Resonant Multiphoton Excitations by Strong Driving Fields

Multiphoton transitions are discussed for the case of a resonant driving field strong enough to produce saturation. The atomic system is described in general terms, and the possibility of inversion asymmetry is allowed. The equations of motion for the density submatrix referring to the pair of resonantly coupled states are found by expanding the full atomic density operator in harmonics of the field frequency, and then systematically reducing the equations of motion which result. The effective $n$-photon coupling parameter and the shift in resonance frequency emerge naturally from this reduction.