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

TL;DR

This paper demonstrates a 1064nm negative dispersion medium using an optomechanical microresonator to enhance the bandwidth of gravitational-wave detectors, including a stabilization method for the system.

Contribution

It introduces a novel 1064nm optomechanical microresonator-based negative dispersion medium for gravitational-wave detectors, extending previous GEIT systems to operational wavelengths.

Findings

Achieved a sensitivity-bandwidth enhancement factor of ~15.

Implemented a feedback control to stabilize the optomechanical system.

Demonstrated negative dispersion at 1064nm in a microresonator.

Abstract

Recently, we had proposed an optically-pumped five-level Gain EIT (GEIT) system, which has a transparency dip superimposed on a gain profile and exhibits 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 the WLC-SR (signal recycling) scheme, we get an enhancement in the quantum noise (QN) limited sensitivity-bandwidth product by a factor of ~18. We have also shown how to realize such a system in practice using Zeeman sublevels in $^{87}$Rb at 795nm [Opt. Commun. 402, 382-388 (2017)]. However, aLIGO operates at 1064nm and suitable transitions in Rb or other alkali atoms are not available at this wavelength. Therefore, it is necessary to consider a system that is consistent with the operating wavelength of aLIGO. Here, we present the realization of such an NDM at 1064nm with a microresonator, which supports optomechanical interaction. A strong control field is applied at a higher frequency, and, under certain conditions, a probe field at a lower frequency experiences a peak at the center of an absorption profile, and a negative dispersion in the transmission. Unlike in the GEIT case, we use the compound-cavity signal-recycling (CC-SR) scheme, where an auxiliary mirror is inserted in the dark port of the detector, and show that the enhancement factor can be as high as ~15. However, using the parameters required for the sensitivity enhancement, the optomechanical system enters an instability region where the control field is depleted. We present an observer based feedback control process used to stabilize the CC-SR system.