  We study entanglement dynamics in dispersive optomechanical systems
consisting of two optical modes and a mechanical oscillator inside an optical
cavity. The two optical modes interact with the mechanical oscillator, but not
directly with each other. The appearance of optical entanglement witnesses
non-classicality of the oscillator. We study the dependence of the entanglement
dynamics with the optomechanical coupling, the mean photon number in the cavity
and the oscillator temperature. An experimental realization with ultracold
atomic ensembles is proposed.
