Dynamics of population of a four-level atom due to one- and three-photon processes

The Schr\"odinger equation in the rotating-wave approximation has been solved nonperturbatively to study the temporal behavior of the occupation probabilities of different levels of a four-level atom interacting with four arbitrarily intense laser fields, such that the frequency of one of them equals the sum of the other three. The three-photon-excitation population dynamics, which is already complex, is strongly modified by one-photon excitation and detunings. Under certain conditions the three-photon excitation traps the population in the state initially populated; the population starts flowing into other states when one-photon excitation is also operative.