Correlations between the final momenta of electrons and their initial phase-space distribution in the process of tunnel ionization

We present both full quantum mechanical and semiclassical calculations of above threshold ionization (ATI) of a hydrogen atom in the tunneling regime by a few-cycle linearly polarized infrared laser pulse. As a quantum treatment, we applied the direct integration of the time dependent Schr\"odinger equation (TDSE). In the semiclassical approximation (SCA), it is assumed that wavepacket propagation in the post-tunneling process can be well described within the classical framework. With these two methods, we analyze the similarities and deviations for ionization of the hydrogen atom. We found that the 3 dimensional semiclassical method can describe reasonably well the momentum correlation pattern of the ATI peaks. We also show good agreement between the results obtained by TDSE method and the semi-classical method. Furthermore, with the semiclassical approximation we clearly identify and separate the regions in momentum distributions of the ejected electrons according to initial conditions. We illustrate the corresponding regions with typical electron trajectories.