Abstract
We theoretically analyze the properties of output spectrum of a quadratically coupled optomechanical system assisted by a gain optical cavity. This hybrid quadratically coupled optomechanical system can exhibit parity-time () symmetry by manipulating the gain-to-loss ratio of two-coupled optical cavities. We show that by adjusting the coupling coefficient of two cavities, optomechanically induced transparency (OMIT) phenomenon can be obtained in the broken--symmetric-like system. Furthermore, the OMIT window can be adjusted by the temperature and the power of the control field. In particular, in the unbroken--symmetric-like system, we can adjust the position of OMIT windows to appear in splitting eigenmodes. Our research will provide a powerful platform to explore the transmission and conversion of light in quantum information processes via microfabricated optomechanical systems.
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