Nonlinear effects in a Floquet-driven optomechanical system

Abstract

We investigate theoretically the nonlinear effects in a Floquet-driven optomechanical system with quadratic coupling. When the periodically modulated driving field is strong, we establish an effective time-dependent model to describe this system. Using the Keldysh approach, we calculate the retarded Green's function to study the response behavior of the system to external probing. We find that when the $n\mathrm{th}$ sideband of a probe field satisfies the condition of two-phonon resonance, the transparency window occurs. In addition, we find some abnormal behaviors of the output field, which have no counterpart in the standard optomechanical models. These results provide a promising platform for controlling light propagation and light manipulation operations which have potential applications in quantum precision measurement techniques.