Above-threshold-ionization (ATI) of atoms in an intense, few-cycle laser pulse

1. Above-threshold-ionization (ATI) of atoms in an intense, few-cycle laser pulse Marlene Wickenhauser Collaborators: Xiao Min Tong and Chii Dong Lin

2. Schematic picture ionization of electron atom Ar laser pulse Calculation: = 10 fs = 400 - 800 nm • Electron spectra • 2D momentum distribution I ~ 2 x 1014 W/cm2

3. A. Rudenko et al. J. Phys. B 37 L407 (2004) 0 0.2 0.4 P(a.u.) atom P|| (a.u.) -1.0 -0.5 0 0.5 1.0 Motivation Recentexperiments: MPI Heidelberg, KSU e- 5 x 1014 W/cm2 800 nm Low energy spectra: -lots of structure -even in tunneling regime

4. Introduction Multiphoton ionization Tunneling ionization Above-threshold-ionization (ATI) Keldysh parameter:

5. Helium I= 2.3 x 1014 W/cm2 = 8 ps, 532 nm Typical ATIspectrum Absorbed Photons P. H. Bucksbaum PRA 37 3615 (1988) 12 14 16 18 20 22 ħω ħω ATI peaks 0 0.1 0.2 0.3 Electrons/eV ponderomotive energy Ionization potential 0 5 10 15 20 25 30 Energy (eV)

6. Outline • Theory • Energy Spectra • 2D electron-momentum distribution • Projection on parallel momentum

7. Theory 1) Numerical solution of TDSE -Single active electron approximation -grid -Split operator method for time propagation 2) Strong field approximation (SFA) Neglect: -Coulomb field on ionized electrons -Depletion of ground state -Other bound states Dipole transition moment Laser-dressed energy

8. Argon I ~ 1.7 x 1014 W/cm2 = 400 nm 10 fs Energy spectrum SFA TDSE Energy (eV)

9. Electron spectra from a short pulse No well defined frequency & intensity time 0 0.5 1 P (arb. unit) 0 2 4 6 8 Energy (eV)

10. -No subpeaks -ATI peaks shifted Energy (eV) Redefined Volkov phase Laser-dressed energy: energy shift: average=Up electron-field coupling

11. Argon I ~ 1.7 x 1014 W/cm2 = 400 nm 10 fs 0 2 4 6 8 Energy (eV) 2D momentum Distribution - SFA P(a.u.) 0 0.3 0.6 -0.8 -0.4 0 0.4 0.8 P|| (a.u.) • ATI peaks • Subpeaks • Parity • Angular momentum

12. P(a.u.) Comparison with TDSE 0 0.3 0.6 SFA 0 0.3 0.6 TDSE -0.8 0.4 0 0.4 0.8 P|| (a.u.)

13. P(a.u.) Intensity dependence Ar 400 nm Ip + Up threshold Channel closing: 6 ħω Ar: Ip = 15.76 eV 1.7 x 1014 W/cm2:Up= 2.55 eV Ip 6 ħω intensity 1.7 x 1014 W/cm2 3.2 x 1014 W/cm2 0 0.3 0.6 -0.8 0.4 0 0.4 0.8 3.9 x 1014 W/cm2 2.4 x 1014 W/cm2 0 0.3 0.6 P|| (a.u.) -0.8 -0.4 0 0.4 0.8 -0.8 -0.4 0 0.4 0.8

14. P (arb. unit) 0 2 4 6 8 10 Interesting points: -1.0 -0.5 0 0.5 1.0 P|| (a.u.) • Dip in contrast to ADK • Neon, Helium: dip • Argon: peak Momentum projection e- Ne: 25 fs, 800 nm, I = 4 x 1014 W/cm2 Rudenko et al. J. Phys. B 37 L407 (2004) atom ~ 0.6

15. Explanation for dip in literature • Rescattering: J. Chen et al, PRA 63 11404(R) (2000) • Coulomb potential: K. Dimitriou et al, PRA 70 061401(R) (2004) • Position of ATI peaks: (in tunneling regime) F. H. M. Faisal et al, J. Phys. B 38 L223 (2005) • Freeman Resonance: A. Rudenko et al, J. Phys. B 37 L407 (2004)

16. peak dip Argon 400 nm 10 fs Multiphoton I = 1.7 x 1014 W/cm2 I = 3.9 x 1014 W/cm2 g ~ 1.76 g ~ 1.13 0 0.3 0.6 0 0.3 0.6 0 0.5 1 0 0.5 1 P|| (a.u.) -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 P|| (a.u.) P|| (a.u.)

17. Argon 800 nm 10 fs dip peak Tunneling I = 1.65 x 1014 W/cm2 I = 1.8 x 1014 W/cm2 g ~ 0.89 g ~ 0.85 0 0.3 0.6 0 0.3 0.6 0 0.5 1 0 0.5 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 P|| (a.u.) P|| (a.u.)

18. Conclusion • Subpeaks in ATI spectra from short pulses • Explained structures in 2D momentum distribution • Dip in parallel momentum: • -Tunneling regime: ATI peaks • -Multiphoton regime: Parity of first ATI peak • -Coulomb effect not relevant • -Longer pulses: Freeman resonances