Classical and quantum stabilization of atoms in intense laser fields

With the help of phase-space pictures we consider the dynamics of a hydrogen atom driven by a high-frequency periodic electromagnetic field. We show that the stabilization phenomenon, widely discussed in the literature, has quantum and classical appearances, which correspond to different physical situations. Classical stabilization relies on the dynamics of the electron in the laser-induced effective potential: the electron repeatedly crosses the separatrix of the Coulomb potential moving along the trajectories of the effective potential. Quantum stabilization results from the decrease of matrix elements of multiphoton transitions, which implies a decrease of the net cross section of multiphoton photoeffect from the new stationary states of the effective potential.