  We propose a method to entangle two distant vibrating microsize mirrors
(i.e., mechanical oscillators) in a cavity optomechanical system. In this
scheme, we discuss both the resonant and large-detuning conditions, and show
that the entanglement of two mechanical oscillators can be achieved with the
assistance of a two-level atom and cavity-radiation pressure. In the resonant
case, the operation time is relatively short, which is desirable to minimize
the effects of decoherence. While in the large-detuning case, the cavity is
only virtually excited during the interaction. Therefore, the decay of the
cavity is effectively suppressed, which makes the efficient decoherence time of
the cavity to be greatly prolonged. Thus, we observe that this virtual-photon
process of microscopic objects may induce the entanglement of macroscopic
objects. Moreover, in both cases, the generation of entanglement is
deterministic and no measurements on the atom and the cavity are required.
These are experimentally important. Finally, the decoherence effect and the
experimental feasibility of the proposal are briefly discussed.
