Steady-state two-atom entanglement in a pumped cavity

In this paper we explore the possibility of a steady-state entanglement of two two-level atoms inside a pumped cavity by taking into account cavity leakage and the spontaneous emission of photons by the atoms. We describe the system in the dressed state picture in which the coherence is built into the dressed states while transitions between the dressed states are incoherent. Our model assumes the vacuum Rabi splitting of the dressed states to be much larger than any of the decay parameters of the system which allows atom-field coherence to build up before any decay process takes over. We show that, under our model, a pumping field cannot entangle two closed two-level atoms inside the cavity in the steady-state, but a steady-state entanglement can be achieved with two open two-level atoms.