  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.
