  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.
