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 ${W}_{0}=\ensuremath{-}0.500\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$) in a laser field of constant amplitude ${E}_{0}$ and frequency $\ensuremath{\omega}$. The excursion parameter ${\ensuremath{\alpha}}_{0}={E}_{0}∕{\ensuremath{\omega}}^{2}$ was varied over the range $0l{\ensuremath{\alpha}}_{0}l100$, at two low frequencies $\ensuremath{\omega}=0.12$ and $0.24\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ $(\ensuremath{\omega}l\ensuremath{\mid}{W}_{0}\ensuremath{\mid})$; the lowest-lying 18 states were computed. We present graphs for the ${\ensuremath{\alpha}}_{0}$ dependence of the energies of the states in the field, $W({\ensuremath{\alpha}}_{0})=\mathrm{Re}\phantom{\rule{0.2em}{0ex}}E$ (``Floquet maps''), and their ionization rates $\ensuremath{\Gamma}({\ensuremath{\alpha}}_{0})$. An intricate behavior of $W({\ensuremath{\alpha}}_{0})$ was revealed at low ${\ensuremath{\alpha}}_{0}$, with many crossings, avoided crossings (ACs), and Floquet states materializing or disappearing at multiples of $\ensuremath{\omega}$ energy thresholds. At large ${\ensuremath{\alpha}}_{0}$, however, the uneventful pattern encountered at high frequencies is regained, in which the levels tend monotonically to zero modulo $\ensuremath{\omega}$ (i.e., the binding energies of all states vanish). Also $\ensuremath{\Gamma}({\ensuremath{\alpha}}_{0})$ varies substantially at low ${\ensuremath{\alpha}}_{0}$, attaining sometimes large values, but at large ${\ensuremath{\alpha}}_{0}$ 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 ${\ensuremath{\alpha}}_{0}$, 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 ${\ensuremath{\alpha}}_{0}$, and in particular the existence of QS and dichotomy.
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May 26, 2021
Yifan Xing + 4
Open Access
