Non-Linear Interactions in Pump-Probe Optical Phenomena

Reduced density matrix descriptions are developed for pump-probe optical phenomena in atomic systems, taking into account atomic collisions as environmental phenomena. Time-domain (equation-of-motion) and frequency-domain (resolvent- operator) formulations are developed in a unified manner. In a semiclassical perturbative treatment of the electromagnetic interaction, compact Liouville-space operator expressions are derived for the linear and the general (n'th order) non-linear electromagnetic-response tensors. These expressions are valid for coherent atomic excitations and for the full tetradic-matrix form of the collision operator in the Markov approximation.