Stable classical configurations in strongly driven helium

Abstract

We present a detailed analysis of the classical dynamics of the frozen-planet configuration of helium in an external, linearly polarized electromagnetic field. It is shown that the phase space of the collinear frozen planet in the field is mixed regular-chaotic and exhibits regular islands corresponding to nonlinear resonances between the periodic external force and the frozen-planet dynamics. An analysis of the transverse stability properties of the configuration shows that — except for regular regions corresponding to high-order atom-field resonances — the configuration is generally unstable with respect to deviations from collinearity. We find that stability of the driven frozen planet in all phase space dimensions can be enforced by the application of an additional, static electric field. The minimum atomic excitation necessary for the localization of a quantum state on the thereby stabilized atom-field resonances is estimated.