Features of the quasienergy spectrum of the hydrogen atom in a microwave field

The nearest neighbour level spacing of the quasienergies of a hydrogen atom in a micro-wave field is studied. There is evidence of level repulsion among states corresponding to classically chaotic regions. In the regions of classical phase space where the motion is approximately regular, the corresponding quasienergy spectrum can be understood in terms of approximate dynamical constants. In particular, grouping the high lying quasienergy states into photons yields level spacing plots that are close to δ functions; there is little fluctuation about the average value predicted by the approximate constant. The grouping suggests a simple explanation of the “photon localization” recently observed by Casati et al. 1].