Superradiance and Collective Gain in the Atom-Assisted Multimode Optomechanical System

We investigate that the muti-mode optomechanical system coupled with the two-level atoms. If the driving pump field is resonance with the anti-Stokes sideband, the system is at the superradiative state. For the driving filed in the Stokes sideband, the collective gain can be observed. We study a scheme that how the atomic medium affect these superradiance and collective gain. Our results show that the presence of the atom can enhance the superradiant behavior. In the mode splitting regime, the mode splits into thirds with the presence of the atoms with the anti-Stokes sideband. In addition, we also show that the use of atoms in this system could provide us a way to switch the system form superradiative state to collective gain.