  We propose using optomechanical interaction to narrow the bandwidth of filter
cavities for achieving frequency-dependent squeezing in advanced
gravitational-wave detectors, inspired by the idea of optomechanically induced
transparency. This not only allows us to achieve narrow bandwidth, comparable
to the detection band of few hundred Hz, with tabletop optical cavities, but
also to tune the bandwidth over a wide range, which is ideal for optimizing
sensitivity for different gravitational-wave sources. The experimental
challenge for its implementation is the stringent requirement on low thermal
noise, which would need superb mechanical quality factor that is quite
difficult to achieve by using currently-available low-loss mechanical
oscillators; one possible solution is to use optical dilution of the mechanical
damping, which can considerably relax the requirement on the mechanics.
