Does the dynamic stabilization reflect the numerical instability of direct integration of time dependent Schrödinger equation? Original Research Article

In view of the controversy on atomic stabilization, two different methods for numerically integrating the time dependent Schrödinger equation (TDSE) are studied and compared, i.e. the direct integration on spatial grids (DISG) and the eigenstate expansion method (EEM) with exact treatment of free–free dipole matrix elements (FFDME). The simulations show that both methods provide the above threshold ionization (ATI) spectra and wavepacket densities that agree very well each other. This comparison is important regarding a claim that DISG may suffer a numerical instability due to the lack of FFDME [T. Mercouris et al., J. Phys. B 29 (1996) L13]. Using the eigenstate expansion method, a series of simulations with high frequency, ultra intense laser were carried out. The results show that the ionization yield first increases, and then decreases or stabilizes when intensity goes to a value beyond the turning point. Simulations using various pulse forms prove that the stabilization presents and is not subject to the pulse form.