Quantum-statistics of stimulated hyper-Raman scattering in an inhomogeneously broadened system under three-photon resonance condition

A fully quantum mechanical density-matrix formalism of stimulated hyper-Raman scattering is presented. The effects of atomic motion, higher-order non-linearities and losses are included. The equations are solved exactly under the three-photon resonance condition and a situation of low losses. The photon-statistics of the Stokes field is studied in the steady-state. The coherence characteristics are studied.