Generalized Kramers-Heisenberg expressions for stimulated Raman scattering and two-photon absorption

The frequency-domain pump-probe signal of a material system interacting with two quantum modes of the radiation field is recast in terms of products of scattering amplitudes (T matrix elements) rather than the third-order susceptibility Im chi((3)). The resulting expression offers a more intuitive physical picture for the optical process compared with the semiclassical approach which treats the radiation field as classical. It can be derived and interpreted using closed-time-path-loop diagrams which represent the joint state of the matter and the field for each contribution to the signal. The signal has two components representing stimulated Raman scattering omega(1)-omega(2) and two-photon absorption omega(1)+omega(2) two-photon resonances. Both are expressed as nonequilibrium steady-state photon and matter fluxes, as is common in the description of dissipative processes in open quantum systems.