In the preceding paper we have shown, based on the high-intensity, high-frequency Floquet theory (HIHFFT), that atomic quasistationary stabilization (QS) and dichotomy are not necessarily high-frequency phenomena as widely believed, but can occur also at photon energies small with respect to the unperturbed ground state binding energy, provided that the field is strong enough. In this paper we approach the issue from the point of view of accurate numerical Floquet computations. We have made a comprehensive determination of the Floquet quasienergies for a one-dimensional (1D) atomic model with a soft-core Coulomb potential (ground state energy W0=−0.500 a.u.) in a laser field of constant amplitude E0 and frequency omega. The excursion parameter alpha0=E0/omega2 was varied over the range 0<alpha0<100, at two low frequencies omega=0.12 and 0.24 a.u. (omega<|W0|); the lowest-lying 18 states were computed. We present graphs for the alpha0 dependence of the energies of the states in the field, W(alpha0)=Re E (“Floquet maps”), and their ionization rates Gamma(alpha0). An intricate behavior of W(alpha0) was revealed at low alpha0, with many crossings, avoided crossings (ACs), and Floquet states materializing or disappearing at multiples of omega energy thresholds. At large alpha0, however, the uneventful pattern encountered at high frequencies is regained, in which the levels tend monotonically to zero modulo omega (i.e., the binding energies of all states vanish). Also Gamma(alpha0) varies substantially at low alpha0, attaining sometimes large values, but at large alpha0 it decreases to zero in an oscillatory manner (QS). The form of the components of the Floquet wave function was also followed from low to large alpha0, and abrupt changes were found in most cases at ACs. The Floquet results were then compared to a computation of the HIHFFT formulas for the quasienergies and good agreement was found (to within the expected accuracy of HIHFFT). This confirms that HIHFFT is fully capable of describing the low-frequency regime at large enough alpha0, and in particular the existence of QS and dichotomy.
Phys. Rev. A

Stroe, M., Simbotin, I., & Gavrila, M. (2008). Low-frequency atomic stabilization and dichotomy in superintense laser fields : Full Floquet results. Phys. Rev. A, 78(Article number: 33405), 1–11. doi:10.1103/PhysRevA.78.033405