  Semiconductor microresonators embedding quantum wells can host tightly
confined and mutually interacting excitonic, optical and mechanical modes at
once. We theoretically investigate the case where the system operates in the
strong exciton-photon coupling regime, while the optical and excitonic
resonances are parametrically modulated by the interaction with a mechanical
mode. Owing to the large exciton-phonon coupling at play in semiconductors, we
predict an enhancement of polariton-phonon interactions by two orders of
magnitude with respect to mere optomechanical coupling: a near-unity
single-polariton quantum cooperativity is within reach for current
semiconductor resonator platforms. We further analyze how polariton
nonlinearities affect dynamical back-action, modifying the capability to cool
or amplify the mechanical motion.
