2D Momentum Spectra of the ATI Electrons by 10 fs Laser Pulses Zhangjin Chen Advisor: C. D. Lin Collaborators: Marlene Wickenhauser, A. T. Le and X. M. Tong Department of Physics Kansas State University

OUTLINE Introduction Theory Results Conclusions Background Motivation Long range Coulomb potential effects Intensity dependence for fixed wavelength Conclusions

Background laser pulse ionization of electron atom Ar intensity

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

Background He Ar Bucksbaum et al: PRA 37, 3615(R) (1988) Wickenhauser et al: PRA 73, 011401(R) (2006) He Ar ħω ATI peaks

Motivation C.M. Marhajan, A. Alanser, ...,C.L. Cocke et al. (submitted) atom Low energy spectra: lots of structure even in tunneling regime

Theory Numerical solution of TDSE Strong field approximation (SFA) Neglect: -Coulomb field on ionized electrons -Depletion of ground state -Other bound states Single active electron approximation Dipole transition moment Split operator method for time propagation Laser-dressed energy X.M. Tong and Shih-I Chu: Chem Phys 217, 119 (1997) M. Lewenstein et al: PRA 49, 2117 (1994)

Effects of Coulomb Potential

Effects of Coulomb Potential Ip=15.759 eV Exact TDSE Ip=15.612 eV TDSE for Rc=2 P (a.u.) P (a.u.) Ip=15.759 eV TDSE for Rc=8 SFA Ip=15.759 eV TDSE for Rc=5 P|| (a.u.) P|| (a.u.)

Effects of Coulomb Potential Exact TDSE TDSE for Rc=2 P (a.u.) TDSE for Rc=8 SFA P|| (a.u.) P|| (a.u.)

Volume Effect x z y S Augst et al: J. Opt. Soc. Am. B 8, 858 (1991) Rayleigh range of the focus z x y Peak Laser Intensity S Augst et al: J. Opt. Soc. Am. B 8, 858 (1991)

Intensity dependence P (a.u.) P|| (a.u.) P|| (a.u.) 600 nm, n=10

P (a.u.) P|| (a.u.) P|| (a.u.) Intensity dependence 600 nm, n=10

Conclusion Coulomb tail effects are crucial for slow photoelectrons Volume effects has to be taken into account when compare theory with experiment

Thank You !

OUTLINE Introduction Theory Results Conclusions Background Motivation Long range Coulomb potential effects Wavelength dependence for fixed Keldysh parameter Wavelength dependence for fixed 1st peak position Intensity dependence for fixed wavelength Conclusions

Background P (a.u.) P (arb units) P|| (a.u.) P|| (a.u.) P|| (a.u.) Wickenhauser et al: PRA 73, 011401(R) (2006) Background P (a.u.) g ~ 1.76 g ~ 0.89 0 0.3 0.6 0 0.3 0.6 P (arb units) 0 0.5 1 P|| (a.u.) 0 0.5 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 P|| (a.u.) P|| (a.u.)

Wavelength dependence for fixed 400 nm, n=7 600 nm, n=10 P (a.u.) 500 nm, n=9 700 nm, n=12 P|| (a.u.) P|| (a.u.)

Wavelength dependence for fixed 400 nm, n=7 600 nm, n=11 P (a.u.) 500 nm, n=9 700 nm, n=13 P|| (a.u.) P|| (a.u.)

Fixed Keldysh parameter I λ Up Up+Ip γ n nһω p-1 3.200 400 4.7770 20.5366 1.2843 7 21.6580 0.3 2.050 500 4.7816 20.5412 1.2837 9 22.2768 0.36 1.420 600 4.7695 20.5291 1.2853 10 20.6267 0.085 1.050 700 4.8003 20.5599 1.2812 12 21.2160 0.22 0.800 800 4.7770 20.5366 1.2843 14 21.6580 0.287

Fixed 1st peak position Intensity wavelength Up Up+Ip gamma n nw k first peak (eV) Energy of photon=3.094000 eV 3.200 400 4.7770 20.5366 1.2843 7 21.6580 0.2872 1.12 Energy of photon=2.475200 eV 2.310 500 5.3881 21.1477 1.2093 9 22.2768 0.2881 1.13 Energy of photon=2.062667 eV 1.730 600 5.8107 21.5703 1.1645 11 22.6893 0.2868 1.12 Energy of photon=1.768000 eV 1.340 700 6.1261 21.8857 1.1341 13 22.9840 0.2842 1.10