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

In a linear and quadratic optomechanical system with optical parametric amplifier’s (OPA) phase noise, we conduct a study on normal-mode splitting, sideband cooling and force sensitivity. The system encompasses an optical cavity, a mechanical membrane and a degenerate OPA. When there is OPA’s pump phase noise, normal-mode splitting still occurs and displays more complex splitting compared to scenarios without phase noise. Specifically, for increasing quadratic coupling, the left peak shrinks steadily until it vanishes, while the right peak increases to a larger value. Moreover, both the nonlinear gain of OPA and the quadratic coupling parameter play key roles in cooling the mechanical membrane in the presence of certain phase noise. Minimal phase noise and optimized values of the nonlinear gain of OPA and the quadratic coupling are essential for achieving enhanced cooling. Furthermore, in the presence of OPA’s phase noise, when the value of quadratic coupling is negative, the standard quantum limit is beaten. Higher negative values of quadratic coupling prove beneficial in achieving more stable force sensitivity. We believe that in the realm of quantum optomechanics, this scheme may have viable applications in quantum manipulation and precision measurement.