Normal-Mode Splitting and Optomechanically Induced Absorption, Amplification, and Transparency in a Hybrid Optomechanical System

The various properties of the output spectrum for a probe field in a hybrid optomechanical system that is composed of two cavities, each containing an atomic ensemble and a mechanical resonator, is analyzed. Also, the normal-mode splitting behaviors induced by the interactions between subsystems in detail are discussed and their respective effects are clarified. The interpretations for the linear variation of the separation between two absorption peaks is given out. In the available parameter regime, three tunnel coupling critical points, which describe the transition behaviors between absorption and amplification, are determined. Based on the first critical point, the influence of the two-level atomic ensemble on absorption (amplification) effect is studied. The effect of the two-level atomic ensemble not only splits the absorption peak (amplification dip), but also realizes the enhancement of the absorption (amplification) effect and the transformation between absorption and amplification effects. Meanwhile, the one-to-one correspondence location relations between the transparency dip and absorption peak for the double optomechanically induced transparency-like and optomechanically induced absorption-like, respectively, are also investigated. With a multi-level atomic ensemble, the multi-transparency (absorption) effect is realized readily. These rich spectrum properties of the probe field may benefit forward achieving of the optical switch in experiment and possible applications in coherent control of light pulses.