Enhancing the force sensitivity of squeezed light optomechanical interferometer

Application of frequency-dependent squeezed vacuum improves the force sensitivity of optomechanical interferometer beyond the standard quantum limit by a factor of $e^{-r}$, where $r$ is the squeezing parameter. In this work, we show that the application of squeezed light along with quantum optical restoring force can enhance the sensitivity beyond the standard quantum limit by a factor of $\sqrt{e^{-2r}\zeta/4\Delta}$, where $0< \zeta/\Delta <1$, with $\zeta$ as the optomechanical cavity decay rate and $\Delta$ as the detuning between cavity eigenfrequency and driving field. The technique described in this article is restricted to frequencies much smaller than the resonance frequency of the optomechanical mirror.