Normal-mode splitting, sideband cooling and force sensitivity in a linear and quadratic optomechanical system with phase noise

Abstract In a linear and quadratic optomechanical system (OMS) with optical parametric amplifier's phase noise, we consider a study on normal-mode splitting, sideband cooling and force sensitivity. The system encompasses an optical cavity, a mechanical membrane and a degenerate optical parametric amplifier (OPA). When there is OPA's pump phase noise, normal-mode splitting still occurs and displays more complex splitting than the case of no phase noise. Specifically, for increasing quadratic coupling, the left peak shrinks steadily until it vanishes while the right peak increases to a larger value. In addition, the nonlinear gain of OPA and the quadratic coupling parameter play a key role as cooling the mechanical membrane in the existence of certain phase noise. Phase noise needs to be reduced, and the proper parameters (i.e., the nonlinear gain of OPA and the quadratic coupling) are helpful to improve the cooling effect. Furthermore, in the presence of OPA's phase noise, when the value of quadratic coupling is negative, the standard quantum limit is beaten and force sensitivity can be enhanced with the higher negative values of quadratic coupling. In the realm of quantum optomechanics, our proposed scheme has viable applications in enhancing the performance of quantum manipulation and precision measurement.