Cavities with 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. Hundred-meter-scale high finesse cavities 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 85mm OMIT cavity with a silicon nitride membrane, we demonstrate a tunable linewidth from 3Hz up to several hundred Hz 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. Introduction-The coherent interaction of laser radiation with widely spaced mirror test masses is used to measure gravitational wave induced motions in interferometric gravitational-wave detectors. The sensitivity of first generation gravitational wave (GW) detectors such as LIGO reached the quantum shot noise limit in the high frequency part of the spectrum. In the second generation detectors now under construction, quantum radiationpressure noise is expected to dominate at low frequencies, while shot noise will dominate at high frequencies. A region around 100Hz is limited by classical test mass thermal noise, but as better optical coatings and test masses become available, future detectors should be limited mostly by quantum noise.In the late 1960s, Braginsky pointed out that there exists a Standard Quantum Limit (SQL) in gravitational wave detectors [1], and proposed that quantum nondemolition (QND) devices could beat the SQL [2]. In 2001, Kimble et al. [3] proposed QND interferometer designs that involved the use of pairs of successive filter cavities for realizing frequency-dependent squeezing (FDS) of the input squeezed light, or frequency dependent (FD) homodyne detection in which the output field of the detector is filtered in the frequency dependent way. They pointed out that pairs of successive Fabry-Pérot filter cavities can be used to convert ordinary squeezed light into FD squeezed light such that the sensitivity of the detector across the entire frequency band is improved below the SQL. Similar cavities could also be installed between the interferometer output and the ordinary homodyne detection to realize FD-homodyne detection. Recently Chelkowski et al. demonstrated FD squeezed vacuum using a short filter cavity in the MHz range [4]. In 2012, Stefszky et al. demonstrated 11.6 dB squeezing in aLIGO detection band [5].To match the filter cavity linewidth to the corner frequency of ground based laser interferometers where the shot noise becomes higher than the radiation pressure noise, the filter cavity must meet very demanding speci-