The Floquet problem for the interaction of an atom with a monochromatic laser field of frequency omega was studied long ago for the case of high omega and arbitrary intensity using the ``high-frequency Floquet theory' (HFFT). The two parameters of the theory are the frequency omega and the classical excursion parameter alpha0[equivalent]E0omega−2, where E0 is the electric field strength. HFFT solves the Floquet system by successive iterations. Convergence of the iteration procedure was shown to be ensured by the condition that omega be suffiently large with respect to some typical atomic excitation energy. We now establish that the same iteration procedure is capable of handling the case of low frequency at sufficiently high intensity. This leads to the conclusion that in this case the ionization rates display quasistationary stabilization also at low omega. The concept is thus not exclusively related to high frequencies, as widely assumed. In addition, it suggests that a more appropriate designation for the theory should be ``high-intensity, high-frequency Floquet theory' (HIHFFT). Our general results are applied to a frequently used one-dimensional (1D) soft-core potential model, for which explicit analytic results can be obtained for the quasienergies and wave functions from the general HIHFFT formulas. The relevance of these quasistationary results for the case of laser pulses is pointed out.
Phys. Rev. A

Gavrila, M., Simbotin, I., & Stroe, M. (2008). Low-frequency atomic stabilization and dichotomy in superintense laser fields from the high-intensity high-frequency Floquet theory. Phys. Rev. A, 78(3, Article number: 33404), 1–12. doi:10.1103/PhysRevA.78.033404