A study on optomechanically induced transparency (OMIT) and the output power at the Stokes (anti‐Stokes) frequency in a hybrid optomechanical system is presented. The system consists of a Fabry–Pérot cavity, two non‐absorbing membranes, and a degenerate optical parametric amplifier (OPA), where the coupling interaction between the cavity and each membrane is quadratic. This study shows that spacing between two transparency window dips in a wider detuning range and the higher transparency efficiency can be achieved by selecting the suitable strength of the quadratic coupling. In addition, it is also found that frequencies of the two mechanical membranes, the nonlinear gain of the OPA, and phase of the field driving OPA can exert a striking influence on the output power at the Stokes (anti‐Stokes) frequency. Specifically, with the increase of the nonlinear parameter of OPA, spacing between two dips on the normalized output power at the Stokes frequency becomes much wider for two membranes with the same frequency. Three peaks on the normalized output power at the anti‐Stokes frequency appear in a larger detuning. In quantum engineering, this scheme may have potential applications in enhancing the performance of OMIT devices.

中文翻译：

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具有参数放大器的多模二次耦合系统中的透明度，斯托克斯和反斯托克斯过程

提出了一种在混合光机械系统中进行光机械诱导透明度（OMIT）和斯托克斯（反斯托克斯）频率输出功率的研究。该系统由一个Fabry–Pérot腔，两个非吸收膜和一个退化的光学参量放大器（OPA）组成，其中腔与每个膜之间的耦合相互作用是二次的。这项研究表明，通过选择合适的二次耦合强度，可以在较宽的失谐范围内获得两个透明窗口下陷之间的间距，并且可以实现更高的透明效率。此外，还发现两个机械膜的频率，OPA的非线性增益以及场驱动OPA的相位都可以在斯托克斯（反斯托克斯）频率下对输出功率产生显着影响。具体来说，随着OPA非线性参数的增加，对于具有相同频率的两个膜，在斯托克斯频率下归一化输出功率的两个骤降之间的间隔变得更宽。反斯托克斯频率下归一化输出功率的三个峰值出现在较大的失谐中。在量子工程中，该方案在增强OMIT器件的性能方面可能具有潜在的应用。