Ionization of Rydberg hydrogen by a half-cycle pulse

We have calculated, by numerically integrating the time-dependent Schr\"odinger equation, the probability for ionization of a hydrogen atom from a high Rydberg state by a half-cycle pulse whose duration is comparable to, or shorter than, the period of the Rydberg orbit. We have chosen a pulse whose parameters are the same as the pulse used in the experiment of R. R. Jones, D. You, and P. H. Bucksbaum [Phys. Rev. Lett. 70, 1236 (1993)]. We compare our results with the classical results and with the experimental data of Jones et al., and we also present results for energy and angular distributions. Finally, we derive an approximate conservation law which applies in the limit of very short pulse times.