Verification of the validity of the short-pulse approximation for one-dimensional Rydberg atoms

Abstract

In this paper, we investigate the short-pulse approximation (SPA) for one-dimensional Rydberg atoms. We analyse the limits that SPA has to fulfil in order to be applicable. These concern the shape, the duration and the displacement caused by the pulse. The correctness of SPA is tested by comparing the results obtained using SPA with a numerical solution of the set of time-dependent Schrödinger equations. We show that the limit for the displacement caused by the pulse is of greatest importance. Violation of the limit for the duration of the pulse is shown to lead to concurrent violation of the limit for the displacement. We also show that the shape of the pulse has no influence on the created wave packet.