Generation of Entangled Bloch States for Two Atomic Samples Trapped in Separated Cavities

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.