Parametric down-conversion and polariton pair generation in optomechanical systems.

We demonstrate that the nonlinear optomechanical interaction leads to parametric down-conversion, capable of generating polariton pairs formed by photons and phonons. The nonlinearity is resonantly enhanced through frequency matching, and such parametric down-conversion does not require the stringent condition that the single-photon optomechanical coupling strength g be on the order of the mechanical resonance frequency ω(m). We provide analytical results for the frequency matching condition and derive the nonlinear coefficient. Numerical simulations on polariton pair generation are presented, showing that photonlike polaritons, phononlike polaritons, and mixed photon-phonon polaritons can be selectively generated. Such nonlinear interaction offers a promising way for harnessing the optomechanical nonlinearity to manipulate photons and phonons.