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Recently, we had proposed an optically-pumped five-level Gain EIT (GEIT)system, which has a transparency dip superimposed on a gain profile andexhibits a negative dispersion suitable for the white light cavity (WLC)enhanced interferometric gravitational wave detector [Phys. Rev. D. 92, 082002(2015)]. Using this system as the negative dispersion medium (NDM) in theWLC-SR (signal recycling) scheme, we get an enhancement in the quantum noise(QN) limited sensitivity-bandwidth product by a factor of ~18. We have alsoshown how to realize such a system in practice using Zeeman sublevels in$^{87}$Rb at 795nm [Opt. Commun. 402, 382-388 (2017)]. However, aLIGO operatesat 1064nm and suitable transitions in Rb or other alkali atoms are notavailable at this wavelength. Therefore, it is necessary to consider a systemthat is consistent with the operating wavelength of aLIGO. Here, we present therealization of such an NDM at 1064nm with a microresonator, which supportsoptomechanical interaction. A strong control field is applied at a higherfrequency, and, under certain conditions, a probe field at a lower frequencyexperiences a peak at the center of an absorption profile, and a negativedispersion in the transmission. Unlike in the GEIT case, we use thecompound-cavity signal-recycling (CC-SR) scheme, where an auxiliary mirror isinserted in the dark port of the detector, and show that the enhancement factorcan be as high as ~15. However, using the parameters required for thesensitivity enhancement, the optomechanical system enters an instability regionwhere the control field is depleted. We present an observer based feedbackcontrol process used to stabilize the CC-SR system.

Negative dispersion medium at 1064 nm in an optomechanical resonator for enhancing the sensitivity bandwidth in a gravitational-wave detector