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Cavities with extremely narrow linewidth of 10-100 Hz are required forrealizing frequency dependent squeezing to enable gravitational wave detectorsto surpass the free mass standard quantum limit over a broad frequency range.Hundred-meter-scale high finesse cavities have been proposed for this purpose.Optomechanically induced transparency (OMIT) enables the creation ofoptomechanical cavities in which the linewidth limit is set by the extremelynarrow linewidth of a high Q factor mechanical resonator. Using an 85mm OMITcavity with a silicon nitride membrane, we demonstrate a tunable linewidth from3Hz up to several hundred Hz and frequency dependent noise ellipse rotationusing classical light with squeezed added noise to simulate quantum squeezedlight. The frequency dependent noise ellipse angle is rotated in closeagreement with predictions.

Classical demonstration of frequency dependent noise ellipse rotation using Optomechanically Induced Transparency