Semiclassical analysis of long-wavelength multiphoton processes: The Rydberg atom

We study the problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons. An exact, nonperturbative approach is applied to the standard vector potential coupling Hamiltonian for a three-dimensional hydrogenlike atom in a microwave field treated semiclassically. Multiphoton probability exchange is calculated in both the velocity and the length gauges, by applying the GoeppertMayer gauge transformation. The expansion of the time-dependent solution in terms of Floquet states delineates the mechanism of multiphoton transitions. A detailed analysis of the Floquet states and quasienergies as functions of the field parameters allows us to describe the relation between avoided quasienergy crossings and multiphoton probability exchange. We formulate analytical expressions for the variation of quasienergies and Floquet states with respect to the field parameters, and demonstrate that avoided quasienergy crossings are accompanied by dramatic changes in the Floquet states. Analysis of the Floquet states, for small values of the field strength, yields selection rules for the avoided quasienergy crossings. In the case of strong fields, the simultaneous choice of frequency and strength of the field producing an avoided crossing results in improved ionization probability.