Optomechanical resonator as a negative dispersion medium for enhancing the sensitivity bandwidth in a gravitational-wave detector
Optomechanical resonator as a negative dispersion medium for enhancing the sensitivity bandwidth in a gravitational-wave detector
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光机谐振器作为负色散介质，用于增强引力波探测器的灵敏度带宽
作者：
Minchuan Zhou;S. Shahriar
最近，我们提出了一种光泵浦五能级增益EIT （GEIT）系统，该系统具有叠加在增益曲线上的透明度dip，并且具有适合于白光腔（WLC）增强干涉引力波探测器的负色散。Rev. D. 92,08(2015)]。在WLC-SR（信号回收）方案中使用该系统作为负色散介质（NDM），量子噪声（QN）的限制灵敏度-带宽积提高了约18倍。我们还展示了如何在795nm下使用$^{87}$Rb的Zeeman子电平在实践中实现这样的系统[Opt. comm . 402, 382-388(2017)]。然而，aLIGO的工作波长为1064nm，而Rb或其他碱原子在该波长没有合适的跃迁。因此，有必要考虑与aLIGO工作波长一致的系统。在这里，我们提出了一个支持光力学相互作用的微谐振器在1064nm实现这样的NDM。在较高的频率处施加强控制场，在一定条件下，较低频率的探测场在吸收剖面的中心处出现峰值，在传输中出现负色散。与GEIT不同的是，我们使用了复合腔信号回收（CC-SR）方案，在探测器的暗口插入一个辅助镜，并表明增强因子可以高达~15。然而，使用提高灵敏度所需的参数，光机械系统进入一个控制场耗尽的不稳定区域。我们提出了一种基于观测器的反馈控制过程，用于稳定CC-SR系统。
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.