1. Few-body quantum dynamics in strong fields:
From "simple" single ionisation to exploding molecular clocks
Max-Planck-Institut
für 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, Heidelberg

2. Outline
Experimental set-up
Single ionisation of atoms
Multiple ionisation of atoms
Molecular fragmentation

3. Ultrashort pulses: 6-7 fs
Experiment: „Reaction Microscope“
MCP Ions E,
Z (ToF)
Y (jet direction)
X (laser beam
propagation) 
Helmholtz coils B
Laser
Spherical
mirror
Supersonic
gas jet
Background pressure 2x10-11 mbar
Target density cm-1
Extraction voltage 1 V/cm;
Ion-electron coincidence
Spectrometer:
MCP electrons
Photon energy eV (l = 800 nm), pulse length 23 fs, Intensity I  W/cm2, repetition rate 3 kHz
Laser (Ti: Sapphire):
Momentum resolution:
ΔP|| < 0.02 a.u.
Ultrashort pulses: 6-7 fs

4. Reaction Microscope

5. Single ionisation of atoms

6.  > 1: Multiphoton (Above Threshhold) Ionisation
Single ionisation of atoms
Ip - ionisation potential
Up = I/42 - ponderomotive potential
Keldysh parameter
 > 1: Multiphoton (Above Threshhold) Ionisation Ek Ek ħ
Ionisation rate:
Ek = N ħ  - Ip*
Electron energy:
Nonresonant
Ip*
Due to AC Stark shift Ip*  Ip + Up
Resonant

7. Single ionisation of atoms
Ip - ionisation potential
Up = I/42 - ponderomotive potential
Keldysh parameter
 < 1: Tunnel ionisation
Transverse momentum distribution
Minimum at ultra–low energies:
counts
P, a.u.
-1,0
-0,5
0,0
0,5
1,0
1000
2000
3000
4000
5000 -3 -2 -1 1 2 3
2000
4000
6000
8000
counts
Pion||, [a.u]
 = 0.42
Ne,1015 W/cm2
Coulomb interaction with
the parent ion?
K. Dimitriou et al, TU Vienna
2-step process:
1) Tunneling through the lowered barrier
2) Classical oscillating motion in the laser field

8. P||, [a.u] Ion momentum distribution: He, 23fs : 0.31 – 0.58 counts-3 -2 -1 1 2 3
5000
10000
15000
20000
P||, [a.u]
counts
0.6 PW/cm2
2.1 PW/cm2
: – 0.58
1.5 PW/cm2
1.0 PW/cm2

9. P||, [a.u] Ion momentum distribution: Ne, 23fs : 0.3 – 0.67 counts -3-2 -1 1 2 3
1000
3000
5000
7000
counts
0.6 PW/cm2
0.4 PW/cm2
1.5 PW/cm2
2.0 PW/cm2
1.0 PW/cm2
: 0.3 – 0.67

10. P||, [a.u] Ion momentum distribution: Ar, 23fs : 0.29 – 1.1 counts-2 -1 1 2
2000
4000
6000
8000
P||, [a.u]
counts
0.25 PW/cm2
0.12 PW/cm2
0.8 PW/cm2
1.5 PW/cm2
0.5 PW/cm2
: – 1.1

11. Electron energy spectra: Ne, 23 fs
Electron energy [eV]
0.6 PW/cm2
0.4 PW/cm2
1.5 PW/cm2
1.0 PW/cm2 2 4 6 8 10 12 14 16 18 20
2000
4000
6000
counts
No ponderomotive shifts observed!

12. Two-dimensional electron momentum distributionsHe
0.6 PW/cm2 
0.6
0.2
0.4
 = 0.58
Z (ToF)
Y (jet direction)
X (laser beam
propagation) 
P|| = Pz - momentum
along laser polarisation
P = (Px2 + Py2)1/2
Area where the
spectrometer has no
resolution in the
transverse direction Ne
0.4 PW/cm2
0.6
0.2
0.4
 = 0.67
P [a.u.]
P [a.u.]
– –0.4 – Ar
0.25 PW/cm2
0.6
0.2
0.4
 = 0.73

13. Two-dimensional electron momentum distributions
0.25 PW/cm2
0.6
0.2
0.4 
Z (ToF)
Y (jet direction)
X (laser beam
propagation) 
P|| = Pz - momentum
along laser polarisation
P = (Px2 + Py2)1/2
 = 0.45
Area where the
spectrometer has no
resolution in the
transverse direction He
1.0 PW/cm2
0.6
0.2
0.4
 = 0.42 Ne
1.0 PW/cm2
P [a.u.]
0.6
0.2
0.4
 = 0.36 Ar
1.0 PW/cm2
– –0.4 –
P [a.u.]

14. Two-dimensional electron momentum distributionsNe
1.0 PW/cm2 
0.6
0.2
0.4
23 fs Ne
0.4 PW/cm2
0.6
0.2
0.4
23 fs
P [a.u.]
P [a.u.]
– –0.4 – Ne
0.4 PW/cm2
0.6
0.2
0.4
6-7 fs
Ultrashort pulses
No resonance-like
structures resolved!

15. 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

16. Double and multiple ionisation of atoms

17. Features of strong-field ionisation
Double and multiple ionisation of atoms
Features of strong-field ionisation
1014 – 1015 W/cm2 wt
E(t) = E0 sin(wt)
Field (tunnel) ionisation
Recollision
Drift momentum related to phase
pd = (qE0/w)cos(wt) = 2q (Up)1/2 cos(wt)

18. Mechanisms for strong-field double ionisation
pion||
sequential
2q(Up)1/2
nonsequential
pion||
recollision (e,2e)
recollision-excitation
subsequent tunnelling
pion||

19. He, Ne, Ar: strong-field double ionisation
4(Up)1/2
sequential
V. B. L. de Jesus et al.
JPB 37 (2004) L161

20. Influence of the atomic structure – a simple model
Cross sections for:
Initial phase average:
Excitation: Van Regemorter formula
Ionization: Lotz-type formula
V. B. L. de Jesus et al.
JPB 37 (2004) L161

21. 23 fs Multiple ionisation Ne2+ Ne3+ Ne4+ P / a.u. 1.5 PW/cm2
Sequential

22. 23 fs Ar3+ Ar4+ 0.3 PW/cm2 P / a.u. 0.5 PW/cm2 0.8 PW/cm2 1.2 PW/cm2
Sequential

23. Multiple ionisation of Ar: ion yield ratio
Y2+ / Y+
Y3+ / Y+
Y4+ / Y+
Y3+ / Y2+
Y4+ / Y2+
Y4+ / Y3+

24. Mechanisms for strong-field multiple ionisation
Ne  Ne+  Nen+
nonsequential
Recollision
(e,ne)
Field
ionisation
2n(Up)1/2
Drift momentum
Ar  Arm+  Arn+
sequential / nonsequential
Recollision
(e,(nm+1)e)
Field
ionisation
(2n 2.52(m 1))(Up)1/2
Feuerstein et al.
JPB 33 (2000) L823

25. Ar  Arm+  Arm+*  Arn+ Ar  Ar2+  Ar4+ Ar  Ar2+  Ar3+
0.3 PW/cm2
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
1.2 PW/cm2
1.5 PW/cm2
2.0 PW/cm2
P / a.u.
8(Up)1/2
Ar  Arm+  Arm+*  Arn+
Role of excited states?
Recollision
excitation
Field
ionisation
 life time (pulse duration)

26. Lifetime of excited states? - Pulse duration dependence
Ar PW/cm2
P / a.u.
23 fs
6-7 fs
Ar PW/cm2
P / a.u.
Ar PW/cm2
P / a.u.

27. Multiple ionisation of Ar: ion yield ratio
Y2+ / Y+
Y3+ / Y+
Y4+ / Y+
23 fs
6-7 fs
Y3+ / Y2+
Y4+ / Y2+
Y4+ / Y3+

28. Double and multiple ionisation: Conclusions
First systematic study of ion momentum distributions for strong-field
double and multiple ionisation of noble gases (He, Ne, Ar)
Core excitation during recollision dominates nonsequential double
ionisation for He and 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

29. 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?

30. Hydrogen molecular potential curves in a strong laser field
Fragmentation channels
Single ionisation (SI):
H2  H2+ + e-
2ppu
H+ + H+
Dissociation:
H2+  H+ + H0
H+ + H(2p)
1- and 2-photon net absorption
recollision - excitation
2psu
H+ + H(1s) 1w
Double ionisation
(Coulomb explosion, CE)
H2+  H+ + H+ + e-
Dressed
states 2w
1ssg 3w
H2+
Sequential (field) double ionisation (SDI):
R = 5 – 10 a.u. (CREI)
H(1s) + H(1s)
Recollision
- e,2e H2
- excitation with subsequent field ionisation

31. H2+ (D2+) as a molecular clock Principle of a molecular clock:
based on the propagation of electronic (recollision) and nuclear wavepacktes
H. Niikura et al.
Nature 417 (2002) 917, 421 (2003) 826
But:
works only if the fragmentation path can be identified
Recent progress:
A.S. Alnaser et al.
PRL 91 (2003)
Experiment: coincident detection of emitted protons
Theory: comprehensive model including
recollision-excitation and ionisation
X.M. Tong, Z.X. Zhao and C.D. Lin
PRL 91 (2003)
PRA 68 (2003)
 recollision-excitation is the dominating mechanism for both dissociation
and double ionisation channels producing high-energy fragments

32. From short to ultrashort pulses: non-coincident spectra
25 fs
0.2 PW/cm2
0.3 PW/cm2
0.5 PW/cm2
Dissociation
H2+ CE
2 w
1 w
counts
10 fs
0.5 PW/cm2
6 fs
0.2 PW/cm2
0.5 PW/cm2
0.8 W/cm2
Time-of–flight [ns]

33. From short to ultrashort pulses: coincident spectra40 20
-20
-40
P1 || [a.u.]
P2 || [a.u.]
counts (log scale)
23 fs
Recollision
CREI
Due to
momentum
conservation
true coincidence
events lie near the
P1 || = - P2 || diagonal!

34. 6 fs 40 counts (log scale) P2 || [a.u.] regions, where20
-20
-40
Recollision
regions, where
false coincidences
can not be excluded
Sequential ionisation?
P2 || [a.u.]
counts (log scale)
P1 || [a.u.]

35. Molecular fragmentation: Conclusions
Dynamics of the H2 fragmentation depends drastically
on the pulse duration
Charge-resonant enhanced ionisation (CREI) is suppressed for 6 fs
Coincidence measurements provide a method to distinguish
dissociation and double ionisation contributions within the
same energy range

36. Open questions and outlook
Single ionisation:
More detailed measurements with well-controlled few-cycle pulses
Other targets, broader range of , molecules, atomic hydrogen
Ultrashort pulses: absolute phase effects
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
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?

37. Acknowledgment Claus Dieter Schröter Robert Moshammer
Max-Planck-Institut
für Kernphysik
Acknowledgment
Claus Dieter
Schröter
Robert Moshammer
(Head of the group)
Artem Rudenko
Karl Zrost
Vitor Luiz Bastos
de Jesus