Testing time-dependent perturbation theory of Langhoff-Epstein-Karplus on multiphoton ionization

We examine a version of time-dependent perturbation theory [P. W. Langhoff, S. T. Epstein, and M. Karplus, Rev. Mod. Phys. 44, 602 (1972)] for application to atomic ionization in a short and intense laser pulse, using a one-dimensional model. The conventional version of time-dependent perturbation theory suffers slow convergence due to secular growth of the respective orders of perturbative amplitudes, and it is not practical for numerical computation in strong-field physics. We examine whether the removal of the secular growth according to the Langhoff-Epstein-Karplus theory accelerates the convergence, and whether the theory has practical utility for ionization in a short and intense laser pulse, which was not widely available at the time of their proposal. We find that the complex-valued energy shift introduced in the Langhoff-Epstein-Karplus theory highly depends on the laser field strength, and hence that the convergence is not appreciably faster than the conventional theory.