We theoretically investigate the optomechanically induced transparency (OMIT) phenomenon and the fast and slow light effects of a four-mode optomechanical system with the Kerr medium. The optomechanical system is composed of an array of three single-mode cavities and a mechanical oscillator. The three cavities are a passive cavity, a no-loss-gain cavity and a gain optical cavity, respectively. A Kerr medium is inserted in the passive cavity. We study the influence of the Kerr medium on the stability of the optomechanical system, and find that the stable regime of the optomechanical system can be adjusted by changing the Kerr coefficient. We demonstrate that the phenomenon of optomechanically induced transparency will appear when the Kerr medium exists in the optomechanical system and find that the frequency position of the absorption peak on the left increases linearly with the Kerr coefficient. In addition, we also investigate the fast and slow light effects in this system. The results show that we can control the fast and slow light by adjusting the Kerr coefficient, tunneling strength, and driving field strength. This study has potential application prospects in the fields of quantum optical devices and quantum information processing.
Squeezing in a coupled two-mode optomechanical system for force sensing below the standard quantum limit
