FLOQUET THEORY RESPONSE OF 2-LEVEL AND 3-LEVEL SYSTEMS INTERACTING WITH PULSED ELECTRIC-FIELDS

Using Floquet theory together with a density matrix formalism, analytic expressions are derived that describe a typical pump-probe experiment on (a) a two-level, one-photon resonant model that mimics a system with two electronic states, and (b) a two-photon resonant three-level model. The time dependence of the amplitude of the pulsed electric fields is approximated by a square envelope. These expressions, which include all orders of the electric field, can be used to describe systems interacting with very intense fields, where perturbation theory fails. This description allows variation of both the order of the pump and probe pulse, as well as the pulse durations. These expressions, once expanded, are equivalent to the usual perturbative series expansion, within the square-envelope approximation. Using a delta function approximation for the pulsed fields, a two-level system with an excited state vibrational manifold is also considered in a nonperturbative manner.