Floquet analysis of the dynamical stabilization of the kicked hydrogen atom

We analyze the quantum dynamics of the one-dimensional periodically kicked Rydberg atom. The time-dependent Schrödinger equation is solved by employing a nonunitary representation of the period-one evolution operator in a finite basis set that accounts for the outbound probability flux. We find a direct correspondence between stable classical islands in phase space and the quantum Husimi distributions of stable Floquet states. These results explain the pronounced peak recently found experimentally in the frequency-dependent survival probability of Rydberg states subject to a sequence of half-cycle pulses.