Normal-mode splitting and ponderomotive squeezing in a nonlinear optomechanical system assisted by an atomic ensemble

We theoretically investigate the displacement spectrum of a movable mirror and squeezing spectrum of the cavity quadrature field in a hybrid optomechanical system (OMS), which contains a degenerate optical parametric amplifier (OPA) and N two-level cold atoms. In comparison with the bare OMS, when there is only an OPA in the optical cavity, with the increasing nonlinear gain of the OPA, peak separation of the normal-mode splitting (NMS) in the displacement spectrum and degree of the squeezing spectrum for the cavity quadrature field increase. Further, the simultaneous presence of both OPA and the atomic ensemble in the optical cavity ensures wider spacing in the NMS and greater degree of the squeezing spectrum than the OMS with just an OPA or an atomic ensemble. Further, a decrease in temperature ends the peak in the squeezing spectrum due to a reduction in mechanical thermal noise.