The dynamics of two two-level dipole-dipole interacting atoms coupled to a common electro-magnetic bath and closely located inside a lossy cavity, is reported. Initially injecting only one excitation in the two-atom cavity system, loss mechanisms asymptotically drive the matter sample toward a stationary maximally entangled state. The role played by the closeness of the two atoms, with respect to such a cooperative behavior, is carefully discussed. Stationary radiation trapping effects are found and transparently interpreted.
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