Normal mode splitting and optical squeezing in a linear and quadratic optomechanical system with optical parametric amplifier

We theoretically investigate the normal mode splitting (NMS) in the displacement spectrum of a moving membrane and the output cavity field squeezing spectrum in an optomechanical system with a degenerate optical parametric amplifier (OPA) placed inside the cavity. In our proposed system, the cavity mode is coupled to this moving membrane (which acts as mechanical mode) through both the linear optomechanical coupling and the quadratic optomechanical coupling. We have shown that the nonlinear OPA gain G and the phase angle theta can effectively alter this NMS behavior in the displacement spectrum of the mechanical mode as well as output cavity field spectrum qualitatively as well as quantitatively. Furthermore, we can also enhance the squeezing bandwidth of the output cavity quadrature through both the parameters of OPA even at higher environment temperature T or in other words a significant mechanical thermal noise. Our study provides an efficient method to control the NMS behavior and the squeezing properties in such kind of generalized optomechanical systems.