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

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

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

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

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

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

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

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

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

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

2D momentum Distribution - SFA Argon I ~ 1.7 x 1014 W/cm2 = 400 nm 10 fs 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 0 2 4 6 8 Energy (eV)

Comparison with TDSE P (a.u.) P|| (a.u.) SFA TDSE 0 0.3 0.6 0 0.3 0.6 0 0.3 0.6 P (a.u.) 0 0.3 0.6 TDSE -0.8 0.4 0 0.4 0.8 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 P (a.u.) 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 2.4 x 1014 W/cm2 3.9 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

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

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)

Argon 400 nm 10 fs dip peak Multiphoton P|| (a.u.) P|| (a.u.) 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.)

Argon 800 nm 10 fs dip peak Tunneling P|| (a.u.) P|| (a.u.) 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.)

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