Dynamical localization in the 3-D kicked Rydberg atom

The dynamical localization for the 3D periodically kicked Rydberg atom is analyzed. For the 1D kicked atom, earlier work shows dynamical localization as the quantum suppression of classically fast ionization associated with unbounded chaotic trajectories. For the experimental observation, the crucial question is the dependence of the dynamical localization on the dimension. As the first step, we simulate the full 3D evolution of an extreme parabolic initial state elongated in the direction of the unidirectional kicks. We compare this simulation with the 1D model and find signatures of localization also in 3D. Implications for the experiment will be discussed.