We study the classical theory of the response of atoms to ultrastrong laser pulses. We argue that the stabilization of atoms in a strong laser field through bound states in a Kramers-Henneberger potential has a classical interpretation. We present results of numerical simulations based on a phase-space-averaging method for a one-dimensional smoothed potential, which agree very well with the results of quantum theory. In a three-dimensional Coulomb potential, classical simulations hardly allow for stabilization, in contrast to recently obtained quantum-mechanical results. We identify physical reasons for this discrepancy with the effect of smoothing the potential singularity. We stress the relevance of our studies in the context of the correspondence principle.

• Received 4 December 1991

DOI:https://doi.org/10.1103/PhysRevA.46.1638