Two-dimensional quantum hydrogen atom in circularly polarized microwaves: Global properties.

Abstract

The ionization of hydrogen Rydberg atoms by circularly polarized microwaves is studied quantum mechanically in a model two-dimensional atom. We apply a combination of a transformation to the coordinate frame rotating with the field, with complex rotation approach and representation of the atomic subspace in a Sturmian-type basis. The diagonalization of resulting matrices allows us to treat exactly the ionization of atoms initially prepared in highly excited Rydberg states of principal quantum number n0’60. Similarities and differences between ionization by circularly and linearly polarized microwaves are discussed with a particular emphasis on the high-frequency regime and on the localization phenomenon. The dependence of the ionization character on the initial state ~circular, elliptical, or low angular momentum state! as well as on the helicity of the polarization is discussed in detail. It is shown that, in the high-frequency chaotic regime, close encounters with the nucleus do not play a major role in the ionization process. @S1050-2947~96!11406-2# The hydrogen atom placed in an external field plays an exceptional role in the studies of quantum-classical correspondence in the vast area of quantum chaos. This system belongs to a small class of problems in this area where accurate theoretical predictions may be confronted with detailed experimental studies. This unique opportunity has led to great progress in understanding the behavior of quantally chaotic systems for which both the experiments and the theory have been providing new ideas and new challenges. Despite over 20 years of intensive investigations @1#, the theory of a highly excited hydrogen atom in the presence of a static uniform magnetic field still brings us unexpected predictions @2#. The ionization of highly excited hydrogen atoms by linearly polarized microwaves ~LPM! also has a long history, which began with the pioneering experiment of Bayfield and Koch@3#. As in the previous example, a complete physical picture of the coupled atom-field dynamics in this problem has yet to be reached. The very first model of the ionization process has been launched @4# using Monte Carlo classical simulations, in which the ionization threshold was associated with the onset of classical chaos in the system. Numerous studies performed since this early work treated the problem either classically or quantum mechanically, at various degrees of approximation. At the same time, improved experiments provided a stimulus as well as new puzzles for the theory ~for recent reviews of the theory see @5‐11#; experimental details may be found in @12‐14#!. A typical quantity measured or calculated in the ionization problem is a microwave field amplitude~called the ionization threshold! required to produce 10% ionization yield as a function of the field frequency for a given duration time