Optomechanical systems with nonlinear interactions: photon blockade, collapse-revival effect and Fano-like resonance

Closed-form expressions for the average amplitude of the optical field in optomechanical systems are obtained, in which, in addition to the linear interaction, quadratic and cubic interactions of the vibrational mode of the mechanical resonator with the mode of the optical resonator are considered. In the framework of the non-secular perturbation theory, using the Bogoliubov averaging method, it is shown that the effects of photon blockade, collapse and revival of optical oscillations in such systems can be realized. The main contribution to the formation of revivals is provided by the Kerr self-action of the optical mode and the cross-Kerr interaction of the fourth degree in optical and mechanical amplitudes. The cross-Kerr interactions of the sixth- and eighth-order in amplitudes destroy the regular structure of revivals. The influence of these cross-Kerr nonlinearities disappears with an increase in the decay rate of the optical mode and is also completely suppressed at zero temperature. It is shown that the asymmetry of the spectral line of the optical field intensity in the cavity is most pronounced with an increase in the degree of nonlinearity and is explained by Fano interference.