Single-photon nonlinearities in a strongly driven optomechanical system with quadratic coupling

Abstract

Optical nonlinearities at the single-photon level are explored in a quadratically coupled optomechanical system, where the cavity frequency is coupled to the square of the mechanical displacement. The effective nonlinear interaction between photons and phonons is enhanced by a strong driving field, which allows one to implement the single-photon nonlinearities even if the single-photon coupling strength ${g}_{0}$ is much lower than the cavity decay rate $\ensuremath{\kappa}$. The photon statistical properties are discussed by calculating the second-order correlation function both analytically and numerically. The results show that the single-photon nonlinearities are robust against mechanical thermal noise in the strong-coupling and sideband-resolved regime, and photon blockade and photon-induced tunneling can be realized with experimentally accessible parameters.