  We provide a systemic theory to entangle excitons with microcavity photons.
This is realized by adopting an exciton-optomechanics system and introducing a
nonlinear dispersive interaction with a mechanical oscillator. We show that
when either the exciton and cavity modes in the weak-coupling regime, or the
two exciton-polariton modes in the strong-coupling regime, are respectively
resonant with the optomechanical Stokes and anti-Stokes sidebands, entanglement
between excitons and cavity photons, or between two exciton polaritons, can be
established. The entanglement is in the steady state and can potentially be
achievable at room temperature. In both cases, genuine tripartite entanglement
is shown to be present.
