  Engineering strong single-photon optomechanical couplings is crucial for
optomechanical systems. Here, we propose a hybrid quantum system consisting of
a nanobeam (phonons) coupled to a spin ensemble and a cavity (photons) to
overcome it. Utilizing the critical property of the lower-branch polariton
(LBP) formed by the ensemble-phonon interaction, the LBP-cavity coupling can be
greatly enhanced by three orders magnitude of the original one, while the
upper-branch polariton (UBP)-cavity coupling is fully suppressed. Our proposal
breaks through the condition of the coupling strength less than the critical
value in previous schemes using two harmonic oscillators. Also, strong Kerr
effect can be induced in our proposal. This shows our proposed approach can be
used to study quantum nonlinear and nonclassical effects in weakly coupled
optomechanical systems.
