Multiple transparency in a multimode quadratic coupling optomechanical system with an ensemble of three-level atoms

Abstract

We theoretically investigate a multimode quadratic coupling optomechanical system (OMS) assisted with N cold Λ-type three-level atoms. The coupling interaction between two mechanical membranes (MR1 and MR2) and the cavity is quadratic. The three-level atoms interact with an external controlling field and an internal cavity field. The optical cavity is driven by a strong coupling field and a weak probe field. In the resolved sideband regime, four transparency windows are obtained due to the atomic coherence and quadratic coupling in the absorption spectrum for the suitable choice of the controlling parameters. We analyze how to vary the number of the transparency window dips and to adjust their mutual spacing by changing the controlling parameters such as strength of the quadratic coupling between MR1 (MR2) and the cavity, the collective coupling strength between the atomic ensemble and the cavity field, the Rabi frequency associated with the coupling interaction between the controlling field and the three-level atom, power of the coupling field, different frequencies and decay rates of MR1 (MR2), decay rate of the cavity field, and the environmental temperature. Further, we also demonstrate the normal-mode splitting in the generated Stokes and anti-Stokes field in the OMS, where the changing collective coupling strength affects the splitting width of the output field at the Stokes (anti-Stokes) frequency.