Attosecond electron dynamics in strong laser fields

Stefanie Gräfe

Institut für Theoretische PhysikTechnische Universität Wien

Timescales

10-18 s1 s1018 s 1 year

My age “Age” of this talk

AttophysicsFemto-chemistry

VibrationsRotationsRadiativetransitions

10-1810-1510-1210-910-6 sec

nano pico femto attomicro

Fast electronic dynamics

World record: shortest light

pulse~ 80 as

World record: shortest light

pulse~ 80 as

Atomic- & Molecular-physics

“Electron-orbit”

in H-atom~ 25 as

“Electron-orbit”

in H-atom~ 25 as

H2 vibration~ 16 fs

H2 vibration~ 16 fs

1 Attosecond

Age of the universe

Krausz, Ivanov, 2009

Strong infrared laser pulse

1000 MV/cmElectric field

1 Million × Atmospheric pressure(106Bar)

Radiation pressure

1-10 µmExtension in space

1015Number of photons

Mariana trench:1000 Bar

Infrared laser pulse(IR)

( ) ( ) ( )ϕω +⋅= ttfFtE cos

Physics in Strong Laser Fields and

“Attophysics”

Ionization in Strong Fields I: Tunneling

Atom (without laser field)

Atom with strong, external field

+

V(x)

V(x) + x .E cos ωt

+

T = 2.7 fs

Strong IR field800 nm, 5fs, 1014 W/cm2

IP

Ionizationpotential

Ionization II: Multiphoton Channel

Keldysh Theory

τωγ ⋅=≡P

P

U

I

2

Tunneling or Multiphoton? (Keldysh, 1967)

F

I

F

v Pel2

==τ

Tunnel Multi-photon

2

2

4ωF

U P =

Ponderomotive potential

( ) ( ) ( )ϕω +⋅= ttfFtE cos

Tunneling time

F

1>>γ1<<γ

( )

−∝Γ

F

I Ptunnel

3

22exp

23

+− ∝Γ

1ωPI

photonmulti I

Ionization rates

After ionization?

Electron in the laser field can acquire in average 2 UP of energy

2

2

4ωF

U P =

Final momentumdetermined by thevector potential at the time of birth

Trajectories follow the vector potentialof the laser field – neglecting atomic potential (strong field approximation)

Krausz, Ivanov, 2009

Re-scattering zoo

Krausz, Ivanov, 2009

Krausz, Ivanov, 2009

Quantum picture: re-scattering

3-Step Model

1. Laser-ionization : A strong, infrared laser pulse induces tunnel ionization

2. Propagation of the free electron in the laser field. As soon as the laser field changes its direction, the electron is accelerated back and re-collides with the parent ion.

3. Recombination of the electron with the parent ion under emission of high energetic radiation. As this process is periodic, a train of high order harmonics of the laser frequency is produced. Corkum, 1993

3. Recombination

1. Laser ionization

2. Re-collision

E cos ωt

Electron Re-Collision - Trajectories

(Chirp of the electron wave-packet)

Recollision energy

Ere

c/U

p ,

U

p=E

2 /4 ωω ωω

22 22

Krausz, Ivanov, 2009

Time-Frequency Analysis

Krausz, Ivanov, 2009

Electron Re-collision generates high-harmonics

Emission periodic in time

Periodic in frequency

Emission of high energeticradiation at each half-cycle of the laser pulse

Only odd harmonicsof the laser frequency

Attosecond pulses from High-Harmonics

Spectral Filtering – make attosecond pulses

Krausz, Ivanov, 2009

Reminder: Emission times

Emission of high-harmonic radiation occurs after each laser half-cycle:

After spectral filtering not one attosecond pulse is obtained but atrain of attosecond pulses

Single attosecond pulses

2max 2.3 λν ⋅∝+⋅= LaserPP IIUh

To make one singleattosecond pulse, thenumber of recollisionshas to be reduced.

Laser pulses with onlyfew cycles

Stabilization of the carrier-envelope phase

Krausz, Ivanov, 2009

Oscillating dipole

( ) ( )[ ]2~tdFS &&=Ω

( ) ψψ rtdr

=

ω

Harmonic spectrum: Harmonic spectrum containsfull information about electronicwavefunction

Krausz, Ivanov, 2009

Orbital-Tomography

Measuring the harmonic spectrum (and phase), it is possible to obtain information about theelectronic wavefunction

THEORY

EXPERIMENT

Itatani et al., 2004

Molecules in strong laser fields

Ionization in strong fields: molecules

Field-free molecule, z.B. H2

+ +

Molecule with intense external field

E cos ωtV(x,R) + x .E cosωt + +

Enhanced ionization

Molecule with intense external field

E cos ωt

Zuo, Bandrauk, 1995

Electrons in a double well potential

Orbitals with even (|g⟩) und odd (|u⟩) symmetry

( )ugleft +=+2

1 ( )ugright −=−2

1

Positive or negative superposition of the orbitals |g⟩ and |u⟩ means that the electron is localized in the right or left potential well.

g

R+ +

u

R+ +

+ + + +

Laser

Recent experiment in H 2

M.F. Kling et al., Science 2006, 312, 246-248.

H2

H2+

H + H

H+ + H

Born-Oppenheimer picture

0 1 2 3 4 5 6 7

R [10-10

m]

-30

-20

-10

0

10V

(R)

[eV

]

H2

H2

+

H2

2+

e-

E

F

ωXUV(T)

1Σg+

X

2Σg+

2Σu+

A

X~

~

12 g

R

2

u

R

2

g

R

1

u

R

1

Barrier comes up – around R = 5 Å, the electronic states are degenerate and tunneling freezes out!

Gräfe, Ivanov, PRL 2007

Model system

-20

-10

0

10

V(R

) [e

V]

H2

+

H2

2+E

F

ωXUV(T)

2Σg+

2Σu+

A

X~

~

( ) ( )tExRxVTTtH Rx ⋅+++= ),(

( ) )(2/

11),(

2 RRxRRxV

ε+±−=

1 nuclear and 1 electronic coordinate

R [Å]

Population dynamics

Efficient population transfer

Persson, Burgdörfer, Gräfe, New J. Phys. 2009

Electron densities

Localization very efficiently

Persson, Burgdörfer, Gräfe, New J. Phys. 2009

Experimental Realization?

Experimental realization

supersonic gas jetelectron detector

ion detector

laser

beam

jet dump

mirror

E = 5-24 V/cmB = 6-20 GE || B

E = 5-24 V/cmB = 6-20 GE || B

COLTRIMS

Outlook

Open questions

Transferring charge (electron or hole)along a chain: antenna-like systems?

CC

CC

Chain-like molecules can be e.g. conjugated hydrocarbons, where electron density is parallel aboveand below the molecular plane

Dynamics in multi-electron systems?Role of electron-correlation vs. controllability?

Acknowledgement

Acknowledgement:

Deutsche Akademie der Naturforscher Leopoldina (Nationale Akademie der

Wissenschaften),

Österr. Fond für wissenschaftliche Forschung: SFB ADLIS and Lise-Meitner-

Programm

Prof. Dr. Joachim Burgdörfer

Dr. Emil Persson TU Wien

Markus Pichler

Thomas Hisch

Prof. Dr. Werner Jakubetz Universität Wien

Prof. Dr. Andrius Baltuska

Dr. Markus Kitzler TU Wien, Experiment

Dr. Daniil Kartashov