Rate equations for multi-photon excitation in strong fields

The excitation of an N-level quantum oscillator by a strong oscillating electric field in the presence of external perturbations can in general be described by a Boltzmann equation for the density matrix. In this paper it is shown that under certain circumstances this may be reduced to a set of rate equations for the level populations. In contrast to the weak field situation, these rate equations explicitly contain multi-photon transition rates.