Tunable Electromagnetically Induced Multi-Transparencies in Hybrid Optomechanical system Incorporating Atomic Medium

We consider a hybrid atom-optomechanical system incorporating N identical $\Lambda$-type atoms. The system is subjected to dual optical and phononic drives. We show that by exploiting the optomechanical linear and quadratic interactions, multiple electromagnetic transparency windows are attained. Furthermore, owing to the incorporated mechanical pump, the transparency windows are controlled and tuned. For instance, by adjusting the phase of the external mechanical pump, additional controlling parameters are enabled, and the absorption/emission profiles are enhanced. Our present study provides an efficient approach to modifying propagating signals inside the quantum devices incorporating cavity-optomechanical systems.