Numerical integration of the time-dependent Schrödinger equation for an atom in a radiation field

We describe an approach for numerically integrating the time-dependent Schrödinger equation for an atom in a radiation field. The time propagation is based on the split-operator technique, with the full Hamiltonian split into two parts, the atomic Hamiltonian and the atom-field interaction. Both parts are represented on a complex Sturmian basis. The method is relatively efficient; ionization yields and level populations for atomic hydrogen can easily be computed on a workstation for modest pulse durations (e.g., 50 cycles or so) and modest intensities (e.g., of order ${10}^{15}$ W/${\mathrm{cm}}^2$ for a frequency of 0.2 a.u.). We present results of an application of the method to atomic hydrogen, and to illustrate the performance we compare our results with those obtained previously by Kulander [Phys. Rev. A 35, 445 (1987)]. We also illustrate the stabilization of atomic hydrogen against ionization by an intense high-frequency field, and the sensitivity of the ionization yield to the relative phase in the case where the field is bichromatic with one field a harmonic of the other.