Rydberg stabilization of atoms in a strong field

During the last years the phenomenon of stabilization of atom in a strong laser field attracted a great deal of attention (Gavrila, Eberly, Shakeshaft, Kulander 1988-1993). While the existence of the stabilization of atom has been clearly demonstrated in the numerical experiments the clear analytical criterion of stabilization is still absent. Usually it is assumed that stabilization condition is satisfied if the energy of the laser photon is larger than the electron coupling energy and the amplitude of electron oscillations in the field is large in comparison with Bohr radius. However, the investigations of the corresponding classical problem [59,60,63,65] demonstrated that stabilization remains also in the classical atom, where the above conditions are violated. According to these results the Rydberg atom becomes stable if the field strength of the linearly polarized field exceeds the stabilization border $\epsilon > \epsilon_{stab} \approx 10\omega/(m+1)$ where $m$ is the magnetic quantum number. A simple description of this effect is achieved on the basis of the derived Kramers map which is very similar to the Kepler map [63]. This map allows to give an estimate for one-photon ionization rate and to show that this rate decreases exponentially with the field strength for $\epsilon > \epsilon_{stab}$. The interesting new property of Rydberg stabilization is that the stabilized Rydberg electron can have enormous kinetic energy (about hundreds eV) which can be radiated during a transition to the ground state. The energy of it is as in a usual hydrogen atom since in the ground state the field is very small $\epsilon_{stab} << 1$. Futher investigations are required for this interesting phenomenon.