Probing quantum states of Rydberg electrons by half-cycle pulses

Recently performed experiments 1 have demonstrated that half-cycle pulses (HCPs), i.e. unimodular electromagnetic pulses, are a useful new spectroscopic tool which is particularly well suited for investigating the dynamics of weakly bound Rydberg electrons. Typically their pulse durations range from the subpicosecond to the nanosecond regime and these pulses have already been produced with electric eld strengths up to 10 5 V=cm. So far work in this context has concentrated mainly on studies of total ionization or survival probabilities and on energy-resolved ionization spectra of Ryd-berg electrons 1, 2, 3. Thus it has been shown with the help of a classical picture of the ionization process that energy-resolved ionization spectra yield direct information about the initial momentum distribution of a Rydberg electron. However, this way any phase information about the initial quantum state is lost. In the following we address the question whether this phase information can be obtained from energy-and angle-resolved ionization probabilities. For this purpose a (multidimensional) semiclassical description of the ionization process of Rydberg electrons by half-cycle pulses is presented. In this theoretical approach it is particularly apparent how phase information about the initial quantum state of the Rydberg electron manifests itself in the angle-and energy-resolved ionization spectra. Furthermore, this way a detailed understanding of the ionization dynamics is obtained which is based on the underlying classical dynamics. In order to emphasize the essential physical aspects our subsequent discussion focuses on the sudden-ionization approximation 2 in which the ionizing HCP can be approximated by a delta-function in time. However, it should be mentioned that besides numerical advantages as far as the treatment of the Coulomb problem is concerned the presented semiclassical approach is also well suited for describing all eeects which might arise from nite pulse durations or from spatial variations of realistic HCPs.