  We investigate theoretically an open dynamics for two modes of
electromagnetic field inside a microwave cavity. The dynamics is Markovian and
determined by two types of reservoirs: the "natural" reservoirs due to
dissipation and temperature of the cavity, and an engineered one, provided by a
stream of atoms passing trough the cavity, as devised in [Pielawa \emph{et al.}
\emph{Phys. Rev. Lett.} \textbf{98}, 240401 (2007)]. We found that, depending
on the reservoir parameters, the system can have distinct "phases" for the
asymptotic entanglement dynamics: it can disentangle at finite time or it can
have persistent entanglement for large times, with the transition between them
characterized by the possibility of asymptotical disentanglement. Incidentally,
we also discuss the effects of dissipation on the scheme proposed in the above
reference for generation of entangled states.
