Resonant Scattering of Photons from an Atom-Lattice System

We investigate the resonant scattering of photons from an atom in the thermal equilibrium with a phonon bath. A two-level model of the atom is discussed in detail. In the model problem, the atom is coupled directly to the lattice through a diagonal interaction which is bilinear in the lattice quanta. Relaxation effects are introduced indirectly via correlation functions. In the limit in which the relaxation time is much shorter than the radiative lifetime, the frequency spectrum of the scattered radiation consists of three parts: (1) a coherent, elastic term weighted by the factor ${tanh}^2\left(\frac{\hslash {\omega }_0}{2KT}\right)$, (2) an incoherent quasielastic term weighted by the factor [$1-{tanh}^2\left(\frac{\hslash {\omega }_0}{2KT}\right)$], (3) a fluorescent term characterizing emission at the natural frequency ${\omega }_0$, which arises from an effective two-photon-two-phonon interaction. The extension of the analysis to the problem of resonant scattering from paramagnetic ions in crystals is outlined with particular emphasis on the influence of neighboring ionic levels and the relative importance of the one- and two-phonon processes.