Generation of maximally entangled atom pairs in driven dissipative cavity QED systems

We investigate the entanglement of an open tripartite system where a cavity field mode in thermal equilibrium is off-resonantly coupled with two atoms that are simultaneously driven by a resonant coherent field. For moderately detuned atom-field coupling and strong atomic driving we show the generation, at given interaction times and for low enough cavity decay rates, of atomic Bell states and of Bell state superpositions relevant for quantum gates implementation. The system can oscillate between bi-separable and fully separable states. Also we describe the distribution of quantum correlations between the atom-atom and the two atom-field subsystems. In the dispersive coupling regime with strongly driven atoms we show the generation of nearly stationary Bell states which remain protected from cavity dissipation.