Classical demonstration of frequency-dependent noise ellipse rotation using optomechanically induced transparency

Cavities with an extremely narrow linewidth of 10-100 Hz are required for realizing frequency-dependent squeezing to enable gravitational wave detectors to surpass the free mass standard quantum limit over a broad frequency range. High-finesse cavities on the scale of tens of meters have been proposed for this purpose. Optomechanically induced transparency (OMIT) enables the creation of optomechanical cavities in which the linewidth limit is set by the extremely narrow linewidth of a high-Q-factor mechanical resonator. Using an 85-mm OMIT cavity with a silicon nitride membrane, we demonstrate a tunable linewidth from 3 Hz up to several hundred hertz and frequency-dependent noise ellipse rotation using classical light with squeezed added noise to simulate quantum squeezed light. The frequency-dependent noise ellipse angle is rotated in close agreement with predictions.