Quantum chaos in the periodically kicked Rydberg atom

A theoretical study of classical-quantum correspondence in the periodically kicked Rydberg atom is presented. Experimental measurements of the Rydberg atom survival probability have found a broad maximum for pulse repetition frequencies near the classical orbital frequency. Comparisons with a detailed classical analysis show that this behavior provides an unambiguous signature of dynamical stabilization. The classical simulations further show that the kicked atom is, depending on the pulse repetition frequency, chaotic or characterized by a mixed phase space with various families of fully stable islands within which the atom is stable against ionization. When the classical Rydberg atom is stable, classical-quantum correspondence is observed, i.e., the quantum counterpart closely mimics the classical phase space structure on the Husimi distribution of the system, which is a quantum wave function projected onto phase space. On the other hand, the quantum system is found to be stable even when the classical system becomes chaotic and leads to a fast ionization rate. In such cases, the corresponding quantum wave functions show enhanced amplitudes along the paths of unstable periodic orbits, which are classical regular motions hidden within disordered chaotic orbits. These enhanced regular motions, stabilize the quantum system against the ionization of the classical atom. In the study of the kicked atom, it is necessary to perform numerical simulations of the quantum system. In practice, only a finite number of basis states can be used in order to explore the solution of the time-dependent Schrodinger equation in the whole Hilbert space. This finite basis set subtends a finite subspace within the Hilbert space. Artificial reflections at the effective "wall" which is the boundary of the finite subspace, and reentering of probability flux into the subspace represent a major limitation for the study of long time evolution of the ionization process in the kicked Rydberg atom. We propose a new method called the repetitive projection method (RPM) and discuss its applicability compared to other conventional methods.