Critical quantum fluctuations and photon antibunching in optomechanical systems with large single-photon cooperativity

A pertinent question in cavity optomechanics is whether reaching the regime of large single-photon cooperativity, where the single-photon coupling rate exceeds the geometric mean of the cavity and mechanical decay rates, can enable any new phenomena. We show that in some multimode optomechanical systems, the single-photon cooperativity can indeed be a figure of merit. We first study a system with one cavity mode and two mechanical oscillators, which combines the concepts of levitated optomechanics and coherent scattering with standard dispersive optomechanics. Later, we study a more complicated setup involving three cavity modes which does not rely on levitated optomechanics and only features dispersive optomechanical interactions with direct cavity driving. These systems can effectively realize the degenerate or the nondegenerate parametric oscillator models known from quantum optics, but in the unusual finite-size regime for the fundamental mode(s) when the single-photon cooperativity is large. We show that the response of these systems to a coherent optical probe can be highly nonlinear in probe power even for average photon occupation numbers below unity. The nonlinear optomechanical interaction has the peculiar consequence that the probe drive will effectively amplitude-squeeze itself. For large single-photon cooperativity, this occurs for small occupation numbers, which enables observation of nonclassical antibunching of the transmitted probe photons due to a destructive interference effect. Finally, we show that as the probe power is increased even further, the system enters a critical regime characterized by intrinsically nonlinear dynamics and non-Gaussian states