Few-body quantum dynamics in strong fields:From "simple" single ionisation to exploding molecular clocks

Max-Planck-Institutfür Kernphysik

Bernold Feuerstein, Artem Rudenko, Karl Zrost, Vitor L. B. de Jesus, Claus Dieter Schröter, Robert Moshammer and Joachim Ullrich

Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg

• Single ionisation of atoms

• Molecular fragmentation

Outline

• Multiple ionisation of atoms

• Experimental set-up

Experiment: „Reaction Microscope“

Ultrashort pulses: 6-7 fs

Photon energy 1.55 eV (l = 800 nm), pulse length 23 fs,

Intensity I 1014-1016 W/cm2, repetition rate 3 kHz

Laser (Ti: Sapphire):

Z (ToF)

Y (jet direction)

X (laser beam propagation)

• Background pressure 2x10-11 mbar• Target density 108-109 cm-1

• Extraction voltage 1 V/cm;• Ion-electron coincidence

Spectrometer:

Momentum resolution: ΔP|| < 0.02 a.u.

Supersonic gas jet

Laser

Spherical mirror

MCP electrons

MCP Ions

E,

Hel

mho

ltz c

oils

B

Reaction Microscope

Single ionisation of atoms

Keldysh parameter p

p

U

I

2 Ip - ionisation potential

Up = I/42 - ponderomotive potential

Ek

ħ

> 1: Multiphoton (Above Threshhold) Ionisation

NIw Ionisation rate:

Ek = N ħ - Ip*Electron energy:

Resonant Nonresonant

Ip*

Due to AC Stark shift Ip* Ip + Up

Ek

Single ionisation of atoms

-3 -2 -1 0 1 2 3

0

2000

4000

6000

8000

cou

nts

Pion||, [a.u]

= 0.42

Ne,1015 W/cm2

Minimum at ultra–low energies:

< 1: Tunnel ionisation

2-step process:

1) Tunneling through the lowered barrier

2) Classical oscillating motion in the laser field

Keldysh parameter p

p

U

I

2 Ip - ionisation potential

Up = I/42 - ponderomotive potential

Coulomb interaction with the parent ion?

K. Dimitriou et al, TU Vienna

cou

nts

P, a.u. -1,0 -0,5 0,0 0,5 1,0

0

1000

2000

3000

4000

5000

Transverse momentum distribution

Single ionisation of atoms

Ion momentum distribution: He, 23fs

-3 -2 -1 0 1 2 30

5000

10000

15000

20000

P||, [a.u]

coun

ts

0.6 PW/cm2

2.1 PW/cm2

1.5 PW/cm2

1.0 PW/cm2

: 0.31 – 0.58

Ion momentum distribution: Ne, 23fs

P||, [a.u]

-3 -2 -1 0 1 2 3

1000

3000

5000

7000

coun

ts

0.6 PW/cm2

0.4 PW/cm2

1.5 PW/cm2

2.0 PW/cm2

1.0 PW/cm2

: 0.3 – 0.67

-2 -1 0 1 2

0

2000

4000

6000

8000

P||, [a.u]

coun

ts

0.25 PW/cm2

0.12 PW/cm2

0.8 PW/cm2

1.5 PW/cm2

0.5 PW/cm2

: 0.29 – 1.1

Ion momentum distribution: Ar, 23fs

Electron energy spectra: Ne, 23 fs

coun

ts

No ponderomotive shifts observed!

Electron energy [eV]

0.6 PW/cm2

0.4 PW/cm2

1.5 PW/cm2

1.0 PW/cm2

0 2 4 6 8 10 12 14 16 18 200

2000

4000

6000

Two-dimensional electron momentum distributions

Z (ToF)

Y (jet direction)

X (laser beam propagation)

P|| = Pz - momentum

along laser polarisation

P = (Px2 + Py

2)1/2

P

[a.

u.]

P [a.u.]

He0.6 PW/cm2

0.6

0.2

0

0.4

= 0.58

Ne0.4 PW/cm2

0.6

0.2

0

0.4

= 0.67

-1.0 -0.8 –0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8 1.0

Ar0.25 PW/cm2

0.6

0.2

0

0.4

= 0.73 Area where the spectrometer has no resolution in the transverse direction

0.25 PW/cm2Two-dimensional electron momentum distributions

Z (ToF)

Y (jet direction)

X (laser beam propagation)

P|| = Pz - momentum

along laser polarisation

P = (Px2 + Py

2)1/2

P

[a.

u.]

P [a.u.]

He1.0 PW/cm2

-1.0 -0.8 –0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8 1.0

Ar1.0 PW/cm2

Ne1.0 PW/cm2

Area where the spectrometer has no resolution in the transverse direction

0.6

0.2

0

0.4

0.6

0.2

0

0.4

0.6

0.2

0

0.4

= 0.45

= 0.42

= 0.36

Two-dimensional electron momentum distributionsP

[a.

u.]

P [a.u.]

-1.0 -0.8 –0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8 1.0

Ne1.0 PW/cm2

0.6

0.2

0

0.423 fs

Ne0.4 PW/cm2

0.6

0.2

0

0.4

23 fs

Ne0.4 PW/cm2

0.6

0.2

0

0.46-7 fs

No resonance-likestructures resolved!

Ultrashort pulses

Single ionisation: Conclusions

• Smooth transition from multiphoton to tunneling ionisation

• Target dependence near zero momenta: Minimum for He and Ne, maximum for Ar

• No ponderomotive shifts observed – resonance-like structures: Contribution of resonant processes can explain the absence of ponderomotive shifts

• Rich structures in two-dimensional electron momentum spectra

• Multiphoton features of the process are washed out for a few-cycle pulse

Double and multiple ionisation of atoms

Features of strong-field ionisation

• Field (tunnel) ionisation

1014 – 1015 W/cm2

E(t) = E0 sin(t)

t

pd = (qE0/)cos(t) = 2q (Up)1/2 cos(t)

• Recollision

• Drift momentum related to phase

Double and multiple ionisation of atoms

Mechanisms for strong-field double ionisation

sequential

nonsequential

recollision-excitationsubsequent tunnelling

recollision (e,2e)

pion||

2q(Up)1/2

pion||

0

pion||

He, Ne, Ar: strong-field double ionisation

sequential

4(Up)1/2

V. B. L. de Jesus et al.JPB 37 (2004) L161

Influence of the atomic structure – a simple model

V. B. L. de Jesus et al.JPB 37 (2004) L161

).()(

,

00,2

0, tdtEtWY

Y

YR

recexcionADKexcion

exc

ion

Cross sections for: Initial phase average:

Excitation: Van Regemorter formulaIonization: Lotz-type formula

P / a.u.

23 fs Ne2+

-20 -10 0 10 200

5000

10000

15000

20000

1.5 PW/cm2

4(Up)1/2

-20 -10 0 10 200

1000

2000

3000

4000

5000

-20 -10 0 10 20

0

1000

2000

3000

4000

5000

6000

P / a.u.

Ne3+

6(Up)1/2

P / a.u.

-20 -10 0 10 200

20

40

60

80

100

120

-20 -10 0 10 200

10

20

30

40

Ne4+

8(Up)1/2

-20 -10 0 10 200

500

1000

1500

2000

P / a.u.

2.0 PW/cm2

Sequential

Multiple ionisation

Sequential

0.3 PW/cm2

P / a.u. P / a.u.

0.5 PW/cm2

0.8 PW/cm2

1.2 PW/cm2

1.5 PW/cm2

2.0 PW/cm2

6(Up)1/2

23 fs Ar3+

-15 -10 -5 0 5 10 150

200

400

600

800

1000

1200

1.2 PW/cm2

1.5 PW/cm2

2.0 PW/cm2

P / a.u.

8(Up)1/2

Ar4+

0.1 11E-5

1E-4

1E-3

0.01

0.1

1

rela

tive

ion

yie

ld

Intensity / PW cm -2

Multiple ionisation of Ar: ion yield ratio

Y2+ / Y+

Y3+ / Y+

Y4+ / Y+

Y3+ / Y2+

Y4+ / Y2+

Y4+ / Y3+

Mechanisms for strong-field multiple ionisation

Ne Ne+ Nen+

nonsequential

Recollision(e,ne)

Fieldionisation

2n(Up)1/2

Drift momentum

Ar Arm+ Arn+

sequential / nonsequential

Recollision(e,(nm+1)e)

Fieldionisation

(2n 2.52(m 1))(Up)1/2

Feuerstein et al.JPB 33 (2000) L823

0.3 PW/cm2

P / a.u. P / a.u.

0.5 PW/cm2

0.8 PW/cm2

1.2 PW/cm2

1.5 PW/cm2

2.0 PW/cm2

Sequential

6(Up)1/2

-15 -10 -5 0 5 10 150

200

400

600

800

1000

1200

1.2 PW/cm2

1.5 PW/cm2

2.0 PW/cm2

P / a.u.

8(Up)1/2

Ar Ar2+ Ar3+Ar Ar2+ Ar4+

Ar Ar3+ Ar4+

Ar Arm+ Arm+* Arn+

Role of excited states?

Recollisionexcitation

Fieldionisation

Fieldionisation

life time (pulse duration)

23 fs

6-7 fs

Ar4+ 1.2 PW/cm2

P / a.u.

Ar2+ 0.5 PW/cm2

P / a.u.Ar3+ 1.2 PW/cm2

P / a.u.

Lifetime of excited states? - Pulse duration dependence

23 fs

0.1 11E-5

1E-4

1E-3

0.01

0.1

1

rela

tive

ion

yie

ld

Intensity / PW cm -2

Multiple ionisation of Ar: ion yield ratio

0.1 11E-5

1E-4

1E-3

0.01

0.1

1

rela

tive

ion

yie

ld

Intensity / PW cm -2

Y2+ / Y+

Y3+ / Y+

Y4+ / Y+

Y3+ / Y2+

Y4+ / Y2+

Y4+ / Y3+

6-7 fs

• First systematic study of ion momentum distributions for strong-field double and multiple ionisation of noble gases (He, Ne, Ar)

• Recollision (e,ne) is the dominating mechanism for creation of Ne2+, Ne3+ and Ne4+ ions (double-hump structure)

• Multiple ionisation mechanism for argon is more complex – most likely combined sequential and nonsequential processes – enhanced double-hump structure for ultrashort pulses indicates importance of core excitations

Double and multiple ionisation: Conclusions

• Core excitation during recollision dominates nonsequential double ionisation for He and Ar

Molecular fragmentation

Confusion reigns when Sir James Dwighton is murdered... Luckily, his broken clock tells the tale -- or does it?

What do broken (Coulomb-exploded)molecular clocks tell us?Does confusion reign also here?

Single ionisation (SI):H2 H2

+ + e-

• 1- and 2-photon net absorption

Fragmentation channels

Double ionisation (Coulomb explosion, CE)

H2+ H+ + H+ + e-

Dissociation:H2

+ H+ + H0

• Sequential (field) double ionisation (SDI): enhanced @ R = 5 – 10 a.u. (CREI)

Hydrogen molecular potential curves

in a strong laser field

0 5 10 15-20

-15

-10

-5

0

5

10

15

20

25

30E

/ e

V

R / a.u.

2pu

H+ + H+

H+ + H(2p)

H+ + H(1s)

H(1s) + H(1s)

Dressedstates

H2

H2+

1sg

123

2pu

• recollision - excitation

- excitation with subsequent field ionisation

• Recollision - e,2e

H2+ (D2

+) as a molecular clock

Principle of a molecular clock:based on the propagation of electronic (recollision) and nuclear wavepacktes

works only if the fragmentation path can be identified

H. Niikura et al.Nature 417 (2002) 917, 421 (2003) 826

But:

Recent progress:

Experiment: coincident detection of emitted protons

Theory: comprehensive model including recollision-excitation and ionisation

A.S. Alnaser et al.PRL 91 (2003) 163002

X.M. Tong, Z.X. Zhao and C.D. LinPRL 91 (2003) 233203PRA 68 (2003) 043412

recollision-excitation is the dominating mechanism for both dissociationand double ionisation channels producing high-energy fragments

100

1000

10000

100000

25 fs

0.2 PW/cm2

0.3 PW/cm2

0.5 PW/cm2

10

100

1000

10000

cou

nts

10 fs

0.5 PW/cm2

H2+DissociationCE CE

1 2

From short to ultrashort pulses: non-coincident spectra

6 fs

0.2 PW/cm2

0.5 PW/cm2

0.8 W/cm2

Time-of–flight [ns]

40

20

0

-20

-40

-20 0 20 40

P1 || [a.u.]

P2

|| [a.u.]

coun

ts (log

scale

)

Due to momentum conservation true coincidence events lie near theP1

|| = - P2 || diagonal!

From short to ultrashort pulses: coincident spectra

Recollision

CREI

23 fs

40

20

0

-20

-40

-20 0 20 40

P1 || [a.u.]

P2

|| [a.u.]

regions, where false coincidencescan not be excluded

coun

ts (log

scale

)

Recollision

Sequential ionisation?

6 fs

• Dynamics of the H2 fragmentation depends drastically on the pulse duration

• Coincidence measurements provide a method to distinguish dissociation and double ionisation contributions within the same energy range

Molecular fragmentation: Conclusions

• Charge-resonant enhanced ionisation (CREI) is suppressed for 6 fs

Single ionisation:• More detailed measurements with well-controlled few-cycle pulses• Other targets, broader range of , molecules, atomic hydrogen• Ultrashort pulses: absolute phase effects

Molecular fragmentation:• Origin of low-energy Coulomb explosion peaks – dependence on temporal pulse shape• Branching ratios for different fragmentation channels• Electron dynamics – breakdown of Born-Oppenheimer approximation?

Open questions and outlook

Multiple ionisation:• Towards higher and lower intensities (transition to sequential regime / threshold effects fpr recollision• More on correlated electron dynamics• Ultrashort pulses: absolute phase effects

Acknowledgment

Robert Moshammer(Head of the group)

Karl ZrostVitor Luiz Bastos

de Jesus

Artem Rudenko

Claus DieterSchröter

Max-Planck-Institutfür Kernphysik