Solving the master equation of a couple of interacting complex subsystems coupled to a bosonic bath

Abstract:
The dynamics of two two-level interacting atoms coupled to common electro-magnetic bath closely located inside a lossy cavity is reportedfor different form of the interaction symmetry. Initially injecting only one excitation in the two dipole-dipole interacting atoms and cavity system, loss mechanisms asymptotically drive the mater system 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. Ising-type interaction between atoms causes another form of cooperative dynamics which is similar to the superradiance effect. In the case of strong interaction, the coupling between the mater sample and cavity mode has multi-photon character which is to be displayed in the two-photon two-atom Rabi oscillation.  From a mathematical point of view we presentour successful approach relying on the choice of a unitary transformation which accomplishes the passage to a simple exactly solvable master equation.