Low frequency quantum stabilization of the hydrogen atom in a microwave field: scarred states and classical stability island overlap

Abstract

Excited hydrogen atoms in pulsed microwave electric fields exhibit a nonclassical increase of stability over a relatively wide range of frequencies even around and below the classical Kepler frequency 1/n3 where Anderson-like localization due to quantum interference plays no role. I show here that the increased stability for microwave frequencies in the whole frequency range 0.7/n3–0.85/n3 is due to selective population of long-lived ‘scarred’ states that are associated with the chaotic separatrix band surrounding the principal classical resonance zone in phase space. A quantum explanation is given in terms of adiabatic evolution of Floquet states and the destabilizing effect of two-level quantum resonances is investigated. The role of neighbouring classical resonance zones in defining the frequency range of stabilization is revealed both by quasienergy curves and by Husimi functions for the instantaneous quantum states. Nonclassical stability peaks as a function of microwave frequency are thus explained as transition points from one classical resonance to another.