Understanding Tunneling Ionization of Atoms in Laser Fields using the Principle of Multiphoton Absorption

The elaborate energy and momentum spectra of ionized electrons from atoms in laser fields suggest that the ionization dynamics described by tunneling theory should be modified. Although great efforts have been carried out within semiclassical models, there are few discussions describing the multiphoton absorption process within a quantum framework. Comparing the results obtained with the time-dependent Schrödinger equation (TDSE) and the Keldysh–Faisal–Reiss (KFR) theory, we study the nonperturbative effects of ionization dynamics beyond the KFR theory. The difference in momentum spectra between multiphoton and tunneling regimes is understood in a unified picture with virtual multiphoton absorption processes. For the multiphoton regime, the momentum spectra can be obtained by coherent interference of each periodic contribution. However, the interference of multiphoton absorption peaks will result in a complex structure of virtual multiphoton bands in the tunneling regime. It is shown that the virtual spectra will be almost continuous in the tunneling regime instead of the discrete levels found in the multiphoton regime. Finally, with a model combining the TDSE and the KFR theory, we try to understand the different effects of virtual multiphoton processes on ionization dynamics.