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Physical Review A

Entanglement dynamics of multimode Gaussian states coupled to the same reservoir

Shao-Hua Xiang, Bin Shao, Kehui Song, Jian Zou

Published Mar 25, 2009• 13 citations
Publisher

Abstract

We investigate the entanglement dynamics of a generic multimode Gaussian state interacting with a common environmental noise by means of the characteristic function method and the defined operators. We find that such operators obey the rather simple commutation relations. This enables us to exactly solve the Fokker-Planck equation and to establish the general form of the input and output covariance matrices of this state. As an application, we consider the separability and entanglement of three-mode squeezed Gaussian state in the common thermal and squeezed thermal bath.

DOI
10.1103/physreva.79.032333

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We investigate the entanglement dynamics of a generic multimode Gaussian state interacting with a common environmental noise by means of the characteristic function method and the defined operators. We find that such operators obey the rather simple commutation relations. This enables us to exactly solve the Fokker-Planck equation and to establish the general form of the input and output covariance matrices of this state. As an application, we consider the separability and entanglement of three-mode squeezed Gaussian state in the common thermal and squeezed thermal bath.
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.
Entanglement in continuous-variable Gaussian systems is a key resource, and common reservoirs can both suppress and generate correlations. Existing work focused on pre-entangled states or Markovian baths, leaving open whether separable squeezed inputs entangle in structured environments or under modulation. We study two bosonic modes coupled to a common reservoir, each initialized in a separable squeezed vacuum. Dynamics are analyzed utilizing Gaussian covariance methods, evolved under approximate Non-Markovian quantum state diffusion (QSD), finite-temperature pseudomode embeddings, and Bures-based non-Markovian diagnostics. We identify three mechanisms absent in Markovian dynamics: (1) A detuning condition that freezes entanglement trajectories across reservoir correlation times; (2) birth, death, and revival of entanglement from orthogonal inputs; and (3) integer-locked beating with square-wave oscillations produced by periodic detuning. All mechanisms persist at finite temperature, with deviations bounded within 5% in cryogenic regimes and 20% at moderate occupations. These deviation bounds align with cryogenic cavity, phononic, and optomechanical platforms, where structured spectral densities and detuning modulation are already accessible. Structured reservoirs are shown to emerge as tunable entanglement resources for continuous-variable quantum technologies.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the quantum correlations of a system consisting of two non-interacting modes embedded in a thermal environment. We describe the evolution of the quantum entanglement in terms of the covariance matrix for Gaussian input states. For all values of the temperature of the thermal reservoir, an initial separable squeezed thermal state remains separable for all times. In the case of an entangled initial squeezed thermal state, entanglement suppression (entanglement sudden death) takes place, for non-zero temperatures of the environment. The Gaussian quantum discord, which is a measure of all quantum correlations in the state, including entanglement, decays asymptotically in time under the effect of the thermal bath.
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 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.