Abstract
The interaction of a model atom with very intense radiation fields is well approximated by a map that describes a free particle being kicked periodically by a double-well potential. Both the classical and quantum versions of the map are studied and are shown to provide a compact description of high-field stabilization in this strongly perturbed quantum system. In particular, we find that the ``stabilized'' wave function results from the excitation of a superposition of eigenstates of the periodic, time-evolution operator that are localized near classically unstable and weakly stable orbits. These ``scarred'' wave functions correspond to localized wave packets that oscillate back and forth in the strong external field while in the neighborhood of the attractive Coulomb field. The periodic bremsstrahlung, emitted as this wave packet passes the nucleus, provides a distinct experimental signature of the stabilized state.
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