Scheme for Entanglement Generation of Two Atoms in Two Bad Cavities

We present a scheme for generation of two-atomic entangled state by using the interference of polarized photons. The scheme does not require complete mapping between the atomic state and the photonic state, nor does it require the establishment of maximal entanglement between the atom and the cavity. And the atom-cavity coupling strength is smaller than the cavity decay rate. This greatly relaxes the requirement on the cavity quality. The scheme is for non-post-selection results and all the steps of the scheme are within the current technologies.