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Physical Review A

Environment-assisted creation and enhancement of two-mode entanglement in a joint decoherent model

Shao-Hua Xiang, Bin Shao, Kehui Song

Published Nov 10, 2008• 23 citations
Publisher

Abstract

We investigate the entanglement dynamics of two modes in a common squeezed thermal environment by means of the characteristic function method and the logarithmic negativity. When the two modes are prepared initially in separable squeezed states, we find that the external environment can not only induce but also enhance the two-mode entanglement if their initial squeezing parameters are suitably chosen. When the two modes are initially in a two-mode squeezed vacuum state, we find that whether the initial entanglement is degraded or increased depends strongly on the difference between the squeezing parameters of the considered bath and of a quantum state. Finally, we give a condition of all two-mode entangled Gaussian states to be the decoherence-free state in a given squeezed bath.

DOI
10.1103/physreva.78.052313

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We investigate the entanglement dynamics of two modes in a common squeezed thermal environment by means of the characteristic function method and the logarithmic negativity. When the two modes are prepared initially in separable squeezed states, we find that the external environment can not only induce but also enhance the two-mode entanglement if their initial squeezing parameters are suitably chosen. When the two modes are initially in a two-mode squeezed vacuum state, we find that whether the initial entanglement is degraded or increased depends strongly on the difference between the squeezing parameters of the considered bath and of a quantum state. Finally, we give a condition of all two-mode entangled Gaussian states to be the decoherence-free state in a given squeezed bath.
We study the evolution of the entanglement of two independent bosonic modes embedded in a thermal environment, in the framework of the theory of open quantum systems. As a measure of entanglement we use the logarithmic negativity. For a non-zero temperature of the thermal reservoir the entangled initial Gaussian states become always separable in a finite time. For initial squeezed thermal states we calculate the survival time of entanglement and analyze its dependence on temperature, squeezing parameter and mean thermal photon numbers. For a zero temperature of the thermal bath an entangled initial state remains entangled for all finite times, but in the limit of asymptotically large times it becomes separable.
We study a system consisting of two identical non-interacting single-mode cavity fields coupled to a common vacuum environment and provide general, explicit, and exact solutions to its master equation by means of the characteristic function method. We analyze the entanglement dynamics of two-mode squeezed thermal state in this model and show that its entanglement dynamics is strongly determined by the two-mode squeezing parameter and the purity. In particular, we find that two-mode squeezed thermal state with the squeezing parameter is extremely fragile and almost does not survive in a common vacuum environment. We investigate the time evolution of nonlocality for two-mode squeezed thermal state in such an environment. It is found that the evolved state loses its nonlocality in the beginning of the evolution, but after a time, the revival of nonlocality can occur.
We describe the evolution of the quantum entanglement in a system composed of two interacting bosonic modes immersed in a thermal reservoir, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. The evolution of entanglement is described in terms of the covariance matrix for Gaussian initial states. We calculate the logarithmic negativity and show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and the strength of interaction between the two modes. After its generation one can observe temporary suppressions and revivals of the entanglement. For entangled initial squeezed thermal states, entanglement suppression takes place, for all temperatures of the reservoir, and temporary revivals and suppressions of entanglement can be observed too. In the limit of infinite time the system evolves asymptotically to an equilibrium state which may be entangled or separable.
Abstract Hellinger geometric quantum discord and interferometric power are investigated for an open system consisting of two bosonic modes interacting with four different environments: vacuum, squeezed vacuum, thermal and squeezed thermal, taking the initial state of the system either a single-mode squeezed state, which presents no correlations, or a squeezed vacuum state. The description of the evolution of the correlations is formulated in the framework of the theory of open systems, based on completely positive quantum dynamical semigroups, using the Gorini-Kossakowski-Lindblad-Sudarshan master equation. We show that both quantum correlations can be generated from an initial factorized state and even amplified, while also studying the back and forth impact of the squeezing parameters on the considered correlations; specifically, for the squeezed vacuum environment, the competition between the influences exerted by the squeezing of the initial state and the squeezing of the environment leads to the decreasing, and even destruction of the correlations, or to their enhancement. In the case of an initial squeezed vacuum state in interaction with the squeezed vacuum environment, for specific conditions one can achieve decoherence-free states (DFS), while for the interaction with a thermal environment there exist regimes of enhancing or decreasing the considered correlations, depending on the parameters of both open system and environment.
Entangled states play a crucial role in quantum information protocols, thus the dynamical behaviour of entanglement is of great importance. In this letter, we consider a two-mode squeezed vacuum state coupled to one thermal reservoir as a model of an entangled state embedded in an environment. As a criterion for entanglement we use a continuous-variable equivalent of the Peres–Horodecki criterion, namely the Simon criterion. To quantify entanglement we use the logarithmic negativity. We derive a condition, which assures that the state remains entangled in spite of the interaction with the reservoir. Moreover for the case of interaction with vacuum as an environment we show that a state of interest after infinitely long interaction is not only entangled, but also pure. For comparison we also consider a model in which each mode is coupled to its own reservoir.
We describe the evolution of the quantum entanglement of an open system consisting of two bosonic modes interacting with a common thermal environment, described by two different models. The initial state of the system is taken of Gaussian form. In the case of a thermal bath, characterized by temperature and dissipation constant which correspond to an asymptotic Gibbs state of the system, we show that for a zero temperature of the thermal bath an initial entangled Gaussian state remains entangled for all finite times. For an entangled initial squeezed thermal state, the phenomenon of entanglement sudden death takes place and we calculate the survival time of entanglement. For the second model of the environment, corresponding to a non-Gibbs asymptotic state, we study the possibility of generating entanglement. We show that the generation of the entanglement between two uncoupled bosonic modes is possible only for definite values of the temperature and dissipation constant, which characterize the thermal environment.