Multistate high-frequency Floquet theory

Floquet theory of laser-atom interactions operates with quasienergy states, either discrete, for the description of ionization, or continuous, for the description of free-free transitions. The use of individual states for these purposes, as currently done, impairs on the ability of the theory to describe realistic physical situations, due to the conditions that have to be met (adiabatic turn-on of the field to access the ionizing state desired, small ionization rate Gamma, etc.). We endeavor to eliminate these conditions by considering coherent superpositions of Floquet states. The possibility that arbitrary quantum mechanical wave packets be represented by such superpositions expresses the mathematical completeness of the states. Whereas rigorous proofs of completeness do exist in terms of states with real quasienergy, the type of expansion of interest for ionization, including states with discrete quasienergy, does not appear to be covered. We assume its possibility, and explore the consequences in the high-frequency case, from a pragmatic point of view. Our starting point is the single-state high-frequency Floquet theory (HFFT), expanded to include the second iteration within the theory. By expressing wave packets as superpositions of single HFFT states, we are introducing the ''multistate HFFT.'' We compare the predictions of the multistate HFFT with the results of wave-packet dynamics (WPD), as given by the time-dependent Schrodinger equation, for the 1D model with soft Coulomb potential, frequently used. We focus on the evolution of the populations in bound ''dressed states,'' which are eigenfunctions of the structure equation of the HFFT. For a variety of initial conditions, the agreement obtained is remarkable, which indicates the potential of multistate HFFT, and confirms operationally our mathematical assumption.