideband polarization dependence via the one-photon ionization asym-metry parameter �2. For the normalized sideband intensity polarization modulation,the characteristic di↵erence between maximum and minimum, corresponding to par-allel and perpendicular relative polarization, reads as:

� =ImaxSB � Imin

SB

ImaxSB

=3 �2

5 + 2 �2. (6.7)

Hence, from this experimentally easily accessible value, the asymmetry parameter canbe deduced within this model as:

�2 =5�

3� 2�. (6.8)

In private communications, R. Taıeb, one of the authors of [60], has pointed out thatthis model should be applicable as first-order approximation for ionization from p-likestates even in small molecules. This could lead to a new simple experimental methodfor identifying the �2 asymmetry parameters of materials in gas-phase.

48

6.3 Experiment

6.3 Experiment

The experiment was carried out at our pump–probe HHG setup, described in chap-ter 2. The 15th harmonic from our source, corresponding to a photon energy of 23.7eV is overlapped with the fundamental IR laser (785 nm, 1.6 eV) in the interactionzone of our experimental chamber, which is equipped with a magnetic-bottle photo-electron spectrometer. Ensuring full spatial and temporal overlap of both beams, wevaried the relative polarization of the two pulses and followed the intensity modula-tion of the sidebands corresponding to ionization of the highest occupied molecularorbital (HOMO) of the system under investigation and simultaneous absorption ofone IR photon. We chose the IR laser intensity such that only first-order sidebandsoccurred. Contributions to these sideband peaks from multiphoton processes, wherefor example two IR photons are absorbed and one is emitted by the electron can beneglected due to their low probability. The measurements were repeated several timesfor each species to check the reproducibility and to estimate the accuracy of the data.

ground state ionized state

Ar 3s2 3p6 (1S0) + ~!vuv ! Ar+ 3s2 3p5 (2P) + (✏s, ✏d) + ~!ir ! (✏p, ✏f )

H2O (1b1 2p)2 (1A1) + ~!vuv ! H2O+ (1b1 2p)1 (2B1) + (✏s, ✏d) + ~!ir ! (✏p, ✏f )

O2 (⇡⇤g

2p)2 (3⌃�g

) + ~!vuv ! O2+ (⇡⇤

g

2p)1 (2⇧g

) + (✏s, ✏d) + ~!ir ! (✏p, ✏f )

N2 (�g

2p)2 (1⌃+g

) + ~!vuv ! N2+ (�

g

2p)1 (2⌃+g

) + (✏s, ✏d) + ~!ir ! (✏p, ✏f )

Ar H2O O2 N2

binding energy (eV) 15.8 12.6 12.3 15.6

Table 6.1: Electronic configurations for sideband formation from the HOMO and the corre-sponding single-photon ionization electron binding energies for all species investi-gated in this work. The binding energies, taken from [59], refer to the dominatingionization chanel. Substructures, for example the splitting for Argon in 2P3/2 and2P1/2, are not taken into account, as they are not properly resolved in this work.The term (✏s, ✏d) + ~!ir ! (✏p, ✏f ) visualizes the interaction of the electronswith the IR field. ✏x denotes an electron continuum state of angular momentumcharacter x .

All systems investigated in this experiment (Ar, H2O, O2, N2) have a p-like HOMO,therefore meeting the requirements for equation (6.6) to be applicable. The groundand ionized state electronic configurations for sideband formation from the HOMO arelisted in table 6.1 for each species.An overview of a typical measurement is given in figure 6.4. Sidebands are clearlyvisible at 14.2 eV and 17.4 eV on both sides of the single photon ionization peak at15.8 eV in figure 6.4.(a). Minor contributions from second order sidebands show up inthe spectrum around 12.6 eV and 19 eV as well, because the laser intensity was slightly

49


0 45 90 135 180

0.6

0.7

0.8

0.9

1

rela

tive s

ideb

an

d in

ten

sity

0 45 90 135 180

0.96

0.97

0.98

0.99

1

relative polarization (°)

rela

tive

pea

k in

tensi

ty

12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

binding energy (eV)

norm

aliz

ed

inte

nsi

ty

!

(b)

(c)

Ar+ 2P

SB SB

(a)

90°

42°

!6°

Figure 6.4: Overview of a typical polarization dependence measurement of two-color two-photon ATI in Argon. Photoelectron spectra for three di↵erent relative polar-izations are shown (a), with the x axis given in binding energies with respectto ionization of the Ar 3p level (15.8 eV, see table 6.1). The dependence of theintensity on the relative polarization of the light pulses is plotted for the leftsideband (b) and the main photoelectron peak (c).

too high. By the time the experiment was carried out no IR power control, excepttuning the width of apertures in the beam path was available, therefore we could notachieve better adjustment of the laser intensity. However, the second order sidebandintensities are very small and their contributions are neglected with respect to ourmodel. Figure 6.4.(b) shows the polarization dependence of the intensity of the first-order sideband of interest from absorption of a VUV and an IR photon around 14 eV,left of the main peak. The intensity was determined by integrating the photoelectronsignal for the whole sideband peak. The intensity of the main photoelectron peak isshown in figure 6.4.(c) and is maximum for minimum sideband intensity at ✓=90�, asexpected. The error bars were calculated before normalization as the square root ofthe total electron counts (Poisson statistics) and scaled with the same normalizationfactor as the data points.Both polarization dependent curves are fit by a cosine-like function and the di↵erencebetween maximum and minimum sideband intensity � is visualized in figure 6.4.(b).The model equation (6.6) can be expressed in terms of a cosine fit function forproviding easier numerical handling during analysis. Assuming normalization to themaximum signal for parallel polarizations, this fit function directly contains the char-acteristic amplitude of the modulation of the normalized sideband intensity � as the

50

6.4 Results

doubled amplitude of the cosine:

ISB(✓) / 12� cos(2✓ + 0) + c , (6.9)

where 0=0� for sidebands, 0=90� for depletion of the single photon ionization peakand c = 1� 1

2� is the zero-o↵set of the cosine function.

6.4 Results

The photoelectron spectra for Ar, H2O, O2 and N2 are presented in figure 6.5 forparallel (red) and perpendicular polarization (blue). The spectra were calibrated tothe binding energies for the individual systems, see table 6.1 and [59]. The sidebandsunder investigation from absorption of one photon from each light field, left of themain peaks and their polarization dependence are clearly visible.Those sidebands showing up right of the main peak, thus corresponding to emission ofa photon to the IR field are not considered here, because for systems with more thanone electronic state close to the ionization threshold it is impossible to disentanglesignals from these lower states, the sidebands from these states and the sidebandsfrom the HOMO. Very small contributions from second-order sidebands are visible in

0.1

0.3

0.5

0.7

0.9 Ar

SB

2P

H2O

SB

2B1

9 11 13 15 17 19

N2

SB

2!

+

g

9 11 13 15 17 19

0.1

0.3

0.5

0.7

0.9 O2

SB

2"

g

binding energy (eV)

norm

aliz

ed s

pect

ral i

nte

nsi

ty

Figure 6.5: Photoelectron spectra for the four systems under investigation for parallel (redline) and perpendicular relative polarization (blue line) of VUV and IR light.

51


all spectra left of the first sidebands, pointing to a slightly too much dressing IR fieldintensity.Figure 6.6 depicts the polarization dependences of the sidebands for all four systemsand compares them with the model presented in section 6.2. The plots are ordered bythe characteristic modulation amplitude �, starting with the highest value for Ar inthe upper left panel. Blue markers represent the measured data, red lines are corre-sponding cosine fits, and black lines show theoretical sideband intensity modulations,calculated from the model, equation (6.6), with values for �2 taken from the literature[64–68]. Colored shades indicate the uncertainties in the model plots originating fromthe uncertainties of the literature values of �2. The measured characteristic modu-lation amplitudes �, derived experimental asymmetry parameters �2 and previouslypublished values for �2 are listed in table 6.2 and table 6.3.

0.5

0.6

0.7

0.8

0.9

1

Ar

H2O

0 90 180

0.5

0.6

0.7

0.8

0.9

1

O2

0 90 180

N2

relative polarization (°)

no

rma

lize

d s

ide

ba

nd

inte

nsi

ty

!1

!0

!1,!

0 not resolved

Figure 6.6: Modulation of the sideband intensity as a function of the relative angle betweenthe polarization vectors of VUV and IR pulses. Experimental data with error bars(blue markers) and cosine fits (red lines) are shown for our four investigatedsystems. Black lines represent the theoretically expected intensity modulationsaccording to our model with values for �2 taken from the literature and col-ored shades indicating the uncertainty. Three model curves are plotted for N2,corresponding to �2 literature values from vibrational decay channel resolvedmeasurements (⌫1, ⌫0) and from an earlier vibrationally unresolved experiment.

52

6.4 Results

We observed that the normalized amplitude of the sideband modulation varies fordi↵erent atomic or molecular species, as expected from the model for varying �2. Thesideband modulation should be highest for the most oriented electronic state, hencehigh �2. This is reflected in the data, as Ar shows the highest modulation amplitude.The data for Ar, H2O and O2 are in reasonably good agreement with the model. ForAr and H2O, the plotted shades indicating the uncertainty from the literature valuesof �2 almost meet the experimental data points, but the model predicts sidebandintensity modulations slightly higher than measured. For O2, the sideband modulationis underestimated, but still in good agreement, especially if one keeps in mind thatthe model was derived for p-states of atoms.The situation is more complex for N2. The molecule shows a resonance for excitationwith the 23.7 eV photons used in our experiment. At this photon energy two decaychannels compete with each other, corresponding to di↵erent vibrational final statesof the created N2

+ ion. Auto-ionization processes take place and perturb the two-color two-photon ATI process forming the sidebands. Hence, here the approximativemodel apparently fails.In the bottom right panel of figure 6.6, the experimental data and the predictions fromthe model are plotted for N2 with �2 values taken from the literature for a vibrationallyresolved measurement [67] and for an experiment where �2 was determined withoutdistinction between vibrational final states [68]. The di↵erent values of �2 are listed intable 6.3. None of the predicted curves or tabulated values is close to the data, whichclearly indicates the failure of the model, as it was not designed to be valid withina resonance. The breakdown of the model in turn demonstrates the sensitivity oftwo-color two-photon ATI to vibrational resonances in the ionized system. Moreover,this sensitivity could be utilized in future pump–probe photoelectron spectroscopyexperiments for quickly testing, if a resonance is hit, without the necessity of a tunablephoton source.

Ar H2O O2 N2

experimental � 0.42± 0.02 0.35± 0.05 0.24± 0.03 0.14± 0.04

(this work) ) �2 0.97± 0.07 0.76± 0.14 0.48± 0.07 0.26± 0.08

literature �2 1.18± 0.12 1.08± 0.17 0.31± 0.08 see

ref. [64] [65] [66] table 6.3

Table 6.2: Magnitudes of the sideband intensity modulation � and the �2 values deducedwith our model compared to �2 values from the literature.

53


N2 �2 value

[67] vibrational channel ⌫0 0.78± 0.05

⌫1 0.50± 0.07

[68] no distinction of ⌫0, ⌫1 0.67± 0.07

this work 0.26± 0.08

Table 6.3: Asymmetry parameter �2 of the HOMO of N2 from a vibrational channel resolvedexperiment and from an experiment not distinguishing between the two decaychannels compared to �2 determined from this experiment.

6.5 Conclusion for this chapter

A theoretical approximation was introduced, describing the polarization dependenceof sidebands in photoelectron spectra, formed by two-color two-photon above thresh-old ionization, valid for p-character initial electronic molecular states. The model linksthe sideband polarization sensitivity with the one-photon ionization asymmetry pa-rameter �2, which describes the asymmetry in photoelectron angular distributions.Experimental tests of this approximation were performed at our HHG based pump-probe setup on four small atomic and molecular systems, namely Ar, H2O, O2 andN2.The model is in reasonably good agreement for three of the investigated systems, Ar,H2O and O2. The disagreement of model and experimental results for N2 shows thatwe stroke a resonance in N2 with our HHG photons and thus the model is not validfor this system. A more precise approach, taking into account more information aboutthe electronic system is desirable, for example higher order asymmetry parameters andresonances. The group around R. Taıeb, one of the authors of [60], where this modelwas introduced, is currently working on extending and more precisely rendering thetheoretical model and on extending it to other initial angular momenta than p-likestates.From an experimentalist’s point of view, repeating the experiment with an angularresolved detection scheme, for example with an angular resolved time-of-flight spec-trometer (ARTOF) [69] or a velocity map imaging spectrometer (VMI) [44], enablingthe determination of photoelectron angular distributions for each relative polarizationangle or at least for the two extremal relative polarizations, parallel and perpendicular,should be the next step. The experiment should be equipped with accurate controlof the IR intensity in order to prevent the formation of higher order sidebands andthus to better meet the assumptions for the theoretical approach. Additionally, moremolecular systems could be investigated with various angular momenta of the HOMO

and the on– and o↵–resonance situation could be specifically compared.

54


This could provide deeper insight into, and understanding of fundamental processesand symmetries in light matter interaction for small molecules and atoms and possiblyclarify the deviations between experiment and theory, observed in this work.

Acknowledgement for this chapter

The presented experiment on polarization control in two-color above threshold ion-ization was carried out at the high-harmonic generation setup at Helmholtz-ZentrumBerlin, Germany, described in chapter 2. Experiment and data evaluation were per-formed by the author of this thesis, Torsten Leitner.Phillipe Wernet (Helmholtz-Zentrum Berlin, Germany) and Michael Meyer (EuropeanXFEL, Hamburg, Germany) greatly contributed with their very help- and fruitful ideasand in numerous discussions. In private email communications, Richard Taıeb (UPMC,Universite Paris 06, France) provided help and insights regarding the theoretical modeladapted from previous work of him and his group.

55

7 Coherent Nuclear and ElectronicWave Packet Dynamics in NaI

In the past decades, femtochemistry has made remarkable progress and intensiveresearch is going into the investigation of dynamic processes in molecules on thefemtosecond time-scale. In 1988 the group of A. Zewail pioneered this progress byperforming extensive studies on the temporal evolution of molecular wave packets inphoto-excited NaI using femtosecond transition state spectroscopy (FTS) by laser-induced fluorescence (LIF) [3, 4]. In the following years they continued with intenseresearch on this subject, yielding a number of publications on the dynamics of photo-excited NaI molecules and on techniques to visualize chemical processes on funda-mental pico- to femtosecond time scales [70–77].In one of their original experiments, the wave packet is prepared from the groundstate of NaI into the first excited state by a pump laser pulse and the evolutionof the system is followed by a delayed probe laser pulse, which induces a transitionto an upper dissociative potential, where the Na atom is an excited 2P

J

state. Theyield of the laser-induced fluorescence of the atomic Na D–line (2P

J

! 2S1/2) at589 nm is followed versus the pump–probe delay time. The wavelength of the probelaser defines a optically coupled region (OCR), where both potentials are resonantlycoupled and the wave packet can undergo a transition to the upper potential. Thus,fluorescence will only be observed for those delays, where the wave packet is at equalintra-molecular distance as the OCR. Varying the probe wavelength enables shiftingof the OCR along the potentials.These studies have enabled the characterization of the potential energy surfaces ofthe excited state and the (lower) unbound states, as well as the characterization ofwave packet oscillations happening in excited NaI molecule, due to an intersection ofthe first excited state A and the ground state X forming an e↵ective trapping potential(see figure 7.1). Since then, a vast number of theoretical and computational papersdealing with potential energy surfaces and wave packet dynamics in NaI moleculeshave been published [78–89].For monitoring dynamics in the electronic structure, time-resolved photoelectron spec-troscopy (TRPES) techniques have shown to be a powerful tool [2, 90, 91]. In TRPES,the system is excited by a pump laser pulse �

pmp

and photo-ionized by a time de-layed probe pulse �

prb

. The kinetic energies of all created photoelectrons are thenmeasured simultaneously, and therefore all electronic states with binding energies be-low the probe photon energy are accessible. Hence, in contrast to FTS by LIF asperformed by Zewail and co-workers, energy resolved photoelectron distributions and

57

7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI

therefore the temporal evolution of the full electronic structure of the system underinvestigation can be recorded, enabling conclusions on the dynamics of the electronicand the nuclear wave packets of the corresponding molecular wave packet.Already in 1989, shortly after the first publications on femtosecond NaI dynamics, itwas pointed out, that TRPES should yield improved, deeper results on the dynamicsthan fluorescence spectroscopy, used in the first experiments [79]. However, to ourknowledge, it took another eight years for the first TRPES study with femtosecondpulses on NaI molecules to be published, in 1997 by C. Jouvet and his group [92, 93].In their experiment, they could only distinguish between slow and fast electrons, hencenot using the advantage of resolving all electronic states simultaneously. Their resultswere well reproduced by numeric simulations of the experiment, published in 2007[87].In this chapter, our results from a photoelectron energy resolved TRPES experiment inApril 2011 at the Max-Born Institute Berlin (MBI) on the electronic and nuclear wavepacket dynamics in photo-excited NaI molecules with 320 nm (3.87 eV) pump and200 nm (6.2 eV) probe pulses are presented. First a description of the experiment,calculated potentials and expected photoelectron spectra, modeled in a simplifiedapproach are introduced. Thereafter the results from our measurements are presentedand discussed in detail.

7.1 How it works

7.1.1 Calculated intra-molecular potentials

In figure 7.1 intra-molecular potentials for the NaI molecule, calculated by MichaelOdelius (Stockholm University, Sweden) [94] based on previous theoretical work [83,85], and an illustration of the principle of our experiment are shown.The intra-molecular potentials for the molecular ionic ground state X, the spin-orbitsplit excited molecular covalent states A and B and the first three states of NaI+

ions, named ↵, � and � are plotted. The labels at the potential curves, on the rightside for long distances give the corresponding free fragments for the asymptotic limitof infinite distances. The energy axis is chosen relative to the lowest energetic freeneutral fragments, for the asymptotic limit of the A potential. An overview of themolecular states of NaI, the corresponding fragments and their ionization energies isgiven in table 7.1. Potential curves for higher lying excited states of the NaI molecule,between the B and ↵ potentials, which are not relevant for our experiment, are notdepicted in order to maintain a clearly laid out picture. Note that in the experimentby Zewail and co-workers, their probe pulses induced a resonant transition to one ofthese higher excited NaI states.

58

7.1 How it works

2 4 6 8 10 12 14 16

!3

!2

!1

0

1

2

3

4

5

6

7

intra!molecular distance (Å)

pote

ntia

l (eV

)

X

A

B

!

"

#

Na+ + I!

Na + I

Na + I

Na+ + I

$pmp

$prb

Ekin

photoelectron

Figure 7.1: Illustration of the pump–probe experiment on NaI with calculated intra-molecular potentials [94] for the NaI molecule (ionic ground state X and thefirst two excited covalent states A and B) and for the NaI+ ion (↵, � and �)versus the intra-molecular distance. A detailed description is given in the text.

The ionic ground state potential X and the covalent excited states A and B intersectat an intra-molecular distance of 7.6 A and 13.5 A, respectively, and form e↵ectivetrapping potentials. Note that the intra-molecular distance for the A–X intersectionwas previously estimated as 6.93 A [77], however, the exact distance of the intersectionis not scope of this work. In our experiment, a molecular wave packet (yellow Gaussianshape) is created on the A state by a pump pulse �

pmp

and oscillates in the A–X trap. In each oscillation, a fraction of the wave packet (gray Gaussian shape) cantunnel through the intersection, breaking the molecular bond and forming free, neutralfragments. A delayed pulse �

prb

is used to probe the system by photo-ionization. Thesystem is lifted to one of the NaI+ ion states ↵, �, � by the probe pulse and theexcess energy is liberated as kinetic energy E

kin

of the photoelectrons. Hence, thedi↵erence �

prb

�Ekin

is the binding energy Eb

of the corresponding ionized molecularorbital. Note that pump, probe and E

kin

arrows are not plotted to scale. In thisintra-molecular potential picture, the binding energy of the valence electrons for agiven intra-molecular distance is the di↵erence between the potential energies ofthe initial molecular and the final ion state. In the following, a notation with thefinal state as superscript to the initial state will be used to denote the transitions, forexample, pumping would read as XA and the probing example as depicted in figure 7.1corresponds to A↵, A� and A� transitions.

59


NaI state fragments (NaI)� state fragments

X (1⌃0+) Na+(1S0) + I�(1S0) ↵ 32

� 12

)

Na+(1S0) + I (2P 32)

A(0,1,2)± Na (2S 12) + I (2P 3

2)

B(0,1)± Na (2S 12) + I (2P 1

2) � 1

2Na+(1S0) + I (2P 1

2)

fragment Na Na+ I I�

ionization energy (eV) 5.14a 47.3a 10.45a 3.06b

Table 7.1: (top) The molecular states of neutral and ionized NaI and corresponding frag-ments for infinite intra-molecular distances. Subscripts denote the molecular oratomic total angular momenta ⌦ or J, respectively. (bottom) Ionization energiesfor the fragments (a ref.[95], b ref.[96]).

7.1.2 Binding energies and simplified modeled photoelectronspectral evolution

The potential di↵erences, hence the electron binding energies depend on the intra-molecular distance upon ionization, thus oscillations of the wave packet translate tooscillations of the energy of the observed photoelectrons. Figure 7.2 depicts bind-ing energies versus the intra-molecular distance calculated for NaI molecules photo-excited to the A state [94] with respect to the intra-molecular potentials introducedin figure 7.1 and provides for an impression of the positions and the dynamic oscilla-

4 4.5 5 5.5 6

4

6

8

10

intra

!mol

ecul

ar d

ista

nce

(Å)

binding energy (eV)

A! A" A#

X!," X#

Figure 7.2: Calculated binding energies for the valence orbitals versus intra-molecular dis-tance for NaI molecules initially exited to the A potential [94]. The lines areplotted in red for ionization from the covalent A state (NaI) and in blue for theionic X (Na+I�), respectively, and labeled with the corresponding electronictransition.

60

7.1 How it works

tion range in binding energy of the photoelectron peaks expected in an experiment.Only the highest of the three A state potentials is included in this calculation, hencethe spin–orbit splitting is not shown in this plot. Red lines mark ionizations from thecovalent A state and blue lines ionization from the ionic X state, on which the wavepacket evolves for distances longer than the position of the A–X crossing.Figure 7.3 magnifies the potential region, where the wave packet dynamics in photo-excited NaI molecules occur. The crossing of the potentials is indicated and innerand outer turn of the oscillating wave packet are defined as the intersection of thepotential curves and the available excitation energy provided by one pump photon(vertical line).

2 4 6 8 10 12

!3

!2

!1

0

1

2

intra!molecular distance (Å)

pote

ntia

l (eV

)

X

A

!pmp

crossing

inner turn outer turn

Figure 7.3: Crossing, inner and outer turn defined and visualized in the calculated intra-molecular potentials picture.

Figure 7.4 schematically shows the expected evolution of photoelectron distributionsfor the first three oscillations of the wave packet, modeled in a simplified approach.It is assumed in the model that upon pumping an excited wave packet is createdon only one of the A potential curves. The photoelectron peaks, originating fromthe initial ground state molecular orbitals 2⇧3/2 ,

2⇧1/2 (X↵, X � transition) and 2⌃(X � transition), now correspond to A↵, A� and A� transitions and shift to higherbinding energies as the wave packet approaches the crossing (red lines). Additionally,the splitting of A↵, A� vanishes. Thereafter the wave packet travels on the ionicX potential and is reflected at the outer turning point, yielding an oscillation of thephotoelectron peaks to lower binding energies and back (blue lines). After passing thecrossing a second time and entering the covalent region again, the wave packet evolveson all spin-orbit A potential curves in a superposition of several internuclear distances.A splitting to many peaks is expected in the photoelectron spectrum (red lines). Thisassumption follows [83], where it is pointed out that due to symmetry reasons theenergetically discernible ⌦=0,1�,1+ multiplet-levels of the A state, corresponding tothe curve triplet in figure 7.1, are accessible via dipole allowed transitions from the

61


ground state X. The oscillation sequence restarts after the wave packet has beenreflected at the inner potential barrier.Contributions from that part of the wave packet, which tunnels through the crossingand evolves further on the A state outside the trapping potential and dissociates tofree neutral fragments are indicated with green lines.

onset

crossing

outer turn

crossing

inner turn

crossing

outer turn

crossing

inner turn

crossing

outer turn

crossing

binding energy (eV)

time !

4 4.5 5 5.5 6

Figure 7.4: Modeled evolution of the photoelectron spectra from the valence orbitals of ex-cited NaI molecules, as expected to be observed in a pump–probe photoelectronspectroscopy experiment with distinguished distances as defined in figure 7.3 in-dicated on the right. The spectra were modeled in a simplified approach and theoscillation period is in the order of 1 ps, but the time axis is plotted non-linear,see text for a detailed description.

Note that, in principle, a similar situation, as assumed in our model can occur, if a wavepacket trapped on a single potential curve or on several closely lying potential curvesinteracts with itself, leading to constructive and destructive quantum interferencesalong the intra-molecular distance coordinate, after the wave packet has evolved andstarted to dephase. Such wave packet quantum interferences have been reportedin [97], for example, where they could visualize quantum beating in dissociating O2

wave packets, due to slightly di↵erent wave packet speeds on closely lying dissociativepotential curves.

62

7.1 How it works

In reality, both e↵ects, splitting onto several potential curves and quantum inter-ference, should occur together and alternately influence each other. However, theresolution in time and energy available in the photoelectron spectroscopy experimentdescribed in this chapter was not suitable for deciding between both e↵ects. In orderto proof wave packet quantum interferences with photoelectron spectroscopy, onewould need resolutions high enough, in order follow the evolution and shifting ofeach photoelectron peak separately at an accuracy level, which allows for detectionof discontinuities in the photoelectron peak’s path. Such discontinuities can serve asa proof that destructive quantum interference took place. Accurate determination ofthese e↵ects becomes even harder, as the ionization cross-section for creating a pho-toelectron varies for the di↵erent potential curves and depends on the intra-moleculardistance, therefore a strong drop in ionization e�ciency due to cross-section jumpsmight be miss-interpreted as quantum beating.In figure 7.4 the photoelectron spectra for each distance are modeled as a sum ofGaussian distributions with their centers located at the binding energy of the cor-responding transition. Three peaks in the photoelectron spectrum for transitions tothe NaI+ ion states ↵, �, � are visible and when the wave packet evolves, they shiftto higher binding energies. The double peak structure for the transitions to ↵ and� morphs to a single peak, as the splitting of the corresponding NaI+ ion statesvanishes for longer distances. After passing the crossing for the first time, the wavepacket travels on the ionic X potential curve (blue lines) and is reflected at the outerturning point (assumed to be around 9 A in this model, without loss of generality).Additionally, contributions from parts of the wave packet on the A potential, whichalready tunneled through the crossing, become visible at around 5.1 eV and 5.95 eV(green lines). The still trapped part of the wave packet passes the crossing a secondtime, coming from long distances on the X potential and can now spread onto all spinorbit split A potential curves (red lines), leading to a multiplet of three photoelectronpeaks for each transition (A↵,�,�). Due to energy conservation, the part of the wavepacket on the upper A potential curve will not reach the initial intra-molecular dis-tance again, as the potential height reaches the excitation energy already for largerdistances – the wave packet is in a superposition of several intra-molecular distances.Further more, it is assumed that the wave packet on the upper A state potentialhas not enough energy to reach intermolecular distances short enough in order todistinguish between transitions to ↵ and � ion states, therefore a splitting to only fiveinstead of six photoelectron peaks is modeled for the oscillations on the left at bindingenergies in the range of 4.5 eV to 5.1 eV. For simplicity, the shift in binding energywith respect to the lowest potential of these additional peaks is modeled increasinglinearly with the distance between the crossing and the position of the wave packeton the lowest potential curve, resulting in the broadest splitting for the inner turn.The variation of the photo-ionization cross-section for di↵erent transitions and varyingintra-molecular distance is not taken into account in this approach, therefore relativeintensities are not modeled correctly for the photoelectron distributions. Also dampingof the wave packet population and therefore of the photoelectron yield due to leakage

63


through the crossing in each oscillation, leading to free fragments, is not included inour simple model. The spectral evolution along the y-axis is generated by equal stepsin intra-molecular distance for each spectrum without accounting for the actual speedof the wave packet. Thus, the visible separations of, for example, crossing and innerturn, relative to crossing and outer turn along the evolution axis (y-axis) in the modelplot do not correlate to visible separations in a plot of a real pump–probe experiment,where the delay time is plotted against the photoelectron energy. Also a relativedephasing of the wave packet fractions on the individual A potential curves or adispersion of the oscillating wave packet in the potential trap is not accounted for inthis simplified approach.

7.1.3 The ground state spectrum of NaI

The ground state spectrum of the NaI molecule was measured in an earlier testcampaing on NaI with two-color two-photon ionization by 370 nm and 200 nm pulsesat the laser laboratory at MBI with a magnetic bottle electron spectrometer (describedin [43]) and is presented in figure 7.5. Peaks originating from ionization out of thespin-orbit split 2⇧3/2 ,

2⇧1/2 molecular orbitals, corresponding to X↵, X � transitions areclearly discernible at 7.8 eV and 8.1 eV. The most intense peak at 9.1 eV correspondsto a X � transition, hence ionization of the 2⌃ orbital of the ground state NaI molecule.Table 7.2 gives an overview of the binding energies of these valence orbitals andcompares values calculated by Michael Odelius [94] to those measured in this exper-iment and to previously published ones. The discrepancy of calculated and measuredbinding energies is in the order of the accuracy of the absolute binding energies ofthe calculation. The di↵erence of our experiment and the literature can be explained,if one takes into account, that the literature values were obtained by single photonionization, but in contrast, our experiment relies on two-color two-photon ionizationand therefore the ground state spectrum is perturbed by ultrafast dynamics occurringwithin the cross-correlation width the pump and probe pulses.

binding energy (eV)

transition molecular orbital calculation this experiment literature

X↵ 2⇧3/2 7.89 7.8 (±.05) 8.03a

X� 2⇧1/2 8.14 8.1 (±.05) 8.25a

X� 2⌃ 9.01 9.1 (±.05) 9.21a / 9.0b

Table 7.2: Overview of the ground state valence orbitals of NaI and their binding energiesfrom a numeric calculation [94] compared to values from this experiment andprevious publications (a ref.[98], b ref.[99]).

64

7.2 Experiment

2!

3/2

2!

1/2

2"

binding energy (eV)

inte

nsi

ty (

a.u

.)

7.5 8 8.5 9 9.5

0

20

40

60

80

100

120

Figure 7.5: Ground state photoelectron spectrum of the NaI molecule measured at zerotime delay, hence with two-color two-photon ionization. The data points (blackdots) are connected with a cubic spline fit (black line) as guide to the eye. Theuncertainty is plotted as gray shade and the corresponding molecular orbitalsare indicated above the peaks.

7.2 Experiment

The experiment was performed in a collaboration with and at the Max-Born-InstituteBerlin (MBI), see chapter 4 for a detailed description of the experimental setup.The molecular oven, described in chapter 3 and developed at HZB served as NaIevaporation source. For the measurements, presented in this chapter, a pump wave-length of 320 nm (3.87 eV) was chosen. Both, the 200 nm (6.2 eV) probe pulses andthe pump pulses were about 70 fs in duration (FWHM) and therefore the FWHM ofthe cross-correlation function is in the order of 100 fs. The bandwidth of the pulseswas in the order of 0.06 eV (FWHM) for pump and for probe, yielding a combinedcross-correlation bandwidth of 0.085 eV (FWHM). Delay time resolved photoelectronvelocity maps were recorded with a velocity map imaging spectrometer (VMI). TheVMI was set to record photoelectrons up to a maximum kinetic energy of 2.35 eVfor a time window from -1.3 ps to +7.7 ps with 53 fs delay step size and for a timewindow from -1.3 ps to +3.1 ps in 27 fs steps (the 320 nm pump pulses arrive firstfor positive delay times). Our collaborators, Per Johnsson and Linnea Rading (LundUniversity, Sweden), post-processed the recorded VMI datasets and extracted pho-toelectron kinetic energy distributions with 10meV bin width for each delay step inorder to obtain TRPES maps for the further analysis presented here.

Figure 7.6 depicts the final photoelectron energy distributions, with the photoelectronkinetic energy E

kin

given in the top axis, whereas the bottom axis shows the totalabsorbed photon energy:

Eabs

= Epmp

+ Eprb

� Ekin

, (7.1)

with the photon energies of pump and probe pulses, Epmp

and Eprb

. This axis gives

65


the total energy, absorbed by the NaI molecule from both pulses for creating thedetected photoelectron, regardless of the time delay between the pulses. In the presentexperiment, pump and probe pulses exchange their role for negative delays and the3.35 eV pump pulses ionize the system, instead of the 6.2 eV probe pulses, hencesame kinetic photoelectron energies do not correspond to same binding energies ofthe electrons in the excited NaI molecules for positive or negative delay times, as theenergy of the ionizing pulse is di↵erent. In contrary, E

abs

can serve as unified axis forall delays, even if the pump and/or probe photon energy is tuned. The binding energyof an electron is estimated as the di↵erence between E

abs

and the photon energy ofthe non-ionizing, first arriving pulse:

Eb

= Eabs

� Epmp

, �t > 0 , (7.2)

Eb

= Eabs

� Eprb

, �t < 0 . (7.3)

For�t = 0, the case of simultaneous two-color two-photon ionization, Eabs

representsthe electron binding energy for the ground state of NaI.In figure 7.6 the expected oscillations in the photoelectron spectra are clearly visiblefor positive delays. The oscillating signal in the range of E

abs

=[8–9] eV corresponds

kinetic energy (eV)

00.511.52

!1

0

1

2

3

4

5

6

7

rela

tive in

tensi

ty

0

0.2

0.4

0.6

0.8

1

kinetic energy (eV)

dela

y (p

s)

00.511.52

!0.5

0

0.5

1

1.5

2

2.5

3

total absorbed photon energy (eV)

8 8.5 9 9.5 10


8 8.5 9 9.5 10

(a) (b)

Figure 7.6: TRPES maps (delay vs. energy) from NaI molecules photo-excited by 320 nm(3.87 eV) photons (a) for pump–probe delay times up to 7.7 ps with 53 fs delaysteps and (b) for the first three oscillations up to 3.1 ps, recorded with 27 fsdelay steps. The excited state binding energy is given in the top axis, whereasthe bottom axis shows the total absorbed photon energy (see equation (7.1) fora definition).

66

7.3 Ultrafast auto-ionizing dissociation

to ionization to final ↵- and �-NaI+ ion states and the signal from ionization to thefinal �-NaI+ ion state is visible for E

abs

=[9–10] eV. On the negative delay side, nooscillations, are visible, but an ultrafast dissociation process, leading to a very intensepeak at E

abs

⇠9.25 eV. The observed processes for both, negative and positive delaytimes, are discussed in detail in the next sections.

7.3 Ultrafast auto-ionizing dissociation

The main process observed for negative delays is auto-ionization to free Na+ andI� ion fragments. The 200 nm (6.2 eV) pulses arrive first and highly excite the NaImolecules. It is not clear to which of the potential curves the system is excited to,either to A, B, a higher excited NaI potential curve not depicted in figure 7.1 or to awave packet superposition involving several of these excited state potentials. In anycase, the amount of energy brought into the system is enough to overcome the Xpotential, therefore the excited molecular wave packet evolves on the ionic X potentialto the asymptotic limit of infinite intra-molecular distances and the system auto-ionizes to free Na+ and I� ion fragments. The photoelectron peaks shift in energy tothe corresponding energies of the fragments during this ultrafast dissociation process,as for example reported in [10] for ultrafast Br2 dissociation.The shift of the intense peak for in figure 7.6 to E

abs

=9.25 eV, corresponding to theground state 2⌃ orbital of the NaI molecule , is magnified in figure 7.7 for a seriesof negative delays up to -1300 fs. The plots in figure 7.6.(a) were extracted fromthe data discussed in this chapter, measured with 320 nm (3.87 eV) ionizing pulsesand a VMI spectrometer, whereas (b) shows results acquired in a test campaign inApril 2011 at the same laser setup with a magnetic bottle electron spectrometer, 370nm (3.35 eV) ionizing pulses and delay steps of 100 fs. The binding energy for thebottom axis is given with respect to ionization of the excited system or dissociationproducts by the ionizing pulses, see equation (7.3). The fitted peak maximum shiftsby 100±15meV within a dissociation time ⌧

diss

⇠ 400 fs to 3.06 eV excited statebinding energy in figure 7.7.(a) and to 3.02 eV in (b), which is in good agreementwith the I� electron a�nity of 3.05 eV (see table 7.1). The di↵erence between thefragment photoelectron energies in (a) and (b) can be explained by uncertaintiesfor the values of the di↵erent ionizing photon energies, which directly influence thetransformation from kinetic photoelectron energies to E

abs

and Eb

.The ionization potential of the created Na+ fragments is 47.3 eV (see table 7.1) andtherefore photoelectrons from free Na+ ions are not observable in this experiment, asthe ionizing pulses do not provide enough photon energy for ionization.

67


excited state binding energy (eV)

2.7 2.8 2.9 3 3.1 3.2

!1300

!1000

!750

!500

!400

!300

!200

!100

0


8.9 9 9.1 9.2 9.3 9.4

(a) �pmp

=200 nm, �prb

=320 nm

de

lay

(fs)


8.9 9 9.1 9.2 9.3 9.4

!1300

!1000

!700

!500

!400

!300

!200

!100

0


2.7 2.8 2.9 3 3.1 3.2

(b) �pmp

=200 nm, �prb

=370 nm

Figure 7.7: Dissociation to free I� ions for negative delays, extraceted from data measuredwith (a) 320 nm ionizing pulses and a VMI spectrometer (see also figure 7.6),and (b) for data acquired in a previous campaign with 370 nm ionizing pulsesand a magnetic bottle electron spectrometer. The orange spectra at �t=0 showthe 2⌃ peak from ground state NaI molecules and the black spectra illustratethe shifting of this peak during the dissociation process. All data sets (blackdots) are interpolated with cubic splines (lines) and the maxima of the splines aremarked by red dots. The excited state binding energy for negative delays is givenin the bottom axis, whereas the top axis shows the total absorbed photon energy.The final peak energy, arising from ionization of free I� fragments is reachedwithin ⌧

diss

⇠ 400 fs after a relative energy shift of the peak by ⇠ 100±15meV(marked by blue lines).

68

7.4 Coherent electronic and nuclear wave packet oscillations

7.4 Coherent electronic and nuclear wave packetoscillations

The molecular wave packet dynamics, proposed in the model introduced in subsec-tion 7.1.2 and figure 7.4 are observed for positive delay times. The 320 nm (3.87 eV)pulses arrive first and excite the NaI molecules onto the A potential, creating a wavepacket in the A–X potential trap (see figure 7.1).For easier discussion of the TRPES data, first a detail view of the photoelectron datafor the first one and a half oscillations of the molecular wave packet in the potentialtrap is shown in figure 7.8 with outer turn, inner turn and the crossings labeled.’Crossing outwards’ denotes the wave packet evolving to long distances towards theouter turn and ’crossing inwards’ denotes the wave packet evolving back to shortdistances. No values for energy and delay time are given in the plot in order to drawthe attention only to the visual appearance of the individual features in the TRPESmap. A black vertical line in the map divides the TRPES map into energy regionsfor photoelectrons arising from (A,X)↵,� transitions on the left and from (A,X)�

transitions on the right.

(A,X)α,β (A,X)γ

dela

y

binding energy

outer turn

outer turn

inner turn

crossing outwards

crossing inwards

crossing outwards

Figure 7.8: Distinguished features indicated in an exemplary detail of the TRPES maps.

Figure 7.9 shows the full TRPES maps recorded in our experiment for the plain dataset in figure 7.9.(a) and with the photoelectron distributions normalized separatelyfor each delay step in figure 7.9.(b). The data recorded for pump–probe delay timesup to 7.7 ps with 53 fs delay steps is shown in the left column and the right columndepicts the data recorded with smaller delay steps of 27 fs for delay times up to 3.1 ps.In the upper panel, figure 7.9.(a), showing the unnormalized plots, reoccurring peaksfor the outer turn of the wave packet on the ionic X potential are visible aroundEb

=4.4 eV, corresponding to the X↵,� transitions, arising from the spin-orbit splitground state 2⇧ orbitals and peaks are visible around E

b

=5.4 eV, corresponding tothe X � transitions and arising from the ground state 2⌃ orbital. Furthermore, thephotoelectron intensity traces right of these peaks visualize, as the wave packet runsthrough the crossing, ’uphill’ to the outer turn and back again, after being reflected.

69



4 4.5 5 5.5 6

!1

0

1

2

3

4

5

6

7

rela

tive

inte

nsi

ty

0

0.2

0.4

0.6

0.8

1

binding energy (eV)

de

lay

(ps)

4 4.5 5 5.5 6

!0.5

0

0.5

1

1.5

2

2.5

3


8 8.5 9 9.5


8 8.5 9 9.5

(a) interpolated TRPES map of the NaI wave packet oscillations


4 4.5 5 5.5 6

!1

0

1

2

3

4

5

6

7

inte

nsi

ty (

a.u

.)

0

0.2

0.4

0.6

0.8

1


de

lay

(ps)

4 4.5 5 5.5 6

!0.5

0

0.5

1

1.5

2

2.5

3


8 8.5 9 9.5


8 8.5 9 9.5

(b) interpolated TRPES map, normalized separately for each delay

Figure 7.9: TRPES maps depicting the wave packet dynamics in NaI molecules photo-excited by 320 nm (3.87 eV) photons: Plain data (a) and the data, normalizedseparately for each delay step (b). The left column depicts a scan for pump–probe delay times up to 7.7 ps with 53 fs delay step size and the right columnshows a scan recorded with 27 fs delay step size for the first 3.1 ps.

70


The individually normalized TRPES maps, figure 7.9.(b), provide for a visualization ofthe evolution of the maximum of the photoelectron distribution versus delay time andvisualize the width or spread of the photoelectron energy distributions. The intensitytraces right of the outer turns, pointing to higher binding energies are now visibleat high contrast. The high energy ends of these features arise from the wave packetpassing through the crossing, as the binding energies of the electrons of the oscillatingwave packet are the highest at the crossing (see figure 7.2).The outer turn is observed for delays around 0.55 ps, 1.65 ps, etc, but at delay timesaround 1.1 ps, 2.2 ps, etc, a spreading of the electron distribution is observed, which isnot visible in the unnormalized TRPES map. This spread arises from the inner turn andsupports our initial assumption for the model (subsection 7.1.2), that the wave packetpopulates all A potential curves, when evolving back through the crossing. Note thatthis spreading out on several states leading to a whole family of photoelectron peaksis not observable with laser-induced fluorescence, used by the Zewail group.The broadening of the molecular wave packet along the evolution axis (intra-moleculardistance) manifests, for example, in the increasing temporal width of the peaks corre-sponding to evolution on the X potential around the outer turn. From the asymmetryof these features, broadened to longer delays, one can conclude that the wave packetdisperses on the low repulsive, rather flat ionic X potential, but is re-sharpened uponthe inner turn, when being reflected by the highly repulsive inner potential barrier.This e↵ect was previously reported and postulated to arise from the Coulombic forcefield counteracting the dephasing of the wave packet due to the anharmonicity ofthe intra-molecular potential A–X trap, in which it evolves, leading to a sharp, highlylocalized wave packet only for short intra-molecular distances around the inner turn,where the potential gradient is comparably large and to a broad wave packet for smallpotential gradients around the crossing region and the outer turn, see [77] and refer-ences therein. However, both TRPES maps, plain and normalized, show that the totaldispersive broadening of the wave packet is still high enough, so that for the thirdand later outer turns part of the wave packet is observed at photoelectron energiescorresponding to the outer turn, whereas part of the wave packet is already at theinner turn or even back on the X potential on its way to the next outer turn. This isespecially visible in the individually normalized TRPES map for long delay times [leftpanel in figure 7.9.(b)], where the end and start points of subsequent ’straight line’features visible at each outer turn overlap in time. These features correspond to theevolution of the photoelectron distribution maximum on the outer turn. Furthermore,for the last two depicted outer turns, end and start point touch, hence for those delaytimes there is evidently always some amplitude of the wave packet on the ionic Xpotential. This is another example for the trapped molecular wave packet existing ina quantum mechanical superposition of several intra-molecular distances and showsthe ability of time-resolved photoelectron spectroscopy to reveal quantum mechanicalphenomena on sub-molecular length scales.Apparently, the positions of the maxima of the outer turns (E

b

⇡4.5 eV & Eb

⇡5.3 eV)shift to higher binding energies by about 50 meV in the first 7 oscillations. This

71


reflects a damping of the oscillations not only in total wave packet intensity, asproposed by Zewail and coworkers, but also a damping of the total energy, availablefor the oscillations. Therefore the maximum and minimum intra-molecular distancefor the wave packet’s outer and inner turn decrease.

7.4.1 Delay scans

In order to quantify some of the visible dynamic and periodic e↵ects and features in theTRPES maps, delay scans have been extracted, where the integrated photoelectronintensities in a defined energy window are plotted versus the delay time. In a firstapproximation, selecting an energy corresponds to selecting a distinguished intra-molecular distance, where a bypassing wave packet is registered as change in theintensity. A single Gaussian wave packet on a single potential curve yields a Gaussianshaped trace in the delay scan, just as in the original experiments on photo-excitedNaI molecules by the Zewail group, when a wave packet passes through the opticalcoupled region defined by the probe pulse energy (see the introduction of this chapteron p. 57 for a brief description of Zewail’s experiment).For the turns of the wave packet the re-occurrence time of the Gaussians directlycorresponds to the oscillation period ⌧osc, if inner and outer turn occur at separablebinding energies, hence, if the transformation between intra-molecular distance andbinding energy is unique. This is not the case for NaI as the binding energies atinner and outer turn overlap. However, the photoelectron intensity for the outer turnexceeds that of the inner turn by orders of magnitude, therefore the transformationbetween intra-molecular distance and binding energy becomes quasi-unique and dis-tinguishable for the outer turn and is observed as peaks separated by ⌧osc in a delayscan, see figure 7.10.(a,b).For a region in between the turns, the wave packet passes by two times in eachoscillation period, thus a doublet of peaks is observed separated by a time ⌧sep,which depends on the intra-molecular distance between the selected energy regionand the turns, see figure 7.10.(c–f). Again, this e↵ect is only determinable, if thedistance–energy relation is at least quasi-unique, hence, if the photoelectron intensityis dominant for one of the intra-molecular distances corresponding to the selectedbinding energy region, for example, for energy regions between crossing and outerturn in the TRPES map.

In those regions, where a quasi-unique relation between intra-molecular distance andbinding energy exists, a model for a delay scan y(t) is described in equation (7.4) as asum of Gaussian peaks with an exponential damping of the peak maxima (decay time⌧exp) to account for the decrease of photoelectron intensity due to the leakage of thewave packet through the crossing in each oscillation, yielding free neutral fragmentsNa and I for the asymptotic limit of infinite distances on the A potential.

72


y(t) = c + A⇥NX

i=1

exp

�4 ln 2

✓t � t

i

± �

wi

◆2

� ti

⌧exp

!⇥ ↵±

ti

= (i � 1) ⌧osc + t1 , � =⌧sep2

, wi

= w1 + (i � 1) dw

(7.4)

The positions ti

are defined via the time t1 of the wave packets first outer turn andthe number of bygone oscillations with period ⌧osc and correspond to the delay timefor the ith outer turn, whereas the ith inner turn is located at �tinner = i⌧osc. Thefirst outer turn should occur after a half period ⌧osc/2, therefore when fitting themodel to a given data set the di↵erence between the half period and parameter t1can be utilized to fine adjust the point of zero pump–probe delay time. The peakdoublets occurring for distances o↵ the turns are modeled at t = t

i

± ⌧sep/2, leftand right of the position of the outer turn. Therefore ⌧sep can be interpreted as thetime, the wave packet needs to evolve from the selected energy/distance region tothe outer turn and back. Furthermore, for an energy window corresponding to thecrossing, ⌧sep represents an estimate for the time the wave packet spends on the Xpotential in each oscillation. The cofactor ↵± is introduced to model the asymmetryof the peak intensities left and right of the outer turn, arising from broadening andre-sharpening of the molecular wave packet due to the antithetical influences on thedispersion of the wave packet by the Coulombic force field and the anharmonicity ofthe intra-molecular potentials [77]. The right peak intensity is modeled as a fraction↵+=q of the left peak intensity (↵�=1), which is defined by the exponential decay(⌧exp) of the initial amplitude A. Broadening of the wave packet is included in themodel by a linear increase of the peak width w

i

in each oscillation period by dw .The coe�cient of the quadratic term in the exponential, representing the Gaussian,is introduced, so that w

i

represents the FWHM of the peak. Possible background isaccounted for by the parameter c and the sum is restricted to N oscillations forcomputational reasons in order to ensure the converging of a fit of the model to adataset, which is intrinsically restricted to a finite number of recorded oscillations.

A set of delay scans for several excited state binding energies Eb

is presented infigure 7.10. The delay scans in (a,b) correspond to the outer turn of the wave packeton the ionic X state at (a) E

b

=4.4±0.05 eV (X↵,�) and (b) Eb

=5.35±0.05 eV (X �).Delay scans (c,d) show spectral intensities from X x transitions of the wave packetbetween crossing and outer turn for (c) E

b

=4.8±0.1 eV and (d) Eb

=5.6±0.1 eV and(e,f) show spectral intensities for the A–X crossing energy regions, (e) E

b

=5.1±0.1 eVfor transitions to final ↵, � ion states and (f) E

b

=5.9±0.1 eV for transitions to the �ion state.The main oscillation period is ⌧osc=1104±14 fs, resulting in an oscillation frequency of⌫osc=0.91±0.01THz and is in good agreement with ⌧osc=1090 fs, reported for a pumpwavelength of 321 nm in [71]. The exponential decay time, describing the damping

73


!1 0 1 2 3 4 5 6 70

2

4

6

8

10

t1

!osc

Eb = 4.4 ± 0.05 eV

delay (ps)

inte

nsi

ty (

a.u

.)

(a) outer turn, transition to ↵,�

!1 0 1 2 3 4 5 6 70

2

4

6

8

10

t1

!osc

Eb = 5.35 ± 0.05 eV

delay (ps)

inte

nsi

ty (

a.u

.)

(b) outer turn, transition to �

!1 0 1 2 3 4 5 6 70

2

4

6

8

10

t1

!osc

!sep

Eb = 4.8 ± 0.1 eV

delay (ps)

inte

nsi

ty (

a.u

.)

(c) in between, transition to ↵,�

!1 0 1 2 3 4 5 6 70

2

4

6

8

10

t1

!osc

!sep

Eb = 5.6 ± 0.1 eV

delay (ps)

inte

nsi

ty (

a.u

.)

(d) in between, transition to �

!1 0 1 2 3 4 5 6 70

2

4

6

8

10

t1

!osc

!sep

Eb = 5.1 ± 0.05 eV

delay (ps)

inte

nsi

ty (

a.u

.)

(e) crossing region, transition to ↵,�

!1 0 1 2 3 4 5 6 70

2

4

6

8

10

t1

!osc

!sep

Eb = 5.9 ± 0.1 eV

delay (ps)

inte

nsi

ty (

a.u

.)

(f) crossing region, transition to �

Figure 7.10: Delay scans for wave packet dynamics in the A–X potential trap at selectedexcited state binding energies E

b

as indicated in the plots: (a,b) Photoelectronspectral intensities vs. pump–probe delay at the outer turn on the ionic X state.(c,d) Spectral intensities from X x transitions of the wave packet betweencrossing and outer turn and (e,f) spectral intensities for the crossing energyregions. The separation of the peaks in the crossing region is ⌧ crosssep =710±9fs for both plots. The oscillation width is ⌧osc=1104±14 fs and therefore thetime of the first outer turn is t1=552 fs (red lines).

74


of the peak intensities for the outer turn is ⌧exp=4.4±0.2 ps in this experiment.The separation of the double peaks in delay scans 7.10.(e,f), taken for energy regionscorresponding to the A–X crossing, where the wave packet undergoes a transitionbetween the covalent A potential and the ionic X potential, is equal for both scansand amounts to ⌧ crosssep =710±10 fs. This time can be interpreted as the time the wavepacket spends beyond the crossing on the X potential in each oscillation. Hence, thepump–probe delay times corresponding to the crossings before and after outer turn ican be approximated as:

�tcrossi

= ti

±⌧ crosssep

2= (i � 1

2)⇥ 1104 fs± 355 fs (±17 fs). (7.5)

The separation times for delay scans (c,d), ⌧ (c)sep=588±8 fs and ⌧ (d)sep=491±6 fs, aresmaller than ⌧ crosssep , therefore one can conclude from the definition of ⌧sep that thesescans depict signals from intra-molecular distances between crossing and outer turn. Inprinciple, the energy windows for delay scans (c,d) also cover intra-molecular distancessmaller than the crossing, but due to the reduced photo-ionization e�ciency on theA potential, the quasi-unique distance–energy relation at this energy refers to themuch more intense signals observed for the wave packet on the X potential beyondthe crossing.The main oscillation period ⌧osc=1104 fs, introduced above, was estimated as averagefrom all presented delay scans. If the oscillation period is estimated separately forthe transitions to final ↵, � ion states, figure 7.10.(a,c,e) and for transitions to thefinal � ion state (b,d,f), one obtains: ⌧↵,�osc =(1115±8) fs and ⌧ �osc =(1093±12) fs,respectively. The di↵erence

�⌧ 320nmosc = ⌧↵,�osc � ⌧ �osc = 22± 14 fs (7.6)

points to di↵erent speeds with which the electronic cloud follows the nuclear motion asdelay scans (a,c,e) and (b,d,f) are taken for transitions to di↵erent final ion states and,hence, the delay scans and the corresponding oscillation periods represent ionizationof di↵erent molecular orbitals of the photo-excited NaI molecule and therefore di↵er-ent geometries of the underlying electron density distributions around the molecule.This finding is supported by a di↵erence in oscillation period of �⌧ 370nmosc =17±10 fs,deduced from TRPES data taken at 370 nm (3.35 eV) pump wavelength in an earliertest campaign on NaI, performed at the same laser setup, but with a magnetic bottleelectron spectrometer. Furthermore, the di↵erence in speed seems to increase withincreasing pump photon energy, hence, with increasing total available energy. How-ever, the relative uncertainties of the oscillation di↵erences are rather high and thevalues for both oscillation di↵erences overlap within their full uncertainty widths.Note that the visualization of such a di↵erence in the evolution speed of electronicwave packets corresponding to di↵erent molecular electronic orbitals is not observablein an experimental arrangement as used by Zewail and co-workers.A closer look to the delay scans additionally reveals that the oscillation period ⌧oscdecreases with time, as the peaks from the data set arise slightly before the fitted

75


peaks for longer delay times. This is in agreement, with the observed damping of thetotal energy available for the oscillations, on which ⌧osc is dependent (see figure 7.9and p.72 in section 7.4).

Delay scan map

The plain TRPES data, figure 7.9.(a), was normalized separately for each energychannel along the (vertical) delay axis, yielding a map of normalized delay scans,presented in figure 7.11. In this norm, a shift of photoelectron intensity along thebinding energy axis, corresponding to energy shifts of the molecular electronic statescan be visualized as reoccurring patterns even in energy regions, where the photo-electron intensity is very small. In contrast, the common method of normalizing thephotoelectron spectra separately for each delay along the (horizontal) energy axis, seefigure 7.9.(b), enables comparing the evolution of the relative intensity distribution,hence the evolution of the shape of the photoelectron spectra for each delay time andmaintains the relative photoelectron intensities for each spectrum, therefore patternsin the low intensity regions remain unrevealed.Figure 7.11.(a) shows a delay scan map from the data set recored for pump–probedelay times up to 7.7 ps with 53 fs delay steps and figure 7.11.(b) depicts the delayscan map of the data set for the first three oscillations up to 3.1 ps delay, recordedwith 27 fs delay steps. The white line is drawn at the binding energy of free Nafragments, 5.14 eV (see table 7.1), generated when the wave packet tunnels throughthe crossing. Furthermore, the line approximately separates the maps into regionsfor (A,X)↵,� on the left and (A,X)� on the right, or at least into regions, wherephotoelectrons from the respective transitions dominate the spectra.A footprint of the main sinusoidal oscillations of the electronic wave packet in theenergy landscape is nicely visible and spreading out of the wave packet to all Apotential curves is suggested for the inner turns (delay = 1.1 ps, 2.2 ps, etc). Newlight is shined on the broadening of the wave packet for the outer turn on the Xpotential. At their low binding energy sides, the sinusoidal traces for both excitedstate orbitals, (A,X)↵,� and (A,X)� transitions, are continued to the left by almoststraight lines with steepnesses increasing in each oscillation. This reflects that thehigh energy part of the dispersed molecular wave packet evolves further to longerdistances, ’uphill’ on the X potential (see figure 7.1), while the main part of the wavepacket is already evolving inwards again, down the X potential.In figure 7.11.(b), where smaller delay steps and longer integration times than in(a) were applied, the straight lines even connect with a periodical feature aroundEb

⇠4.1 eV. This binding energy is in the order of the energy needed for photo ioniza-tion of the molecular wave packet evolving around the crossing region of the higherexcited covalent B potential and the ionic X potential, hence for a (B,X)↵,� transition(see figure 7.1). This points to the high energy part of the dispersed wave packeton the outer turn tunneling through the B–X crossing and oscillating in the B–X po-tential trap. There are traces visible for the wave packet running up the X potential

76



4 4.5 5 5.5 6

!1

0

1

2

3

4

5

6

7

inte

nsi

ty (

a.u

.)

0

0.2

0.4

0.6

0.8

1


dela

y (p

s)

4 4.5 5 5.5 6

!0.5

0

0.5

1

1.5

2

2.5

3


8 8.5 9 9.5


8 8.5 9 9.5

(a) (b)

Figure 7.11: Delay scan map from normalization of the TRPES map for photo-excitedNaI molecules [figure 7.9.(a)] along the delay axis separately for each electronenergy channel. (a) shows a scan for pump–probe delay times up to 7.7 pswith 53 fs delay steps and (b) for the first three oscillations up to 3.1 ps,recorded with 27 fs delay steps. The excited state binding energy is givenin the top axis, whereas the bottom axis shows the total absorbed photonenergy. The white lines indicate the ionization potential of free, neutral Nafragments (E

b

=5.14 eV), generated when the wave packet tunnels through thecrossing and approximately separate the plots into energy regions for (A,X)↵,�

transitions (left) and (A,X)� transitions (right).

to lower binding energies only, but no traces are visible for the wave packet comingback to higher binding energies, therefore we conclude that the complete high energypart of the wave packet tunnels through the B–X crossing and dissociates on the Bpotential or further oscillates in the B–X potential trap. This represents a one-sidedcoupling of the wave packet dynamics for the two degrees of molecular excitation (ex-citation to the A–X or the B–X potential trap), where the higher excited state (B–Xtrap) seems to be fed by the high energy part of the wave packet in the A–X trap ineach oscillation and gives rise to a second oscillation period for the part of the wavepacket in the B–X trap. However, a second dissociation channel on the dissociative Bpotential, beyond the B–X crossing, is opened up and the photoelectron intensity forcontributions from the B–X potential strongly decrease in time, pointing to a highprobability for the wave packet to dissociate.

The trace at the very left in figure 7.11.(b) for Eb

<4 eV, visible in the measured energywindow already around a delay of 0.3 ps, therefore before the 1st outer turn, seems to

77


come from lower binding energies. This points to a finite probability for an excitationdirectly to the B state upon pumping by two pump photons (7.74 eV). Hence, the B-state potential is populated by parts of the wave packet already at �t =0. Pumpingwith two photons yields a molecular wave packet with enough energy to overcomethe X potential and the system dissociates to free ion fragments Na+ and I�. Inour experiment these fragments are not observable for positive delays, as for bothfragments, the lowest bound photoelectrons show up at binding energies outside therecorded energy window (E

b

=47.3 eV for Na+ and Eb

=3.06 eV for I�, see table 7.1).

0 1 2 3 4 5 6 70

2

4

6

8

10 Eb = 4.1 ± 0.1 eV

delay (ps)

inte

nsi

ty (

a.u

.)

(a) transition to ↵,�

0 1 2 3 4 5 6 70

2

4

6

8

10 Eb = 3.85 ± 0.05 eV

delay (ps)

inte

nsi

ty (

a.u

.)

(b) transition to ↵,�

Figure 7.12: Delay scans for transitions of the wave packet in the B–X potential trap to ↵,�

ion states. The re-occurrence periods of the peaks are (a) ⌧ (a)B–X=1410±10 fs,determined from the data set recorded up to 7.7 ps delay time and (b)

⌧ (b)B–X=1100±10 fs, determined from the data set recorded up to 3.1 ps delaytime.

The oscillation period in the B–X potential trap is longer than for the A–X trap, dueto the relative flatness of the B–X trap and because the B–X crossing is at longerintra-molecular distances. In order to determine the B–X oscillation period, the delayscans, depicted in figure 7.12 were analyzed. However, the expected longer oscillationperiod in the B–X potential trap is disturbed by a transfer of wave packet intensityto the higher excited potential at a repetition rate determined by the oscillationperiod in the A–X potential plus the time the high energy part of the A–X wavepacket needs to evolve from the outer A–X turn to the B–X crossing. Thus, there-occurrence periods of the peaks in the delay scans in figure 7.12 do not representtime scales for pure B–X oscillations, but represent time scales for a beating betweenthe molecular wave packet fractions transfered from A–X to B–X oscillations andthe wave packet fractions already evolving in the B–X potential. The period for thewave packet beating is ⌧ (a)B–X=1410±10 fs at E

b

=4.1±0.1 eV, determined from the

data set recorded up to 7.7 ps delay time and ⌧ (b)B–X=1100±10 fs at Eb

=3.85±0.05 eV,

determined from the data set recorded up to 3.1 ps delay time. ⌧ (a)B–X is larger thanthe period ⌧osc for the main oscillations in the A–X trap and the respective delay

78


scan, and points to the high energy part of the wave packet evolves further on theX potential beyond the main outer turn towards the B–X potential crossing. ⌧ (b)B–X

meets the period ⌧osc for the main oscillations, however it is not clear, if this is for adeeper reason or if the period of the beating for the respective binding energy regioncoincides with ⌧osc just by chance.In order to completely understand this beating and the determined re-occurrenceperiods, accurate quantum mechanical wave packet dynamics simulations are desired,including population and coupling of both potential traps, A–X and B–X.The delay scan maps in figure 7.11 show a similar situation on the right side of thewhite separator lines for transitions to final � ion states than discussed above fortransitions to final ↵, � ion states left of the separator lines. The coupling of the wavepacket in the A–X trap to the higher lying B–X potential trap is visible as a shiftingof parts of the X� photoelectron peak to lower binding energies. However, the (B,X)�

transitions from the wave packet oscillating in the B–X trap occur around the samephotoelectron energies than the highly intense (A,X)↵,� transitions and are thereforenot observable.To our knowledge, a transfer of photoelectron intensity and therefore wave packetamplitude between the first two excited states at the outer turn as observed here hasnever been reported to be visualized experimentally.

7.4.2 Photoelectron spectra – model vs. experiment

In a next step, the photoelectron spectra for distinguished distances from the modeledevolution, introduced in subsection 7.1.2, are compared to the measured spectra forassociated pump–probe delay times. Figure 7.13 depicts the modeled photoelectronspectra for the initial onset (brown), the 1st crossings (black) for outwards propagationof the wave packet to longer distances and for inwards propagation on the way backto the inner turn, the 1st and 2nd outer turn (green) and the first four inner turns(blue) in subplot (a) and the corresponding measured photoelectron spectra in subplot(b). All measured spectra are depicted for those experimental delay times, which areclosest to the predicted times for the respective situations. The left y-axis in subplot(b) states the relative maximum intensity of the experimental spectra, providing fora comparison intensity and statistical quality of the individual spectra. Gray shades inboth subplots indicate the lowest electron binding energy (ionization potential) for thefree, neutral, atomic Na fragments (E

b

=5.14 eV), which are generated in a moleculardissociation process when part of the wave packet tunnels through the A–X crossing.They approximately separate the plots into energy regions for (A,X)↵,� transitions(left) and (A,X)� transitions (right). The series of inner turns is plotted, to visualizean energy transfer within these spectra, observed for increasing oscillation numbers,as discussed below. The spectra for the outer turns and the crossings only show anintensity damping and spectral broadening due the broadening of the molecular wavepacket for increasing oscillation numbers, therefore these spectra are not explicitlyshown in figure 7.13.

79


The initial onset at �t =6 fs (brown) in figure 7.13 should correspond to the theground state spectrum of the NaI molecule as discussed earlier in subsection 7.1.3.The left peak doublet corresponding to the spin-orbit split ground state 2⇧ orbitalsis significantly shifted to higher binding energies, compared to our previous mea-surements presented in figure 7.5 and to values from the literature and calculations,whereas the 2⌃ peak is visible around the expected 9.1 eV, see table 7.2. The width ofthe cross-correlation function of pump and probe is around 100 fs, thus the spectrumaround �t =0 fs is perturbed by the early dynamics for short pump–probe time de-lays. These dynamics can lead to a shift of the photoelectron peaks to higher bindingenergies for positive and for negative delays, hence, signals from already dynamicallyshifted spectra for small positive and negative delays govern the measured spectrumand can explain a shift of the photoelectron peaks obtained for two-color two-photonionization.The black spectra for �t =f<5192 fs and �t =913 fs depict as the wave packet travelsthrough the crossing, evolving to long or short distances, respectively. In this region,where the nature of the molecular bond changes from covalent (A potential) to ionic(X potential), an intra-molecular electron transfer takes place transforming the sys-tem from covalent (Na I) to ionic (Na+ I�) or vice versa. Therefore, the outer electronlocalized around the Na atom is transfered to the I atom or vice versa. In the mod-eled spectrum, a minor peak as foot on the right of the main peak becomes visible(E

b

⇠4.85 eV), which arises from that part of the wave packet, which tunneled throughthe crossing and further propagates beyond on the A potential towards the asymp-totic limit of infinite intra-molecular distances yielding free neutral Na atoms withlowest electron binding energy (ionization potential) of E

b

=5.14 eV (gray shades).The broad peaks in the measured spectrum represent the modeled spectra for tran-sitions to ↵, � ion states (E

b

=4.0–5.2 eV) and the less intense transition to the final� ion state (E

b

=5.2–6.0 eV). They are smeared out due to the width of the cross-correlation function and the combined bandwidth of pump and probe (⇠100 fs and⇠0.1 eV, respectively), leading to an averaging of the wave packet around the cross-ing. Therefore a clear distinction of photoelectrons from the trapped wave packetbroadened and smeared out partly on the ionic X potential and partly on the covalentA potential and from electrons from the tunneled dissociating part of the wave packetis not possible, although a minor feature possibly arising from Na for long or infiniteintra-molecular distances is visible in the spectra at the left edge of the gray shadeindicating the atomic Na ionization potential.For the two depicted outer turns (green), at 539 fs and 1660 fs, model and measure-ment match. In the modeled spectra, on each side of the gray line, a major peakcorresponding to the turn of the wave packet and a minor feature, indicating thedissociating part of the wave packet are visible. The two intense peaks for ioniza-tion at the outer turn are well visible in the measured spectra. They are asymmetricwith a foot to the right, where the dissociating wave packet on the A potential isexpected. However, the ionization e�ciency on the A potential is much smaller thanon the X potential and therefore we conclude that the observed peak broadening

80


arises from the dispersed wave packet on the X potential being reflected at the outerbarrier, associated to the smallest binding energies within the peaks rather than fromdissociating parts of the wave packet outside the crossing.The blue spectra depict the first four inner turns (1110 fs, 2220 fs, 3321 fs and 4442 fs)and contain the most fascinating information, as the spreading out to the wholefamily of the spin-orbit split A potential curves is observed, as claimed in the modelintroduced in subsection 7.1.2. For all four depicted turns, the photoelectron intensityfrom the A↵ and A� transitions in the range from 4.0–5.1 eV dominates the spectraldistributions and the corresponding spectra are broadened to the full energy region, inwhich the photoelectron signals from the oscillating molecular wave packet are shiftingfor the respective molecular orbital. The first inner turn at 1110 fs shows a maximumfor the distribution at high binding energies around 5 eV and six distinct peaks andshoulders in the electron intensity distribution are observed down to ⇠4 eV, provingthe initial claim, that all A potential curves are populated when the wave packetreturns from the X potential through the crossing. This is additionally supported bythe high degree of qualitative agreement between the measured spectrum and themodeled spectrum shown for the A↵ and A� transitions. The model shows a broaddistribution built up from several peaks, as well. A spreading out of the wave packetis motivated even on the high binding energy side for A� transitions (E

b

& 5.2 eV),where a broad spectral socket is seen as well, but here the signal intensity is notsu�cient to distinguish individual peaks. Again, distinct features around the expectedphotoelectron energy for free Na atoms (gray shades) are visible in all spectra shownfor the inner turns. However, it is not possible from the spectra to clearly identifythese features as arising from Na atoms — they might as well arise from the wavepacket distributed on all potentials.Furthermore, the photoelectron spectra corresponding to the 2nd and later inner turnsshow an increasing population of the states corresponding to lower binding energies,which manifests in the center of mass of the spectral distributions shifting from rightto left. For the 3rd and 4th inner turn, the spectral intensity maximum is observedat the low binding energy end of the spectral distribution for binding energies evenlower than that for the outer turn. One could conclude from this finding that thewave packet more and more populates the highest lying of the A potential curvesin each oscillation, which yields the lowest binding energies at the inner turn (seealso figure 7.1). However, as mentioned before and visible in the TRPES maps infigure 7.9, the dispersed wave packet is broadened strong enough for longer delays,so that part of it is still or again evolving on the X potential during the inner turnof the main part of the wave packet. Furthermore, the photo-ionization cross-sectionfor ionization from the ionic X potential is by orders of magnitude higher than forionization from the covalent A potential curves, therefore already a small fraction ofionic nature in the molecular wave packet is amplified and becomes prominent in thephotoelectron distribution.This is not reflected in the modeled spectra, as the model does not include anyexchange of intensity between the potential curves. Such an exchange of wave packet

81


7.5 8 8.5 9 9.5

inital onset

1st crossing outwards

1st outer turn

1st crossing inwards

1st inner turn

2nd outer turn

2nd inner turn

3rd inner turn

4th inner turn


binding energy (eV)

4 4.5 5 5.5 6

(NaI)+ state: ! , " #

7.5 8 8.5 9 9.5

6 fs

192 fs

539 fs

913 fs

1100 fs

1660 fs

2220 fs

3321 fs

4442 fs


binding energy (eV)

4 4.5 5 5.5 6

(NaI)+ state: ! , " #

rela

tive

ma

xim

um

inte

nsi

ty

0.1

0.23

1

0.22

0.16

0.89

0.13

0.14

0.15

(a) simplified model calculation (b) experiment

Figure 7.13: Simplified model photoelectron spectra (a) compared to experimental photo-electron spectra (b) at distinguished intra-molecular distances and the closestassociated experimental pump–probe delay times. The respective situations tothe distances and the associated delay times are indicated in the very left andright axis, respectively. The left y-axis in (b) gives the relative maximum in-tensity for the experimental spectra and straight lines mark the zero intensitylevel for each spectrum. For both subplots, the excited state binding energy forpositive delays is shown in the top axis and the total absorbed photon energyin the bottom axis. The gray shades indicate the ionization potential of free,neutral Na fragments (E

b

=5.14 eV), generated when the wave packet tunnelsthrough the crossing and approximately separate the plots into energy regionsfor (A,X)↵,� transitions (left) and (A,X)� transitions (right).

82


intensity between the di↵erent potentials is not directly observable in a LIF experimentas performed by Zewail and coworkers, but only indirectly by a decrease in intensity ofthe fluorescence signal in each oscillation. Hence, this finding shows the power of time-resolved photoelectron spectroscopy, where known phenomena can be investigated ingreater detail and new previously ’invisible’ e↵ects in the dynamics of the electronicand nuclear coherent wave packet dynamics in molecules can be visualized.


In this chapter time-resolved photoelectron spectroscopy was applied to visualizemolecular wave packet dynamics in photo-excited NaI molecules by following theevolution of the valence electronic structure, arising from an oscillation of the intra-molecular distance of the atomic nuclei.The results from a TRPES experiment on NaI molecules for pumping with 3.87 eV(320 nm) photons and probing by ionization through 6.2 eV (200 nm) photons werepresented and discussed in detail.The main oscillation frequency of the wave packet, the delay times for the wave packetevolving through the potential crossing region, and around the inner and outer turnsand the time constant for the exponential damping of the wave packet oscillations,due to leakage through the crossing of the potentials, could be directly extractedfrom these delay scans. Furthermore, a spreading of the wave packet was observed.An indication was found, pointing to di↵erent speeds, with which the electronic wavepackets corresponding to di↵erent excited state molecular orbitals follow the nuclearwave packet motion, as the oscillation period ⌧osc appears to be �⌧ 320nmosc =22±14 fsshorter for the (A,X )� orbital than for the spin-orbit split (A,X )↵,� orbitals. Addi-tionally, this di↵erence in oscillation period seems to decrease for decreasing availableenergy, supported by �⌧ 370nmosc = 17±10 fs for a longer pump wavelength of 370 nm,determined from TRPES data measured in an earlier test campaign at the same lasersetup.Furthermore, a one-sided coupling of states corresponding to di↵erent degrees ofexcitation was visualized in a map of normalized delay scans and revealed that thehigh energy part of the wave packet oscillating in the A–X potential trap transfers tothe higher excitation state B–X potential trap, giving rise to a wave packet beatingin the B–X trap and opening a second decay channel for the system by dissociationto free fragments on the B potential, after tunneling through the B–X crossing. Acoupling back, hence wave packet intensity being transfered from the B–X trap tothe A–X trap was not observed.Simplified modeled photoelectron spectra for distinguished intra-molecular distances,corresponding to onset, crossing, inner and outer turns were compared to measuredspectra for closest respective pump–probe delay times. The spectra for the innerturns were the most fascinating and motivated, that the whole family of spin-orbitsplit A potential states take part in the coherent electronic and nuclear wave packet

83


oscillations in A–X potential trap, as initially proposed within a simplified modelfor photoelectron spectral evolution. A transfer of photoelectron intensity to lowerbinding energies was observed within the spectral distributions for subsequent innerturns. We conclude, that each time the wave packet evolves through the crossingtowards the inner turn, the higher lying spin-orbit split A potential states are moreand more populated.The observed spreading out to many of the A potential curves has not been re-ported previously and to our knowledge, the coupling of A–X and B–X wave packetoscillations as well as the time di↵erences for the oscillation periods of di↵erent elec-tronic orbitals was never observed experimentally before. In an experiment using laser-induced fluorescence, as in the pioneering work by the group around Zewail [3, 4], theobserved signal depends on the optical coupling of the investigated potential and ahigher lying fluorescing state and is measured as pump–probe delay time dependencescan of the fluorescence intensity. A two-dimensionality of the data set is introducedonly by varying the coupling probe wavelength, but as the coupling constant to thefluorescing state is di↵erent for the individual states under investigation (A potentialcurve family, B or X potential) and as it depends, for example, on the symmetry ofthe coupled states, the low- or non-coupling states will be shaded for all probe wave-lengths and at best be recognized as background to the main delay scan signal. Inphotoelectron spectroscopy, the measurement becomes intrinsically two-dimensionalin energy and time within one scan of all pump–probe delay times. Therefore it ispossible to determine contributions from all states at once for each delay step andthus none of the states are shaded, although one has to deal with di↵erent ionizationcross-sections for the individual molecular states.Our finding of the spreading out of the molecular wave packet from a photo-excitedNaI molecule to a whole family of spin-orbit split states, the coupling of the A–X andB–X potential traps and the observed oscillation period di↵erences are therefore anexample, where the technique of time-resolved photoelectron spectroscopy (TRPES)can reveal deeper insights in the dynamics of a photo-excited molecular wave packet,than absorption techniques as laser-induced fluorescence spectroscopy, where shadingof states and of information can occur. In contrast, the dynamic information fromfluorescence or absorption delay scans is contained in delay scans from the TRPESdata, as well, where the photoelectron intensity is plotted versus delay time for adefined photoelectron energy window.

Outlook

The VMI data additionally provides the first two asymmetry parameters �2 and �4,from which the photoelectron angular distributions for two-photon ionization andthus basic asymmetry properties of the underlying electronic structure can be deter-mined for each kinetic photoelectron energy at each delay step. The post processingand analysis of the angular resolved data is currently under way. The combination ofboth, energy and angular resolved photoelectron distributions can provide deeper in-

84


sight into the intra-molecular electron transfer around the crossing, where the natureof the molecular bond between the Na atom and the I atom undergoes a transitionform covalent kind (Na I) to ionic kind (Na+ I�) and an electron is transfered betweenboth atoms. It was reported in theoretical work by Arasaki et al. [84] that photoelec-tron angular distributions and their asymmetries can reveal at which of the atomsinside the molecule the electronic wave function was localized when the electron wasejected upon ionization. Therefore an accurate determination of the photoelectronangular distribution has the potential of revealing the degree of covalence or ionic-ity, respectively, at each photoelectron energy, allowing for a deeper distinction ofthe origin of the individual features in the photoelectron distributions. Moreover, thiscan enable the determination of the time scale for the intra-molecular exchange of avalence electron in the charge transfer process.During this campaign, we recorded electron and ion time-of-flight pump–probe datafor a series of pump wavelengths in the range of �

pmp

=320–370 nm (3.87–3.35 eV)at the same experimental setup. The dataset is currently under analysis. Combiningelectron and ion data can reveal more details about the dynamics of the total molec-ular wave packet and correlate the time-resolved intensity of the ion species Na+ and(NaI)+ with respective features in the TRPES maps. Furthermore, the analysis of thevariation of characteristic times, i.e. the oscillation period ⌧osc, the separation time ofthe wave packet appearing at the crossing ⌧ crosssep and the di↵erence in oscillation pe-riod �⌧osc, observed for the molecular orbitals corresponding to (A,X)↵,� and (A,X)�

transitions, respectively, can shine new light on the understanding of the moleculardynamics in photo-excited NaI molecules and on the understanding of photo-excitedmolecular wave packet dynamics in general.To our knowledge quantum dynamics simulations of the electronic and nuclear wavepacket dynamics in photo-excited NaI molecules, presented in this chapter, with in-clusion of all spin-orbit split A and B potential curves has not been carried out yet. Acomparison of the experimental data with an accurate simulation is highly desirableand can provide for deeper insights into the details of the dynamics observed in theexperiment. It would be thrilling to see, if state-of-the-art theoretical and computa-tional methods can reproduce the di↵erence in oscillation period �⌧osc. Furthermorequantum dynamics simulation can help to understand the dynamics of the couplingof the wave packets in the A–X and B–X potential traps. Hans O. Karlsson (Upp-sala University, Sweden) is currently working on a quantum mechanical wave packetdynamics simulation remodeling our TRPES experiment. Preliminary results with-out inclusion of the A potential splitting look very promising and yield qualitativelyaccurate spectra, as for example previously reported in [84]. However, the accurateinclusion of the spin-orbit splitting of the A potential curves and the coupling to thehigher excited B state is non-trivial and the work is still under progress.Controlling natures elementary reactions, such as electron transfer in molecular bondsis an ultimate goal of modern science. Therefore, a next experimental step should beto perform a three pulse experiment, where an additional third laser pulse at individualtime delay is used to control the molecular dynamics in the NaI molecule. For example

85


one could control the branching ratio for production of ground state I (2P3/2) or excitedstate I⇤ (2P1/2) due to the wave packet leakage in each oscillation as proposed intheoretical work by Hosseini et al. [85]. This corresponds to controlling, which of thepotential crossings A–X or B–X is preferred for tunnel ionization through the crossingand subsequent dissociation on either the A or B potential, respectively. Furthermore,it would be interesting to investigate if it is possible to control the dynamics aroundthe crossing and hence the inter-atomic electron transfer, for example, in a way thatalmost the complete wave packet tunnels through the crossing, therefore forcing thesystem to dissociate and e↵ectively influencing the damping time constant observedin the delay scans.


The presented campaign on the electronic and nuclear wave packet dynamics in NaImolecules was carried out in a collaboration with the Max-Born Institute (MBI),Berlin, Germany and Lund University, Sweden. The members in this collaboration arelisted below, first grouped by their a�liations and second sorted alphabetically.The measurements were performed at the femtosecond laser laboratory at MBI. Theextraction of the photoelectron kinetic energy distributions from the raw VMI imageswas performed by Linnea Rading and Per Johnsson. Further analysis of the experimen-tal data as presented here was performed by the author of this thesis, Torsten Leitner.The data for the theoretical intra-molecular potentials and the expected binding en-ergies were calculated by Michael Odelius, but the modeled spectral evolution wassimulated and all plots were created by the author himself. Philippe Wernet supervisedthe whole project.

Experiment:

Franziska Buchner, Andrea Lubcke, Arnaud Rouzee, Marc Vrakking – Max-Born In-stitute, Berlin, Germany

Per Johnsson, Linnea Rading – Lund University, Sweden

Torsten Leitner, Philippe Wernet – Helmholtz-Zentrum Berlin, Germany

Theory:

Michael Odelius – Stockholm University, Sweden

Hans O. Karlsson – Angstrom Laboratory, Uppsala University, Sweden

86

8 Transient Electronic Structures inPhoto-Dissociation of Fe(CO)5

It is well known that a CO group is eliminated in metal carbonyl compounds uponUV photolysis [100]. However, the precise nature of the elimination and especiallythe electronic structure dynamics during this photo-dissociation are not yet fully un-derstood. For example, the story of characterizing Fe(CO)4 molecules created byelimination of one of the CO ligands of Fe(CO)5 (iron-pentacarbonyl) has been run-ning since more than 40 years now [101]. The open questions are partly due to thefact that the experimental methods mainly employed so far, such as time-resolvedion time of flight spectroscopy [102] are not unique in their interpretation. This isthe case as in these experiments already the pump pulse creates ions and becausethe same ions arise from the various species during the decay sequence. The datapresented here are the first to characterize dynamics of the electronic structure of theintermediates. They can be seen as complementary to the structural characterizationby time-resolved electron di↵raction [103].

Fe(CO)5⇤ Fe(CO)4 Fe(CO)3

CO CO

. 100 fs ⇠ 3.2 ps

Figure 8.1: The photo-dissociation sequence of gas-phase Fe(CO)⇤5 after excitation of aFe(CO)5 molecule by a UV photon. Two CO ligands are split o↵ on the way tostable Fe(CO)3.

The major time-scales involved in photo-dissociation of Fe(CO)5 in the gas phasehave been determined in an ultrafast pump–probe transient ionization ion time-of-flight experiment by Trushin et al. [102]. They found that after pumping with 267 nmphotons, two CO ligands are eliminated until the system has transformed to stableFe(CO)3. It is furthermore claimed that only the first CO ligand is eliminated photo-chemically within a time of 100 fs, whereas the elimination of the second CO ligandarises from relaxing dissociation of the vibrationally hot intermediate Fe(CO)4 to final,stable Fe(CO)3 within 3.2 ps. This dissociation sequence is sketched in figure 8.1.To our knowledge, transient photoelectron spectra have never been determined forFe(CO)5 photo-dissociation. This chapter presents the TRPES data on Fe(CO)5

87

8 Transient Electronic Structures in Photo-Dissociation of Fe(CO)5

photo-dissociation, measured in a campaign at the free electron laser FLASH in Ham-burg in April and May/June 2011. The main scope hereby is the extraction of timescales for characterizing the dynamics in the dissociation sequence and the disentan-glement of the TRPES data in order to obtain photoelectron spectra for the daughterproducts of Fe(CO)5, especially for the short lived intermediate Fe(CO)4.

8.1 Rate model

There are two general temporal behaviors in gas-phase dissociation of Fe(CO)5: astep function, describing species, created or destroyed upon pumping and an expo-nential decay function, describing the temporal evolution of unstable species. Thetemporal evolution of products created from decaying species can be expressed as lin-ear combinations of these two processes. For describing the real world, the evolutionfunctions have to be convolved with the cross-correlation function of the pump andprobe pulses to account for the finite time resolution in a real experiment.The general form of the convolution function for an impulse g(x) and a responseh(x) is described by the convolution integral:

f (t) =

tZ

�1

g(x)h(t � x) dx . (8.1)

The impulse g(x) corresponds to the cross-correlation function of pump and probepulses and is approximated as an area normalized Gaussian impulse with width w(FWHM):

g(x) =q

2 ln 2⇡w2 exp

��4 ln 2

w

2 x2�. (8.2)

This leads to a convolved function, describing the evolution for instantaneous creationof a stable species upon pumping, where the response is a simple step function:

h(x) = ✓(x) =

⇢1 x � 00 otherwise

=) fs

(t) = 12

⇣1 + erf

⇣2pln 2w

t⌘⌘

, (8.3)

with the error function erf(x). Instantaneous destruction of a species is described bya convolved step-down and reads 1 � f

s

(t). The response function for a decayingspecies is an exponential decay (lifetime ⌧ , decay constant ↵ = 1/⌧), multiplied by astep function ✓(x) to ensure that the decay mathematically starts at t=0 in order toachieve a physically meaningful description and to maintain causality. Its convolutionreads as:

h(x) = ✓(x) e�↵x

=) fd

(↵, t) = e�↵(t��) fs

(t � 2�) , (8.4)

with � = ↵w 2/(16 ln 2) = w 2/⌧(16 ln 2).

88

8.1 Rate model

From these mathematical considerations, a rate model can be formulated as a setof equations describing the time evolution N

x

(t) for the number of entities of allspecies occurring in the dissociation sequence of photo-excited Fe(CO)5, presentedin table 8.1.The rate model starts with Fe(CO)5 which is instantaneously transformed to highlyunstable, excited state Fe(CO)⇤5 upon pumping and a two-stage chain via Fe(CO)4 tostable Fe(CO)3 begins, where the total number of molecules of all Fe(CO)

x

specieshas to be conserved: X

x=5,5⇤,4,3

Nx

(t) = 1, 8 t (8.5)

The decay of the unstable species Fe(CO)⇤5 and Fe(CO)4 is characterized by theirlifetimes ⌧5⇤ and ⌧4 (or the respective decay constants ↵5⇤ and ↵4). In each decaystep, corresponding to a reduction of the number of ligands to the central Fe atom,a free CO molecule is created. The non-convolved equations and the correspondingconvolutions are listed in table 8.1 for each species.

species infinite time resolution finite resolution (convolved)

Fe(CO)5 N5(t) 1� ✓(t) 1� fs

(t)

Fe(CO)⇤5 N5⇤(t) ✓(t) e�↵5⇤ t fd

(↵5⇤ , t)

Fe(CO)4 N4(t) ✓(t)A (e�↵4 t � e�↵5⇤ t) A (fd

(↵4, t)� fd

(↵5⇤ , t))

Fe(CO)3 N3(t) 1� N5 � N5⇤ � N4 =

✓(t) [1� (1� A)e�↵5⇤ t � A e�↵4 t ] fs

(t)� (1� A)fd

(↵5⇤ , t)� A fd

(↵4, t)

CO Nco

(t) (1� N5 � N5⇤) + N3 =

✓(t) [2� (2� A)e�↵5⇤ t � A e�↵4 t ] 2 fs

(t)� (2� A)fd

(↵5⇤ , t)� A fd

(↵4, t)

↵x

= 1/⌧x

, A = ↵5⇤/(↵5⇤ � ↵4)

Table 8.1: Rate model equations for the Fe(CO)5 photo-dissociation sequence. Note thatA ⇡ 1 for the decay times ⌧5⇤⇡100 fs and ⌧4⇡3.2 ps reported in [102].

Figure 8.2 shows the evolution of the species following the rate model equationsfor initial photo-excitation of all Fe(CO)5 molecules in the sample, where a cross-correlation width of w= 400 fs (FWHM), as approximately available (±200 fs) in ourexperiment at FLASH and decay times ⌧5⇤=100 fs and ⌧4=3.2 ps, reported in [102],are assumed. The model plot shows that the fast decaying species Fe(CO)⇤5 (lightblue trace) never reaches more than about 20% of relative content and vanishes veryrapidly and will thus hardly be observable with our limited time resolution.Furthermore, the experiment described in the following is based on photoelectronspectroscopy, where complex photoelectron spectra are measured for each time delay,which are a mix of the overlapping individual spectra from all species and therefore

89


!1 0 1 2 3 4 5 6 7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

delay (ps)

rela

tive c

onte

nt

Fe(CO)5Fe(CO)5*Fe(CO)4Fe(CO)30.5*CO

Figure 8.2: Rate model for Fe(CO)5 photo-dissociation for a cross-correlation width ofw= 400 fs (FWHM), as available in the present experiment and decay times⌧5⇤=100 fs and ⌧4=3.2 ps, reported in [102]. The (brown) trace, describing theproduction of free CO molecules is multiplied by 0.5 for better visualization, astwo CO molecules are created during the dissociation sequence, leading to amaximum relative content of 2.

hard to disentangle, as the photoelectron peaks, especially for the Fe(CO)x

moleculeslie closely next to each other. Additionally, not all Fe(CO)5 molecules will be photo-excited, yielding a strong background in the signal from these unpumped molecules.Therefore, delay scan traces extracted for defined photoelectron energy windows fromthe experimental data will be a weighted superposition of the traces for all speciesdepicted in figure 8.2 and listed in table 8.1. The general form of a delay scan tracefrom our experiment reads:

fgeneral(c0, cs , c4, c5⇤ ,↵4,↵5⇤ ,w , t) = c0+cs

fs

(t)+c4fd(↵4, t)+c5⇤fd(↵5⇤ , t) , (8.6)

depending on a total of 7 parameters: the width w of the pump–probe cross-correlation,↵4 and ↵5⇤ (or the respective lifetimes ⌧

x

) characterizing the decay steps and the pa-rameters c0, cs , c4, c5⇤ 2 R describing a constant background and the weights of thesuperposition.The very fast first decay step from excited Fe(CO)⇤5 to Fe(CO)4 will hardly be ob-servable in a superposed delay scan trace extracted from our limited time resolutionexperimental data, as its contributions vanish very fast and as the relative contentdoes never exceed about 20%. Therefore the delay scan traces can be approximatelydescribed by only 5 free parameters, enabling easier fitting of the model to experi-mental data sets:

fmix(c0, cs , c4,↵4,w , t) ⇡ c0 + cs

fs

(t) + c4fd(↵4, t) . (8.7)

90

8.2 Experiment

However, this approximated fit function is still not unique to a high degree, meaningthat di↵erent sets of fit parameters can yield almost equal delay traces, with di↵er-ent mixing parameters c

x

and time scales ↵4 and w . Thus, not all fit results givereasonable values for any delay scan trace and one always has to be careful aboutwhat is fitted, especially when extracting time scales for the cross-correlation widthw and the decay constant ↵4 from the data. Furthermore, in time-resolved pump–probe photoelectron spectroscopy, some of the photoelectron peaks undergo dynamicenergy shifts, therefore not only the decay of a species, but as well the shift of thecorresponding photoelectron peak(s) out of or into the respective delay scan energywindow influence and alter the time scales estimated from a fit of the delay scantrace. This shifting of photoelectron peaks relative to the selected energy windowcorresponds to a non-linear and unknown time-dependence of the mixing parameterscx

in equation (8.7). This can result in widened fitted cross-correlation widths w andshifted fitted values for the position of �t=0 along the delay axis. Additionally takinginto account the arguments given above, one sees that the mixing parameters do notevidently correlate with the real amount of contributions from the individual speciesin the spectra, but are just a set of motivated, but still artificial model parameters.However, for carefully selected energy regions, where one is aware of the dynamicsin the spectra or at best where contributions from one electronic state of one of thespecies dominates the photoelectron spectrum, it is possible to determine time scales,which characterize the dynamic processes happening in Fe(CO)5 photo-dissociation.

With four parameters I can fit an elephant,and with five I can make him wiggle his trunk.

John von Neumann

8.2 Experiment

The experimental setup used at FLASH is described in detail in chapter 5. In brief:An experimental chamber, equipped with a magnetic bottle electron spectrometer wasmounted to the PG2 beamline at FLASH. The monochromator unit in the beamlinewas tuned to 123 eV photon energy (10.1 nm) and 0.1 eV bandpass, resulting inmonochromatized probe pulses fluctuating in the range from approximately a fewtens of nJ to µJ pulses and a focal spot size of about 280 µm in horizontal and 400µm in vertical direction at the interaction region. The third harmonic of a Ti:Sapphirelaser system is generated, delivering 267 nm pump pulses to the interaction zone witha focal spot size of about 400 µm in diameter, shorter than 80 fs FWHM in durationand attenuated to 25 µJ pulse energy. A delay stage in the laser path allows for varyingthe relative arrival time of pump and probe pulses over a total range of 9 ns. A metaltube just underneath the interaction volume serves as sample gas inlet. For detectingphotoelectrons, a magnetic bottle time-of-flight electron spectrometer is installed.The photoelectron time-of-flight distributions are determined from a micro channel

91


plate (MCP) in current mode and stored to the FLASH data storage system via anetwork connected 10 bit digitizer system. The electron spectrometer was calibratedwith the additionally recorded photoelectron spectrum from pure CO molecules (seefigure 8.4). The binding energies for the CO photoelectron peaks are: 5� – 14.01 eV,1⇡ – 16.91 eV and 4� – 19.72 eV [59].The intensity of the FLASH pulses is highly stochastic and can vary by orders ofmagnitude from shot to shot. Therefore, the photoelectron intensities for di↵erentdelays cannot be directly compared, even after time sorting (see chapter 5) andbinning of the data in time slots up to 200 fs wide (half the cross-correlation width).Hence, the data for each delay time slot has to be individually normalized. The mostphysical normalization is normalizing the photoelectron spectra to the incoming pulseintensity, but unfortunately, no shot-to-shot resolved pulse intensity data is availableafter the monochromator at the PG2 beamline at FLASH. Therefore an area normwas applied to the spectra for each time slot, where each spectrum is divided by itstotal sum along all photoelectron energies. This norm assumes, that the total intensityin the spectra is preserved for all delays. The area normalized data set will be furtherreferenced as Znorm.An approximate value for time zero (�t = 0) with an accuracy of ±500 fs couldbe determined from the experimental signal by stepwise comparing the photoelectronspectra for a series of nested delay time intervals on a LeCroy digital oscilloscope. Timezero could be further ascertained with an accuracy of ± 70 fs, by a fit of equation (8.7)to a delay scan (integrated photoelectron intensity vs. delay time) in a region ofinterest (ROI) of E

b

2 [12.2–13.2] eV, where the fastest feature in the normalizeddata set Znorm is observed [see also figure 8.4, ROI (2)]. The delay scan is depictedin figure 8.3. Furthermore, a cross-correlation width of w=400± 200 fs (FWHM) isextracted from the fit, arising from the pulse widths and from the relative timing jitterof the FEL (see chapter 5).

!3 !2 !1 0 1 2 3 4 5 6 7

0

0.2

0.4

0.6

0.8

1

delay (ps)

inte

nsi

ty (

a.u

.)

Figure 8.3: Integrated photoelectron intensity versus delay time for the fastest feature inthe TRPES data for E

b

2 [12.2–13.2] eV to determine �t = 0 (accuracy ±70fs) and to estimate the width of the pump–probe cross-correlation functionw = 400± 200 fs.

92

8.2 Experiment

8.2.1 Di↵erence spectra

The photoelectron spectrum for Fe(CO)5 was extracted by averaging the data for longnegative delays, Znorm(�t < -2 ps), and a TRPES map of di↵erence spectra D wasobtained by subtracting the Fe(CO)5 spectrum from the data set Znorm separately foreach delay time slot. Figure 8.4 gives an overview of the data recorded for the valenceregion up to E

b

=23 eV. The photoelectron spectra for pure Fe(CO)5, spectra frompure CO, separately recorded at the same setup and di↵erence spectra for selecteddelays are shown and labeled with the corresponding valence orbitals. The Fe(CO)5spectrum is plotted downwards for comparison with the negative contents in thedi↵erence spectra, visualizing the depletion of Fe(CO)5 in the interaction zone. Ashift to lower binding energies is suggested for the Fe 3d peaks at binding energiesbelow ⇠10 eV, and the creation of CO molecules during the dissociation sequence isclearly observed in the spectra around 14.0 eV, 16.9 eV and 19.7 eV.

difference spectra

inte

nsi

ty

(1) (3)(2)

+6.0 ps+3.0 ps+1.0 ps+0.0 ps!3.0 ps

CO

5! 1" 4!

6 8 10 12 14 16 18 20 22

Fe(CO)5

Fe 3dCO (!+")

CO (!+")

binding energy (eV)

Figure 8.4: Comparison of Fe(CO)5 and CO photoelectron spectra with pump–probedi↵erence spectra for the valence energy region and selected delays. (see textfor a description)

93


Further more all ROIs, referenced in this chapter are indicated in the plot: (1) thescaling ROI, see next subsection 8.2.2, (2) the fastest dynamic feature for calculatingthe cross-correlation function, see above, and (3) the ROI for characterizing thecreation of CO and at the same time the decay of transient Fe(CO)4, see section 8.3.

8.2.2 Relative amount of non-excited Fe(CO)5 in the data

For determination of the relative amount of photo-excited Fe(CO)5 molecules in theinteraction volume, the integrated photoelectron intensity in a scaling ROI E

b

2 [9.7–10.0] eV was extracted versus delay time. The scaling ROI was chosen at a position inthe Fe(CO)5 photoelectron spectrum, where the corresponding Fe 3d photoelectronpeak splits to lower and higher binding energies and therefore the signal in the scalingROI disappears as Fe(CO)5 disappears [see also figure 8.4, ROI (1) and figure 8.7, ROI(1)]. Figure 8.5 shows the delay scan with a fit of equation (8.7) and visualizes the timeevolution of the relative content of non-excited Fe(CO)5 molecules in the interactionvolume. The plot clearly shows that within 1 ps all initially pumped Fe(CO)5 moleculeshave dissociated to daughter products. Note that for this energy region the widthof the negative step arises from the ultrafast (sub time resolution) Fe(CO)⇤5 decayperturbed by the experimental time resolution.

!3 !2 !1 0 1 2 3 4 5 6 792

94

96

98

100

102

delay (ps)

rela

tive F

e(C

O) 5

conte

nt (%

)

Figure 8.5: Depletion of the content of signals from non-excited Fe(CO)5 molecules in thedata set. Approximately 6% of the Fe(CO)5 molecules in the interaction regionwere pumped in this experiment.

The normalized spectrum of Fe(CO)5 is scaled according to the fit function andsubtracted from the normalized TRPES data set Znorm for each delay time, yieldinga new data set of scaled di↵erences Dscaled, free of contributions from Fe(CO)5,enabling an approximation of photoelectron spectra for the transient Fe(CO)4 andstable Fe(CO)3 daughter products, presented in section 8.4, figures 8.7 and 8.8.Additionally, the scaling ROI could be manually optimized by ensuring that there areno negative di↵erences in Dscaled.A note on the scaling region of interest: The borders for the scaling ROI wheremanually varied throughout the whole negative di↵erence regions in the unscaled

94

8.3 Decay of transient Fe(CO)4

and creation of free CO

di↵erences D, figure 8.4. The finally chosen ROI was the only one, where a scalecould be extracted without yielding negative di↵erences in the scaled di↵erence mapDscaled. As this ROI is not at the edge of the corresponding Fe 3d peak in the Fe(CO)5spectrum, see figure 8.4, ROI (1), but in between, we can conclude that the Fe 3dpeak splits to both sides for the daughter products of Fe(CO)5. Furthermore, the scaleis perturbed by the edges of the new peaks, reaching into the scaling ROI window,which leads to a slight overcompensation for non-excited Fe(CO)5 in the spectrawithin the strength of this perturbation.

8.3 Decay of transient Fe(CO)4 and creation offree CO

The dynamics of the dissociation sequence can be identified and characterized fromthe photoelectron fingerprint of the CO molecules, created in each decay step. Fig-ure 8.6 shows a fit of equation (8.7) to a delay scan extracted from the data forEb

2 [16.6–17.3] eV, where the strongest CO peak occurs in the valence band photo-electron spectra [see also figure 8.4, ROI (3)], and at the same time, there is no oronly very few signal of any of the Fe(CO)

x

species expected, as this energy regionlies in a gap in the photoelectron spectrum of Fe(CO)5. This gap even increases forthe daughter species.

!3 !2 !1 0 1 2 3 4 5 6 7

0

0.2

0.4

0.6

0.8

1

delay (ps)

inte

nsi

ty (

a.u

.)

Figure 8.6: Integrated photoelectron intensity versus delay time for Eb

2 [16.6–17.3] eV,describing the dynamics of the dissociation sequence with the help of a finger-print in the photoelectron spectra from the CO molecules, created in each decaystep.

The initial creation of CO molecules upon pumping is reflected in the initial step inthe data, as motivated by the rate model, figure 8.2. This process is much faster thanthe time resolution, therefore no reliable time scale can be determined from the stepfor the formation of the first CO molecule created during the transition of photo-excited Fe(CO)⇤5 to transient Fe(CO)4. The life time for the exponential growth ofCO molecules corresponds to the exponential decay time of the transient Fe(CO)4

95


molecules, which decay to stable Fe(CO)3, producing the second CO molecule. Thisdecay time is determined from the fit to ⌧4=3.2± 1.7 ps, hence nicely matching the3.2 ps determined from ultrafast pump–probe transient ionization ion time-of-flightexperiments, previously reported by Trushin et al. [102].

8.4 Transient photoelectron spectra

Figure 8.7 compares, the Fe(CO)5 spectrum, extracted for �t < -2 ps (blue) and av-eraged scaled di↵erence spectra, estimated from Dscaled for �t=1±0.2 ps, dominatedby photoelectrons from transient Fe(CO)4 (green) and for �t=6.5±0.2 ps, wherethe spectrum is dominated by photoelectrons from Fe(CO)3 (yellow). For compari-son, the photoelectron spectrum from free CO molecules (gray), recorded during thesame campaign is plotted in the top panel. A shifting and splitting of the Fe 3d peaksis visible for binding energies below ⇠12 eV and the growth of photoelectron contentfrom CO molecules is observed around 14.0 eV, 16.9 eV and 19.7 eV.

6 8 10 12 14 16 18 20 22

Fe(CO)5

Fe(CO)4 + CO

Fe(CO)3 + CO

CO

binding energy (eV)

inte

nsi

ty

scaling ROI

Fe 3d

CO (!+")

# t < !2 ps

# t = 1.0 ± 0.2 ps

# t = 6.5 ± 0.2 ps

Figure 8.7: Scaled di↵erence photoelectron spectra at selected delays for initial Fe(CO)5,transient Fe(CO)4 and stable Fe(CO)3 molecules. (see text for a detailed de-scription)

96

8.4 Transient photoelectron spectra

In order to obtain transient photoelectron spectra for the daughter species Fe(CO)4and Fe(CO)3, the spectra for free CO molecules have to be subtracted from the scaleddi↵erences Dscaled for estimating a data set DCOfree of transient, Fe(CO)x only photo-electron distributions. The general time dependence of the amount of photoelectronsfrom CO molecules has been determined in section 8.3, figure 8.6. Furthermore, theCO spectrum has to be multiplied by an additional delay time independent scaleto account for di↵erent photo-ionization e�ciencies for probing of CO or Fe(CO)

x

molecules, respectively, before subtracting it, scaled by the fit function for CO cre-ation (figure 8.6), separately for each delay time from the scaled di↵erences Dscaled,yielding a data set DCOfree, free of contributions from CO molecules and non-excitedFe(CO)5 and therefore containing the evolution of the transient photoelectron spec-tra during the photo-dissociation of Fe(CO)5 to Fe(CO)3. However, as the additionalscaling due to the individual photo-ionization e�ciency is not determinable from thedata, its value relies on an educated guess. The main criterion for this guess is tomaintain a comparable background signal for binding energies corresponding to theright most CO peak and higher, hence for E

b

& 19 eV, as no signals arising from anyof the Fe(CO)

x

species are expected for these photoelectron energies.Figure 8.8 gives an overview of the resulting transient spectra for Fe(CO)4 (green),estimated from DCOfree for �t=1±0.2 ps and Fe(CO)3 (yellow), �t=6.5±0.2 ps, andcompares them to the Fe(CO)5 spectrum (blue), extracted for �t < -2 ps and thespectrum from free CO molecules (gray).In figure 8.9, calculated photoelectron spectra are shown for Fe(CO)5, Fe(CO)4 andFe(CO)3 molecules. The spectra were calculated by Michael Odelius (Stockholm Uni-versity, Sweden) [94] with a partial density of states (PDOS) numerical method. Thismethod does not deliver accurate absolute binding energies, therefore the calculatedspectra where shifted such that the lowest peaks from experiment and calculationmatch. Furthermore, a comparison with the measured spectra shows, that the rela-tive peak distances are not reproduced, as well.In both, the measured and the calculated spectra, a shifting of the photoelectron peaksto lower binding energies is observed for each elimination of a CO ligand and the grossshape of the calculated spectra matches the experimental data. The outermost Fe3d peak, at lowest binding energy undergoes a shift from ⇠8.1 eV for Fe(CO)5 to⇠7.6 eV for Fe(CO)4 and Fe(CO)3 and an additional feature at around 10.6 eV showsup for Fe(CO)4 and Fe(CO)3 in the measurement, as the right peak of the Fe 3dpeak doublet at ⇠9.6 eV splits into two peaks at lower and higher binding energies of⇠8.5 eV and ⇠10.6 eV, respectively, after the elimination of the first CO ligand. Thecalculated spectra suggest this splitting as well, but with both new peaks shifted tolower binding energies, with respect to the Fe(CO)5 spectrum.The method of subtracting non-photo-excited Fe(CO)5 from the spectra by using ascaling ROI and furthermore, the subtraction of CO by using a scale obtained froman educated guess is not fully reliable, especially in the region for E

b

>12 eV, wherecontributions from bound and free CO molecules dominate the spectra. Thereforethe spectra for Fe(CO)4 and Fe(CO)3 for this energy region, depicted in figure 8.8,

97


6 8 10 12 14 16 18 20 22

Fe(CO)5

Fe(CO)4

Fe(CO)3

CO

binding energy (eV)

inte

nsi

ty

Fe 3d

CO (!+")

# t < !2 ps

# t = 1 ± 0.2 ps

# t = 6.5 ± 0.2 ps

Figure 8.8: Suggested valence photoelectron spectra for the dominating Fe(CO)x

speciesat selected delays. Scaled CO spectra were additionally subtracted from thescaled di↵erences Dscaled. (see text for a detailed description)

6 8 10 12 14 16 18 20 22

Fe(CO)3

Fe(CO)4

Fe(CO)5

Fe 3d CO (!+")

binding energy (eV)

inte

nsi

ty

Figure 8.9: Calculated valence photoelectron spectra for Fe(CO)5, Fe(CO)4 and Fe(CO)3.

98


show structures and reveal a reshu✏ing, shifting, creation and destruction of statesand suggest a gross shape for the valence spectra, but are neither good to determinereliable values for the peak shifts, nor to reliably determine how many new states arewhere visible in the spectra.The variations in the valence electron spectra show as electronic states in the valenceelectronic structure shift and new states are generated under the influence of a chang-ing ligand field due to elimination of CO ligands, hence breaking of molecular bondsand therefore transfer of charge between the CO ligands and the central Fe atomduring the photo-dissociation process. Furthermore, the peak shifts can reveal infor-mation about the degree of localization of the molecular orbitals and where they arelocalized. In order to accurately disentangle the spectra for the participating Fe(CO)

x

species and the CO molecules and in order to better understand the dynamics ob-served, accurate molecular dynamics simulations are desired for comparing theory andexperiment. For example, if a numerical method can reproduce the measured Fe(CO)5photoelectron spectra with high accuracy, this method most likely leads to accuratespectra for the daughter species and the resulting spectra can be utilized to improvethe educated guess for CO subtraction, as well as to extract a more accurate scalefor subtraction of non-excited Fe(CO)5 content in the data set.Furthermore, the area normalization, applied to the acquired spectra leads to pertur-bations, which can only be overcome by either recording spectra for as much timeas needed to overcome the highly fluctuating nature of the FLASH pulses by sheerstatistical averaging or by measuring the incoming intensity of FLASH for each shot,hence enabling the reliable intensity normalization.However, the presented spectra already show the power of TRPES for determiningphotoelectron spectra of transient species in ultrafast photo-dissociation processesin complex molecules of in this case 11 atoms, but it is as well illustrated that themethods for data acquisition , the light source and the on-line determination of thelight’s properties are still to be improved.


This chapter presented a scheme for disentangling complex TRPES data from UVphoto-dissociation of Fe(CO)5. Photo-excited Fe(CO)⇤5 in gas-phase decays in twosteps to Fe(CO)3 via intermediate Fe(CO)4. In each decay step, a CO ligand is splito↵, therefore the recorded data set contains contributions from the Fe(CO)

x

species,as well as from the created free CO molecules. Furthermore, only a minor fraction ofthe sample gas (⇠6%) was photo-excited upon pumping in this experiment.In order to extract the main time characteristic of the dissociation sequence, delayscans were extracted for selected photoelectron energy regions and fitted according toa fit function motivated by a rate model, describing the decay sequence. Due to thelimited time resolution in the experiment, no reliable time scale for the eliminationof the first CO ligand could be estimated, but the time constant for the second

99


CO ligand elimination, related to the decay time for the transition from Fe(CO)4to Fe(CO)3 was determined to 3.2±1.7 ps, in agreement with previously publishedresults [102]. Furthermore, a scaling region of interest was identified, describing thetime evolution of non-excited Fe(CO)5 molecules in the data and therefore enablingsubtraction of content from non-excited sample molecules from the recorded data set– the first step to transient photoelectron spectra. In a second step, the contributionsfrom the created free CO molecules were subtracted from the TRPES data, yieldingtransient Fe(CO)4 and final, stable Fe(CO)3 photoelectron spectra. The gross shapeand qualitative dynamics of these transient spectra are in reasonable agreement withtheoretical spectra calculated with a PDOS method. A shifting of the valence peaksand creation of a new peak for the Fe 3d region was identified and furthermore,a shifting and creation of various new peaks during the dissociation sequence wasobserved for the CO (�+⇡) orbital region. However, for subtraction of the CO content,it was necessary to introduce an artificial scaling to the photoelectron spectra for freeCO molecules, only motivated by an educated guess. Therefore, no concrete numbersfor characterizing the dynamics in the orbitals corresponding to bound CO ligandswere extracted. Nevertheless, to our knowledge, this was the first time that Fe(CO)

x

especially Fe(CO)4 photoelectron spectra were determined experimentally.In order to improve the disentangling procedure, accurate state-of-the-art simulationsfor the photoelectron spectra of Fe(CO)5, Fe(CO)4 and Fe(CO)3 are desired. Knowing,what is expected from theory can provoke new ideas of how and where to lookin the data. Furthermore, these calculations might help to improve the subtractionprocedures on the way to transient, Fe(CO)

x

only spectra.

In general, it turned out that the intrinsic timing jitter of FLASH is to large toresolve processes as fast as 100 fs and below (see chapter 5). Additionally, the pulsesfrom FLASH underly an intrinsic spectral jitter, which at the PG2 beamline, uponmonochromatization, translates to a shot-to-shot jitter of the probe pulse intensityby several orders of magnitudes. Hence, the spectra for the individual pump–probedelay times have to be normalized before being compared. There is no shot-to-shotintensity measurement installed after the monochromator at the PG2 beamline atFLASH, thus the most physical, relative intensity preserving normalization of eachspectrum to the respective shot-to-shot intensity is not possible. Therefore, an areanormalization was applied to the spectra, scaling all spectra by their area and thusassuming that the total photoelectron intensity in the recorded photoelectron energywindow stays constant for all delay times. Hence, another perturbation is introducedby the lack of a suitable normalization scheme.

100



The presented campaign on transient electronic structures during photo-dissociationof Fe(CO)5 was carried out in a larger collaboration at the free-electron laser facilityFLASH at the DESY site in Hamburg, Germany. The members in this collaborationare listed below, first grouped by their a�liations and second sorted alphabetically.The project was lead and the evaluation of the experimental data was performedby the author of this thesis, Torsten Leitner. The theoretical photoelectron spectrawere calculated and provided by Michael Odelius. Philippe Wernet supervised theproject. All other members of the collaboration greatly supported the campaign duringplanning and performing the experiment and in numerous discussions thereafter.

Members of the Collaboration:

Tommaso Mazza, Michael Meyer, Paul Radcli↵e – European XFEL, Hamburg, Ger-many

Stefan Dusterer – DESY, Hamburg, Germany

Michael Odelius – Stockholm University, Sweden

Martin Beye, Alexander Fohlisch, Kristjan Kunnus, Torsten Leitner, Simon Schreck,Philippe Wernet – Helmholtz-Zentrum Berlin, Germany

101

9 Conclusion

The main objective of this thesis was to visualize ultrafast processes in molecules bymeans of time-resolved photoelectron spectroscopy (TRPES) and contribute to thegrand challenge of understanding chemistry on a fundamental level.

“Methods and Instruments” used for performing TRPES experiments were intro-duced in Part I. Especially the implementation and operation of the HHG basedTRPES setup at HZB was explained in detail. The HHG source provides monochro-matized VUV pulses of 120 fs duration and up to 30 eV photon energy for probing.Furthermore, the realization of a high-temperature sample evaporation source to en-able the investigation of the electronic dynamics in the gas-phase for a wider range ofmaterials, and two existing TRPES setups, at the Max-Born-Institute in Berlin andat the free electron laser FLASH in Hamburg have been presented. Schemes havebeen detailed for accurate timing in pump–probe experiments at FLASH, where thephoton pulses underly a large intrinsic shot-to-shot arrival time jitter.

In Part II, “Experiments”, three separate experimental campaigns on investigating theelectronic structures of molecules and the dynamics therein were presented: Polariza-tion dependence in two-color two-photon ionization (chapter 6), coherent nuclear andelectronic wave packet dynamics in photo-excited NaI molecules (chapter 7) and thedetermination of the transient electronic structures during photo-dissociation in thegas-phase of the metal-carbonyl Fe(CO)5 (chapter 8).In all three gas-phase experiments the power of TRPES for investigating moleculeson their fundamental time and length scales could be demonstrated.The polarization dependence in two-color two-photon ionization was linked directlyto the asymmetry of the electronic structure via the asymmetry parameter for pho-toelectron angular distributions, �2, as the main free parameter in a theoretical ap-proximation. The model is in good agreement for most of the experimental data. Thebreak down of the model when hitting a photo-absorption resonance points towardsnecessary extensions of the model and shows that there is still a lot to learn and un-derstand about two-photon ionization processes and their dependence on symmetryproperties.The experiment on the coherent wave packet oscillations in NaI, which have beenearlier investigated in great detail with femtosecond transition state spectroscopy bylaser-induced fluorescence by A. Zewail and coworkers [3, 4], showed that TRPESenables to reveal deeper insight, even for well investigated systems. The generaltime scales characterizing the oscillations have been extracted from the data and ahint, pointing to di↵erent evolution speeds for di↵erent molecular electron orbitals

103

9 Conclusion

was identified. Further, the coherent superposition of a single molecule on severalbranches of a spin-orbit split intra-molecular potential, corresponding to the moleculeco-existing in several intra-molecular distances, could be shown and a transfer ofmolecular wave packet population between two excitation levels of the NaI moleculewas clearly visualized. Hence, it was demonstrated how TRPES resolves electronicdynamics in molecules even on a scale, where quantum mechanical e↵ects do play animportant role.Finally, the results from a TRPES campaign at the free electron laser FLASH in Ham-burg on the step-wise photo-dissociation of a complexer molecule, Fe(CO)5, with atotal of 11 atoms were presented. After photo-excitation, the Fe(CO)5 molecules de-cay to the short-lived transient Fe(CO)4, which is vibrationally hot and decays within⇠3.2 ps to stable Fe(CO)3 molecules. In each decay step, one of the ligands is splitof and free CO molecules are created. The stepwise creation of CO molecules wasconfirmed with the time resolved photoelectron data and the lifetime of the Fe(CO)4intermediate was determined. Furthermore, the valence photoelectron distributions forinitial Fe(CO)5, transient Fe(CO)4 and final Fe(CO)3 molecules could be extractedfrom the data. To our knowledge, this was the first time that photoelectron distri-butions, for Fe(CO)4 and Fe(CO)3 were determined experimentally. However, it wasalso found that the achievable time resolution at FLASH is not su�cient for revealingthe very early transient dynamics occurring within ⇠100 fs, when the photo-excitedFe(CO)⇤5 molecules decay to Fe(CO)4 and a photo-induced breaking of the bondbetween the Fe center and one of the CO ligands takes place.

104

Bibliography

[1] A Report from the Basic Energy Sciences Advisory Committee (BESAC). “DirectingMatter and Energy: Five Challenges for Science and the Imagination”. http://

science.energy.gov/

~

/media/bes/besac/pdf/GC_rpt.pdf (2007).

[2] A. Stolow. “Femtosecond Time-Resolved Photoelectron Spectroscopy of PolyatomicMolecules”. Annu. Rev. Phys. Chem. 54, 89 (2003).

[3] M. J. Rosker, T. S. Rose, A. H. Zewail. “Femtosecond real-time dynamics ofphotofragment-trapping resonances on dissociative potential energy surfaces”. Chem.Phys. Lett. 146, 175 (1988).

[4] T. S. Rose, M. J. Rosker, A. H. Zewail. “Femtosecond real-time observation of wavepacket oscillations (resonance) in dissociation reactions”. J. Chem. Phys. 88, 6672(1988).

[5] A. L’Huillier, P. Balcou. “High-order harmonic generation in rare gases with a 1-ps1053-nm laser”. Phys. Rev. Lett. 70, 774 (1993).

[6] T. Brabec, F. Krausz. “Intense few-cycle laser fields: Frontiers of nonlinear optics”.Rev. Mod. Phys. 72, 545 (2000).

[7] F. Krausz, M. Ivanov. “Attosecond physics”. Rev. Mod. Phys. 81, 163 (2009).

[8] T. Pfeifer, C. Spielmann, G. Gerber. “Femtosecond x-ray science”. Rep. Prog. Phys.69, 443 (2006).

[9] T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn. “Theattosecond nonlinear optics of bright coherent X-ray generation”. Nat. Photon. 4,822 (2010).

[10] P. Wernet, M. Odelius, K. Godehusen, J. Gaudin, O. Schwarzkopf, W. Eber-hardt. “Real-Time Evolution of the Valence Electronic Structure in a DissociatingMolecule”. Phys. Rev. Lett. 103, 013001 (2009).

[11] Z.-H. Loh, S. R. Leone. “Ultrafast strong-field dissociative ionization dynamics ofCH2Br2 probed by femtosecond soft x-ray transient absorption spectroscopy”. J.Chem. Phys. 128, 204302 (2008).

[12] E. Gagnon, P. Ranitovic, X.-M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn,A. S. Sandhu. “Soft X-ray-Driven Femtosecond Molecular Dynamics”. Science 317,1374 (2007).

105

http://science.energy.gov/~/media/bes/besac/pdf/GC_rpt.pdf

http://science.energy.gov/~/media/bes/besac/pdf/GC_rpt.pdf

Bibliography

[13] L. Miaja-Avila, G. Saatho↵, S. Mathias, J. Yin, C. La-O-Vorakiat, M. Bauer,M. Aeschlimann, M. M. Murnane, H. C. Kapteyn. “Direct Measurement of Core-Level Relaxation Dynamics on a Surface-Adsorbate System”. Phys. Rev. Lett. 101,046101 (2008).

[14] C. La-O-Vorakiat, M. Siemens, M. M. Murnane, et al. “Ultrafast DemagnetizationDynamics at the M-Edges of Magnetic Elements Observed Using a Tabletop High-Harmonic Soft X-Ray Source”. Phys. Rev. Lett. 103, 257402 (2009).

[15] A. Ravasio, D. Gauthier, F. R. Maia, et al. “Single-Shot Di↵ractive Imaging with aTable-Top Femtosecond Soft X-Ray Laser-Harmonics Source”. Phys. Rev. Lett. 103,028104 (2009).

[16] H. J. Worner, J. B. Bertrand, P. B. Corkum, D. M. Villeneuve. “High-HarmonicHomodyne Detection of the Ultrafast Dissociation of Br2 Molecules”. Phys. Rev.Lett. 105, 103002 (2010).

[17] S. Sukiasyan, S. Patchkovskii, O. Smirnova, T. Brabec, M. Y. Ivanov. “Exchange andpolarization e↵ect in high-order harmonic imaging of molecular structures”. Phys.Rev. A 82, 043414 (2010).

[18] J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kie↵er, P. B. Corkum,D. M. Villeneuve. “Tomographic imaging of molecular orbitals”. Nature 432, 867(2004).

[19] W. Li, X. Zhou, R. Lock, S. Patchkovskii, A. Stolow, H. C. Kapteyn, M. M. Mur-nane. “Time-Resolved Dynamics in N2O4 Probed Using High Harmonic Generation”.Science 322, 1207 (2008).

[20] J. Caillat, A. Maquet, S. Haessler, B. Fabre, T. Ruchon, P. Salieres, Y. Mairesse,R. Taıeb. “Attosecond Resolved Electron Release in Two-Color Near-Threshold Pho-toionization of N2”. Phys. Rev. Lett. 106, 093002 (2011).

[21] S. Haessler, J. Caillat, W. Boutu, et al. “Attosecond Resolved Electron Release inTwo-Color Near-Threshold Photoionization of N2”. Phys. Rev. Lett. 106, 093002(2011).

[22] P. Wernet, J. Gaudin, K. Godehusen, O. Schwarzkopf, W. Eberhardt. “Femtosecondtime-resolved photoelectron spectroscopy with a vacuum-ultraviolet photon sourcebased on laser high-order harmonic generation”. Rev. Sci. Instrum. 82, 063114(2011).

[23] J. Krause, K. Schafer, K. Kulander. “High-order harmonic generation from atomsand ions in the high intensity regime”. Phys. Rev. Lett. 68, 3535 (1992).

[24] P. Corkum. “Plasma perspective on strong field multiphoton ionization”. Phys. Rev.Lett. 71, 1994 (1993).

106

Bibliography

[25] E. Constant, E. Mevel. “Attosecond Pulses”. In: C. Rulliere (editor), “FemtosecondLaser Pulses: Principles and Experiments”, chapter 12, 395–422. Springer, Berlin,2nd edition. ISBN 9780387017693 (2005).

[26] T. Leitner. “High Order Harmonic Generation as a possible Seed Source for theBESSY Free Electron Laser”. Diploma thesis (http://tinyurl.com/tldipl2007-pdf),Humboldt-Universitat zu Berlin (2007).

[27] M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Pop-mintchev, M. M. Murnane, H. C. Kapteyn. “Bright, Coherent, Ultrafast Soft X-RayHarmonics Spanning the Water Window from a Tabletop Light Source”. Phys. Rev.Lett. 105, 173901 (2010).

[28] K. Budil, P. Salieres, M. Perry, A. L’Huillier. “Influence of ellipticity on harmonicgeneration”. Phys. Rev. A 48, 3437 (1993).

[29] X. Zhou, R. Lock, N. Wagner, W. Li, H. C. Kapteyn, M. M. Murnane. “EllipticallyPolarized High-Order Harmonic Emission from Molecules in Linearly Polarized LaserFields”. Phys. Rev. Lett. 102, 073902 (2009).

[30] P. Balcou, P. Salieres, A. L’Huillier, M. Lewenstein. “Generalized phase-matchingconditions for high harmonics: The role of field-gradient forces”. Phys. Rev. A 55,3204 (1997).

[31] T. Leitner, A. A. Sorokin, J. Gaudin, H. Kaser, U. Kroth, K. Tiedtke, M. Richter,P. Wernet. “Shot-to-shot and average absolute photon flux measurements of afemtosecond laser high-order harmonic photon source”. New J. Phys. 13, 093003(2011).

[32] B. L. Henke, E. M. Gullikson, J. C. Davis. “X-Ray Interactions: Photoabsorption,Scattering, Transmission, and Reflection at E = 50-30,000 eV, Z = 1-92”. AtomicData and Nuclear Data Tables 54, 181 (1993).

[33] M. Ibek. “Reflective o↵-axis zone plates as focussing monochromators for a fem-tosecond high-order harmonic VUV photon source”. Diploma thesis, Freie UniversitatBerlin (2012).

[34] J. H. D. Eland, O. Vieuxmaire, T. Kinugawa, P. Lablanquie, R. I. Hall, F. Penent.“Complete Two-Electron Spectra in Double Photoionization: The Rare Gases Ar, Kr,and Xe”. Phys. Rev. Lett. 90, 053003 (2003).

[35] P. Radcli↵e, S. Dusterer, A. Azima, et al. “An experiment for two-color photoioniza-tion using high intensity extreme-UV free electron and near-IR laser pulses”. Nucl.Instrum. Meth. A 583, 516 (2007).

[36] W. Demtroder. Laser spectroscopy - Volume 2: Experimental techniques, chapter6.2.2, 313–323. Springer, Berlin, 4th edition. ISBN 9783540749523 (2008).

107

Bibliography

[37] T. E. Glover, R. W. Schoenlein, A. H. Chin, C. V. Shank. “Observation of LaserAssisted Photoelectric E↵ect and Femtosecond High Order Harmonic Radiation”.Phys. Rev. Lett. 76, 2468 (1996).

[38] M. Richter, A. Gottwald, U. Kroth, et al. “Measurement of gigawatt radiation pulsesfrom a vacuum and extreme ultraviolet free-electron laser”. Appl. Phys. Lett. 83,2970 (2003).

[39] K. Tiedtke, J. Feldhaus, U. Hahn, et al. “Gas detectors for x-ray lasers”. J. Appl.Phys. 103, 094511 (2008).

[40] N. Saito, P. N. Juranic, M. Kato, et al. “Radiometric comparison for measuring theabsolute radiant power of a free-electron laser in the extreme ultraviolet”. Metrologia47, 21 (2010).

[41] M. Kato, N. Saito, K. Tiedtke, et al. “Measurement of the single-shot pulse energyof a free electron laser using a cryogenic radiometer”. Metrologia 47, 518 (2010).

[42] K. J. Ross, B. Sonntag. “High temperature metal atom beam sources”. Rev. Sci.Instrum. 66, 4409 (1995).

[43] F. Buchner, A. Luebcke, N. Heine, T. Schultz. “Time-resolved photoelectron spec-troscopy of liquids”. Rev. Sci. Instrum. 81, 113107 (2010).

[44] A. T. J. B. Eppink, D. H. Parker. “Velocity map imaging of ions and electrons usingelectrostatic lenses: Application in photoelectron and photofragment ion imaging ofmolecular oxygen”. Rev. Sci. Instrum. 68, 3477 (1997).

[45] FLASH, DESY, Hamburg. http://flash.desy.de/.

[46] W. Ackermann, G. Asova, V. Ayvazyan, et al. “Operation of a free-electron laserfrom the extreme ultraviolet to the water window”. Nat. Photon. 1, 336 (2007).

[47] K. Tiedtke, A. Azima, N. von Bargen, et al. “The soft x-ray free-electron laser FLASHat DESY: beamlines, diagnostics and end-stations”. New J. Phys. 11, 023029 (2009).

[48] P. Emma, R. Akre, J. Arthur, et al. “First lasing and operation of an angstrom-wavelength free-electron laser”. Nat Photon. 4, 641 (2010).

[49] D. Pile. “X-rays: First light from SACLA”. Nat. Photon. 5, 456 (2011).

[50] M. Altarelli. “The European X-ray free-electron laser facility in Hamburg”. Nucl.Instrum. Meth. B 269, 2845 (2011).

[51] M. Wellhofer, M. Martins, W. Wurth, A. A. Sorokin, M. Richter. “Performance ofthe monochromator beamline at FLASH”. J. Opt. A 9, 749 (2007).

[52] M. Martins, M. Wellhofer, J. T. Hoeft, W. Wurth, J. Feldhaus, R. Follath.“Monochromator beamline for FLASH”. Rev. Sci. Instrum. 77, 115108 (2006).

108

http://flash.desy.de/

Bibliography

[53] T. Maltezopoulos, S. Cunovic, M. Wieland, et al. “Single-shot timing measurementof extreme-ultraviolet free-electron laser pulses”. New J. Phys. 10, 033026 (2008).

[54] A. L. Cavalieri, D. M. Fritz, S. H. Lee, et al. “Clocking Femtosecond X Rays”. Phys.Rev. Lett. 94, 114801 (2005).

[55] A. Azima, S. Duesterer, H. Schlarb, J. Feldhaus, A. Cavalieri, D. Fritz, K. Sengstock.“Jitter measurement by spatial electro-optical sampling at the FLASH free electronlaser”. In: “Conf. Proc. of EPAC”, 71–73 (2006).

[56] A. Azima, S. Dusterer, P. Radcli↵e, et al. “Time-resolved pump-probe experimentsbeyond the jitter limitations at FLASH”. Appl. Phys. Lett. 94, 144102 (2009).

[57] C. Gahl, A. Azima, M. Beye, et al. “A femtosecond X-ray/optical cross-correlator”.Nat. Photon. 2, 165 (2008).

[58] A. Agababyan, G. Grygiel, B. Fominykh, et al. “Data Acquisition System for a VUV-FEL Linac”. In: “Conf. Proc. of PCaPAC, Hayama, Japan”, (2005).

[59] K. Kimura, S. Katsumata, Y. Achiba, S. Iwata. Handbook of HeI photoelectronspectra of fundamental organic molecules: ionization energies, ab initio assignments,and valence electronic structure for 200 molecules. Japan Scientific Societies Press(1981).

[60] P. O’Kee↵e, R. Lopez-Martens, J. Mauritsson, A. Johansson, A. L’Huillier,V. Veniard, R. Taıeb, A. Maquet, M. Meyer. “Polarization e↵ects in two-photonnonresonant ionization of Argon with extreme-ultraviolet and infrared femtosecondpulses”. Phys. Rev. A 69, 051401 (2004).

[61] M. Meyer, D. Cubaynes, P. O’Kee↵e, et al. “Two-color photoionization in XUVfree-electron and visible laser fields”. Phys. Rev. A 74, 011401 (2006).

[62] M. Meyer, D. Cubaynes, D. Glijer, et al. “Polarization Control in Two-Color Above-Threshold Ionization of Atomic Helium”. Phys. Rev. Lett. 101, 193002 (2008).

[63] K. Reid. “Photoelectron angular distributions”. Annu. Rev. Phys. Chem. 54, 397(2003).

[64] D. P. M. Holland, A. C. Parr, D. L. Ederer, J. L. Dehmer, J. B. West. “The Angu-lar Distribution Parameters of Argon, Krypton and Xenon for use in Calibration ofElectron Spectrometers”. Nucl. Instrum. Meth. 195, 331 (1982).

[65] D. Kilcoyne, S. Nordholm, N. Hush. “Di↵raction analysis of the photoionizationcross-sections of Water, Ammonia and Methane”. Chem. Phys. 107, 213 (1986).

[66] D. G. McCoy, J. M. Morton, G. V. Marr. “The angular distribution of photoelectronsas a function of photon energy for the ground state photoionisation of molecularoxygen”. J. Phys. B 11, L547 (1978).

109

Bibliography

[67] T. A. Carlson, M. O. Krause, D. Meha↵y, J. W. Taylor, F. A. Grimm, J. John D. Allen.“Angular distribution in the photoelectron spectrum of the ground and first excitedvibrational bands of the X 2⌃+

g

state in N+2 measured as a function of photon energy”.

J. Chem. Phys. 73, 6056 (1980).

[68] R. M. Holmes, G. V. Marr. “The angular distribution of photoelectrons from N2, O2,and CO as a function of photon energy”. J. Phys. B 13, 945 (1980).

[69] G. Ohrwall, P. Karlsson, M. Wirde, et al. “A new energy and angle resolving electronspectrometer – First results”. J. Electron Spectrosc. Relat. Phenom. 183, 125 (2011).

[70] A. Mokhtari, P. Cong, J. L. Herek, A. H. Zewail. “Direct femtosecond mapping oftrajectories in a chemical reaction”. Nature 348, 225 (1990).

[71] T. S. Rose, M. J. Rosker, A. H. Zewail. “Femtosecond real-time probing of reactions.IV. The reactions of alkali halides”. J. Chem. Phys. 91, 7415 (1989).

[72] P. Cong, A. Mokhtari, A. Zewail. “Femtosecond probing of persistent wave packetmotion in dissociative reactions: up to 40 ps”. Chem. Phys. Lett. 172, 109 (1990).

[73] A. Materny, J. L. Herek, P. Cong, A. H. Zewail. “Femtosecond Real-Time Probing ofReactions. 16. Dissociation with Intense Pulses”. J. Phys. Chem. 98, 3352 (1994).

[74] M. Motzkus, S. Pedersen, A. H. Zewail. “Femtosecond Real-Time Probing of Reac-tions. 19. Nonlinear (DFWM) Techniques for Probing Transition States of Uni- andBimolecular Reactions”. J. Phys. Chem. 100, 5620 (1996).

[75] A. H. Zewail. “Femtochemistry”. J. Phys. Chem. 97, 12427 (1993).

[76] J. C. Polanyi, A. H. Zewail. “Direct Observation of the Transition State”. Acc.Chem. Res. 28, 119 (1995).

[77] P. Cong, G. Roberts, J. L. Herek, A. Mohktari, A. H. Zewail. “Femtosecond Real-Time Probing of Reactions. 18. Experimental and Theoretical Mapping of Trajectoriesand Potentials in the NaI Dissociation Reaction”. J. Phys. Chem. 100, 7832 (1996).

[78] V. Engel, H. Metiu. “Two-photon excitation of NaI with femtosecond laser pulses”.J. Chem. Phys. 91, 1596 (1989).

[79] V. Engel, H. Metiu. “The study of NaI predissociation with pump-probe femtosecondlaser pulses: The use of an ionizing probe pulse to obtain more detailed dynamicinformation”. Chem. Phys. Lett. 155, 77 (1989).

[80] T. J. Martinez, R. Levine. “Dynamics of the collisional electron transfer and fem-tosecond photodissociation of NaI on ab initio electronic energy curves”. Chem.Phys. Lett. 259, 252 (1996).

[81] M. Braun, C. Meier, V. Engel. “The reflection of predissociation dynamics inpump/probe photoelectron distributions”. J. Chem. Phys. 105, 530 (1996).

110

Bibliography

[82] E. Charron, A. Suzor-Weiner. “Femtosecond dynamics of NaI ionization and disso-ciative ionization”. J. Chem. Phys. 108, 3922 (1998).

[83] A. B. Alekseyev, H.-P. Liebermann, R. J. Buenker, N. Balakrishnan, H. R. Sadegh-pour, S. T. Cornett, M. J. Cavagnero. “Spin–orbit e↵ects in photodissociation ofsodium iodide”. J. Chem. Phys. 113, 1514 (2000).

[84] Y. Arasaki, K. Takatsuka, K. Wang, V. McKoy. “Studies of electron transfer in NaIwith pump–probe femtosecond photoelectron spectroscopy”. J. Chem. Phys 119,7913 (2003).

[85] B. H. Hosseini, H. R. Sadeghpour, N. Balakrishnan. “Control of polarized iodineatom branching ratio in NaI photodissociation”. Phys. Rev. A 71, 023402 (2005).

[86] P. Marquetand, V. Engel. “Complete local control of molecular excited state photo-fragmentation”. Chem. Phys. Lett. 426, 263 (2006).

[87] X. Y. Miao, L. Wang, H. S. Song. “Theoretical study of the femtosecond photoion-ization of the NaI molecule”. Phys. Rev. A 75, 042512 (2007).

[88] X. Y. Miao, J. F. Zhang, X. F. Jia. “Probing the process of photodissociation of theNaI molecule with pump-probe femtosecond spectroscopy”. EPL 82, 33001 (2008).

[89] Y.-F. Liu, H.-S. Zhai, Y.-L. Gao, R.-Q. Liu. “Theoretical Investigation ofFemtosecond-Resolved Photoelectron Spectrum of NaI Molecules”. Chin. Phys. Lett.25, 2016 (2008).

[90] A. Stolow, A. Bragg, M. Neumark. “Femtosecond Time-Resolved PhotoelectronSpectroscopy”. Chem. Rev. 104, 1719 (2004).

[91] P. Wernet. “Electronic structure in real time: mapping valence electron rearrange-ments during chemical reactions”. Phys. Chem. Chem. Phys. 13, 16941 (2011).

[92] C. Jouvet, S. Martrenchard, D. Solgadi, et al. “Experimental Femtosecond Photoion-ization of NaI”. J. Phys. Chem. A 101, 2555 (1997).

[93] G. Gregoire, M. Mons, I. Dimicoli, et al. “Photoionization of NaI: inward-outwardasymmetry in the wave packet detection”. Eur. Phys. J. D 1, 187 (1998).

[94] M. Odelius. Stockholm University, Sweden. Private communication.

[95] C. E. Moore. “Selected Tables of Atomic Spectra, Atomic Energy Levels and MultipletTables – C I, C II, C III, C IV, C V, C VI”. Nat. Stand. Ref. Data Ser. 3, 73. Nat.Bur. Stand., U.S. (1970).

[96] D. Hanstorp, M. Gustafsson. “Determination of the electron a�nity of iodine”. J.Phys. B: At., Mol. Opt. Phys. 25, 1773 (1992).

111

Bibliography

[97] A. Pietzsch, Y.-P. Sun, F. Hennies, et al. “Spatial Quantum Beats in VibrationalResonant Inelastic Soft X-Ray Scattering at Dissociating States in Oxygen”. Phys.Rev. Lett. 106, 153004 (2011).

[98] A. W. Potts, T. A. Williams, W. C. Price. “Photoelectron spectra and electronicstructure of diatomic alkali halides”. Proc. R. Soc. Lond. A 341, 147 (1974).

[99] T. D. Goodman, J. D. Allen Jr, L. C. Cusachs, G. K. Schweitzer. “The photoelectronspectra of gaseous alkali halides”. J. Electron Spectrosc. Relat. Phenom. 3, 289(1974).

[100] A. Vlcek Jr. “The life and times of excited states of organometallic and coordinationcompounds”. Coord. Chem. Rev. 200–202, 933 (2000).

[101] M. Poliako↵, J. J. Turner. “The Structure of [Fe(CO)4] - An Important New Chapterin a Long-Running Story”. Angew. Chem. Int. Ed. 40, 2809 (2001).

[102] S. A. Trushin, W. Fuss, K. L. Kompa, W. E. Schmid. “Femtosecond Dynamics ofFe(CO)5 Photodissociation at 267 nm Studied by Transient Ionization”. J. Phys.Chem. A 104, 1997 (2000).

[103] H. Ihee, J. Cao, A. H. Zewail. “Ultrafast electron di↵raction: structures in dissociationdynamics of Fe(CO)5”. Chem. Phys. Lett. 281, 10 (1997).

112

Acknowledgement

I want to thank every one whom I had the great pleasure to work with on the presentedprojects and everyone who supported me during the last years, while working on this thesis.At first I would like to thank Dr. Philippe Wernet who supervised this thesis and providedgreat tips and directions for my research. I am very grateful for his patience and for e�cient(and work-intense) proofreading of every last bit of this thesis, for his ideas and criticism andfast support, especially during the final spurt. I want to thank Prof. Dr. Dr. h.c. WolfgangEberhardt for giving me the opportunity to work at the Helmholtz-Zentrum Berlin and forexamining this thesis. I thank Prof. Dr. Alexander Fohlisch, head of the institute G-I2 atHZB, for his great support and for examining this thesis.I am thankful for the great, friendly and helpful working environment at HZB. I want tocordially thank all colleagues from HZB and all further collaborators whom I have workedwith during this thesis. Here’s an unordered and by far incomplete list:

! Mateusz Ibek for great times working together, great support in endless aligningsessions and lots of meaningful discussions about science, society and far beyond

! Rolf Mitzner and Torsten Quast for keeping the laser up and running! Jerome Gaudin, Olaf Schwarzkopf and Kai Godehusen for introducing me to the

HHG setup and supporting my first steps in the world of laser and x-ray optics! Michael Odelius for providing insight into simulating the molecular world and for

supporting our experiments with various computer simulations! Michael Meyer for his friendly support and our fruitful collaborations for the beamtime

on Fe(CO)5 and on the polarization dependence in two-color photo-ionization! Mathias Richter and Andrej Sorokin for the e�cient collaboration on determining the

absolute flux of the HZB HHG source and the reliability of semiconductor photodiodes! Franziska Buchner, Andrea Lubcke, Arnaud Rouzee, Marc Vrakking, Per Johnsson,

Linnea Rading and Hans Karlsson for enabling and performing the experiments onwave packet dynamics in NaI

! Tommaso Mazza, Paul Radcli↵e, Stefan Dusterer, Simon Schreck, Kristjan Kunnusand Martin Beye, who greatly supported the beamtime on Fe(CO)5 at FLASH

! Kerstin Kalus and Tino Noll for the design of the sample source! Christian Kalus for great vacuum support

I am indebted to Atoosa Meseck for inspiring and infecting me with her passion for science.

I want to thank all my fellow PhD colleagues at HZB for nice Stammtisch evenings afterthe monthly seminar and for the good times at the yearly Klausurtagung. I especially thankStephan Werner and Ruslan Ovsyannikov for the traditional ’co↵ee and cigarette’ breaks.

Benjamin Pitt, Wilson Quevedo, Benjamin Riedl, Christian Sußner, Ralph Schwarz and Ju-lia Weinhold gave helpful criticism on language and lay out – thank you!

I am very grateful to Nils Krebs, a really good friend, a fellow scientist and a dialog partner,for driving discussions from serious science all the way to utopia land and back again.

My greatest and warmest gratitude goes to my parents for their infinite support and en-couragement throughout my entire life.

Last but not least, I thank Johanna for her incomparable ability to motivate and strengthenme at any time.

Thank you . . .

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