A hybrid microwave-optomechanical system under the effect of an optical parametric amplifier

We theoretically investigate a hybrid electro-optomechanical system consisting of an optomechanical cavity and a microwave one. Optomechanical cavity is filled with an optical parametric amplifier, and the system is driven by two optical fields (a pump laser and a weak probe one) and a microwave signal. We describe the dynamics of the system by the Heisenberg-Langevin equations of motion. We show that the presence of the optical parametric amplifier can affect dramatically on the transmission coefficient of the optomechanical cavity at the frequency of the probe field. Also, we demonstrate that the presence of the parametric amplifier can enhance the sensitivity of the system to changing of the input microwave power. Therefore, it is observed that, the parametric amplifier can improve the detection of a weak microwave signal via proposed system.