Generalized Floquet theoretical methods for nonperturbative treatments of Schrodinger and Liouville equations in the presence of strong fields

Abstract

Abstract We present a brief description of some generalized Floquet formalisms and numerical methods recently developed in our laboratory for nonperturbative treatments of the time-development of wave functions or density matrix operator of quantum systems driven by intense periodic or multi-color (multi-frequency) laser fields. Both the Schrodinger and Liouville equations are considered. In all cases, it is shown that the time-dependent (monochromatic or polychromatic) problems can be exactly transformed into equivalent time-independent infinite-dimensional (Hermitian or non-Hermitian) matrix (or super matrix) eigenvalue problems. These yield numerically stable and computationally efficient techniques for the unified treatment of one- and multiple- photon, resonant and non-resonant, steady-state and transient phenomena in strong fields. Applications of the methods to intense-fielde multiphoton and nonlinear optical processes of current significance are briefly discussed.