MASTER EQUATION FOR 2-PHOTON TRANSITIONS

We utilize Liouville-space and projection operator methods, introducing additional atomic projection operators, and derive master equations for an atom coupled to a radiation reservoir and to an additional external field via multi-photon interactions; the explicit forms of the equations are studied in detail for two-photon processes. The coupling coefficients of the equations are expressed in terms of effective operators for two-photon transitions. The expression for the probability of transfer of coherence via the two-photon transitions and for the dephasing due to elastic interactions with the reservoir are obtained quantum mechanically for the first time.