Generation of entangled Bloch states for two atomic samples trapped in separated cavities

A scheme is presented for the generation of entangled states for two atomic ensembles trapped in two distant cavities. In the scheme, each atomic sample is initially in a Bloch state and the cavity mode is initially in a coherent state with a small amplitude. The dispersive atom - cavity interaction leads to a photon- number dependent phase shift on the atomic system. The detection of a photon leaking from the cavities makes the two atomic samples collapse to an entangled Bloch state.