Semiclassical interferences and catastrophes in the ionization of Rydberg atoms by half-cycle pulses

High-power, nearly unipolar electromagnetic-field pulses are a useful spectroscopic tool, in particular for studying the dynamics of weakly bound Rydberg electrons. Various experimental @1‐3# and theoretical @4,5# investigations on the interaction between Rydberg atoms and half-cycle pulses ~HCPs! have already been performed. In particular, the theoretical approaches that have been used so far involve either fully quantum-mechanical calculations, purely classical simulations, or simplified one-dimensional model problems. Fully quantum-mechanical treatments are capable of yielding quantitatively exact results, but due to the large spatial extension of highly excited Rydberg states they demand a huge computational effort. Furthermore, they allow only for a restricted qualitative understanding of the system, in general. Purely classical approaches are of interest, as they yield insight into the underlying classical aspects of the motion of the Rydberg electron. But they cannot deal properly with quantum-mechanical interference effects and are therefore also of limited applicability. One-dimensional model problems, finally, are not capable of describing all spatial aspects of the excitation process. Thus the natural question arises whether a proper three-dimensional theoretical description of the excitation process can be developed that is numerically highly accurate even for very large principal quantum numbers, which gives direct insight into the underlying classical aspects of the dynamics of the Rydberg electron and which is capable of dealing with all quantum-mechanical interference phenomena properly. In this Rapid Communication it is shown that such a theoretical description can be developed on the basis of a multidimensional semiclassical description of the excitation process. This approach is easily applicable to any spatial or temporal pulse form of the exciting HCP, and it is particularly accurate in the region of high principal quantum numbers, which is difficult to access by fully quantummechanical calculations. Based on this treatment different oscillatory structures are discussed, which appear in energyand angle-resolved ionization spectra and which should be accessible to experimental observation in view of the recently developed imaging method @6#. It is shown that these structures are caused by quantum-mechanical interferences between probability amplitudes that can be associated with classical trajectories of the ionized Rydberg electron. In order to demonstrate the numerical accuracy of the multidimensional semiclassical approach a comparison with numerical results is presented in the impulse approximation. Modifications of these oscillatory structures due to finite pulse durations are also discussed. Let us consider a typical HCP-excitation process. Initially an atom is prepared in a Rydberg state un0l 0m0& with a large principal quantum number n0@1 and a small angularmomentum quantum number l 0! n0. Around t50 a linearly polarized HCP with vector potential A(x,t)ez and duration t interacts with the Rydberg electron. The time evolution of the state c(x,t) of the Rydberg electron is determined by the ‘