We analytically exploit the two-mode Gaussian states nonunitary dynamics. We show that in the zero temperature limit, entanglement sudden death (ESD) will always occur for symmetric states (where initial single mode compression is $z_0$) provided the
two mode squeezing $r_0$ satisfies $0 < r_0 < 1/2 log (cosh (2 z_0)).$ We also give the analytical expressions for the time of ESD. Finally, we show the relation between the single modes initial impurities and the initial entanglement, where we exhibit that the later is suppressed by the former.
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 cavi
ty, 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.
