Optomechanically Induced Transparency of Double-Cavity Optomechanical System with $$\mathcal{P}\mathcal{T}-$$ Symmetry and $$\mathcal{P}\mathcal{T}-$$ Asymmetry

Opto-mechanical systems have been investigated both theoretically and experimentally characteristic of optomechanically induced transparency (OMIT), i.e., sharp transmission features controlled by a second control beam. We studied theoretically the opto-mechanically induced transparency (OMIT) properties of double-cavity opto-mechanical system with \(\mathcal{P}\mathcal{T}-\)symmetry and \(\mathcal{P}\mathcal{T}\)-asymmetry within the setting of cavity quantum electrodynamics. By means of Fourier transformation we get the pump-probe spectroscopy exactly and find the second cavity plays important roles in the properties of probe beam transmission. The dip value of OMIT can reach zero which means perfect transmission. There appear two transparency windows for the probe beam in one resonator with the increasing power of control laser beam fed into the other resonator, especially the probe beam can obtain significant gain even without direct tunneling of photons between two resonators. We expect our results would be realized experimentally and be useful for the future designs of quantum functional devices.