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, 69117 Heidelberg

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

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 108-109 cm-1 Extraction voltage 1 V/cm; Ion-electron coincidence Spectrometer: MCP electrons 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): Momentum resolution: ΔP|| < 0.02 a.u. Ultrashort pulses: 6-7 fs

Reaction Microscope

Single ionisation of atoms

 > 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

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

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 : 0.31 – 0.58 1.5 PW/cm2 1.0 PW/cm2

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

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 : 0.29 – 1.1

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!

Two-dimensional electron momentum distributions He 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.] -1.0 -0.8 –0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8 1.0 Ar 0.25 PW/cm2 0.6 0.2 0.4  = 0.73

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 -1.0 -0.8 –0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8 1.0 P [a.u.]

Two-dimensional electron momentum distributions Ne 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.] -1.0 -0.8 –0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8 1.0 Ne 0.4 PW/cm2 0.6 0.2 0.4 6-7 fs Ultrashort pulses No resonance-like structures resolved!

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 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)

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

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

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

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

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

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) 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

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)

Lifetime of excited states? - Pulse duration dependence Ar2+ 0.5 PW/cm2 P / a.u. 23 fs 6-7 fs Ar3+ 1.2 PW/cm2 P / a.u. Ar4+ 1.2 PW/cm2 P / a.u.

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

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

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?

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): enhanced @ R = 5 – 10 a.u. (CREI) H(1s) + H(1s) Recollision - e,2e H2 - excitation with subsequent field ionisation

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) 163002 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) 233203 PRA 68 (2003) 043412  recollision-excitation is the dominating mechanism for both dissociation and double ionisation channels producing high-energy fragments

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]

From short to ultrashort pulses: coincident spectra 40 20 -20 -40 -20 0 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!

6 fs 40 counts (log scale) P2 || [a.u.] regions, where 20 -20 -40 -20 0 20 40 Recollision regions, where false coincidences can not be excluded Sequential ionisation? P2 || [a.u.] counts (log scale) P1 || [a.u.]

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

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?

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