  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.
