Enhanced Nonlinear Interaction Effects in a Four-mode Cavity Optomechanical Ring*

With a perturbative treatment based on the Keldysh Green's function technique, we study the resonant enhancement of nonlinear interaction effects in a 4-mode optomechanical ring. In such a system, we identify five distinct types of resonant scattering between non-perturbed polariton modes, induced by the nonlinear optomechanical interaction. By computing the cavity density of states and optomechanical induced transparency (OMIT) signal, we find that the largest nonlinear effects are induced by a decay process involving the two phonon-like polaritons. In contrast to the conventional two-mode optomechanical system, our proposed system can exhibit prominent nonlinear features even in the regime when the the single-photon coupling is much smaller than the cavity damping.