Theory of coherent oscillation of phonon-polaritons

We formulate a theory to describe the coherent dynamics of phonon-polaritons in nonlinear ionic crystals. By quantizing the Born-Huang theory of the coupled phonon-photon system we first construct our model Hamiltonian. Then, applying a nonequilibrium statistical mechanics for the open quantum system, we derive the macroscopic equations for the transverse, coherent amplitudes. The resulting nonlinear equations with damping axe solved for the coupled harmonic oscillators numerically. Our theory predicts the nontrivial, nonlinear beating between two coherent polariton modes with the characteristic decay.