Giant enhancement of tunable optomechanical coupling via ultrarefractive medium

Exploring the fundamental quantum behaviour of optomechanical resonators is of great interest recently but requires the realization of the strong coupling regime. We study the optical photon-phonon coupling of the so-called membrane in the middle (MITM) optomechanical system. Using coupled-mode theory we find that the optomechanical coupling is proportional to the electric susceptibility of the membrane. By considering the doping atoms or spins into the membrane and driving these appropriately we induce a tunable ultra-large refractive index without absorption which enhances the optomechanical coupling. Using this we predict an ultra-strong single-optical photon strong coupling with large quantum cooperativity for Er3+ dopants at low temperature, while Cr3+ in a Ruby membrane may display ultra-large quantum cooperativity at room temperature. Our scheme also can tune the strength of the coupling over a wide range and can also control whether the optomechanical force is attractive or repulsive. Our work opens a door for fundamental physics and applications relying on the realization of the strong coupling regime in quantum optomechanical systems.