Numerical investigation of strong-field photoionization rates

Abstract

The time-dependent Schr\odinger equation for a two-dimensional model atom is solved exactly (numerically) for pulses of a circularly or linearly polarized strong laser field (in the dipole approximation). Although exact final ionization (or survival) probabilities do not depend on the choice of gauge, we show (both analytically and numerically) that ionization rates, calculated for a flat part of the strong laser pulse, may be gauge dependent. Differences between the length gauge and the velocity gauge ionization rates or survival probabilities (calculated through projections on ``textbook'' bound states) usually grow with an intensity of the laser field. The differences, which vanish in the limit of a weak field, may reach even a factor of 4 to the advantage of the length gauge for stronger fields. This fact points out that such a method of computing ionization rates may be not reliable in strong laser fields. Gauge-invariant ionization rates, calculated through a probability of finding an electron in a vicinity of a nucleus, usually have values being found between values of the previously mentioned gauge-dependent ionization rates.