Packet spreading, stabilization, and localization in superstrong fields

We examine the stabilization regime for an atom interacting with a superintense laser field. We investigate the transition from the ground-state wave function to the formation of a stable localized wave function. The quantum mechanical wave-packet spreading plays a key role in determining the final degree of stabilization. We compare simple analytical predictions with exact numerical calculations and stress the importance of the laser pulse shape for the final ground-state probability.