Real photons from vacuum fluctuations in optomechanics: the role of polariton interactions

We study nonlinear interactions in a strongly driven optomechanical cavity, in regimes where the interactions give rise to resonant scattering between optomechanical polaritons and are thus strongly enhanced. We use a Keldysh formulation and self-consistent perturbation theory, allowing us to include self energy diagrams at all orders in the interaction. Our main focus is understanding how non-equilibrium effects are modified by the polariton interactions, in particular the generation of non-zero effective polariton temperatures from vacuum fluctuations (both in the incident cavity drive and in the mechanical dissipation). We discuss how these effects could be observed in the output spectrum of the cavity. Our work also provides a technical toolkit that will be useful for studies of more complex optomechanical systems.