Multiphoton processes in an intense laser field. V. The high-frequency regime

We present results of Floquet calculations of shifts and widths of the 1s and 2s energy levels of atomic hydrogen irradiated by intense linearly or circularly polarized light whose frequency ω is above the (weak-field) threshold ${\mathrm{\omega }}_{\mathrm{thr}}^{\left(\mathit{i}\right)}$ for one-photon ioinzation from state i. We have studied the dependence of the shifts and widths on ω and on the intensity I. Where possible, we compare our results with those obtained from a high-frequency theory [M. Pont and M. Gavrila, Phys. Rev. Lett. 65, 2362 (1990)] that yields shifts that depend only on ${\mathrm{\alpha }}_0$ (∝ √I /${\mathrm{\omega }}^2$), the excursion amplitude of a free electron, rather than on I and ω separately. As I increases, with ω fixed, the width reaches a maximum value ${\mathrm{\Gamma }}_{\max }$ at an intensity ${\mathit{I}}_{\max }$ for which √(ħω/2P) ≊1, where P==2πI/μc${\mathrm{\omega }}^2$, the ponderomotive shift. As I increases beyond ${\mathit{I}}_{\max }$, the width decreases toward zero, in accord with the high-frequency theory, and the shift approaches the result of that theory. (For different fixed ω, the shifts first cross the ω=∞ curve as ${\mathrm{\alpha }}_0$ increases, and they intersect, almost at a common value of ${\mathrm{\alpha }}_0$, before approaching the ω=∞ curve.) As ω increases, ${\mathit{I}}_{\max }$ increases as roughly ${\mathrm{\omega }}^3$, and ${\mathrm{\Gamma }}_{\max }$ decreases. If ω is sufficiently large, we find that (2π/ω)${\mathrm{\Gamma }}_{\max }$/ħ${\mathrm{\omega }}_{\mathrm{thr}}^{\left(\mathit{i}\right)}$, we detect states that emerge from ‘‘shadow’’ states; these states allow for a continuous variation of the shift and width across the threshold. Furthermore, we conjecture that the rise and fall of the width, in the vicinity of ${\mathit{I}}_{\max }$, occurs through an interaction between shadow and real (or ‘‘dominant’’) states.