Quantum Entanglement of Two-mode Gaussian Systems in Two-reservoir Model

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous variable entanglement for a system consisting of two non-interacting bosonic modes embedded in two independent thermal environments. By using the Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the evolution of entanglement in terms of the covariance matrix for Gaussian input states. In the case of an entangled initial squeezed thermal state, entanglement suppression (entanglement sudden death) takes place, for all temperatures of the thermal baths. For definite values of temperatures, dissipation constants, squeezing and damping parameters, one can observe temporary revivals and suppressions of the entanglement, but in the limit of large times the system evolves to an equilibrium state which is always separable.