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We study two continuous variable systems (or two harmonic oscillators) andinvestigate their entanglement evolution under the influence of non-Markovianthermal environments. The continuous variable systems could be two modes ofelectromagnetic fields or two nanomechanical oscillators in the quantum domain.We use quantum open system method to derive the non-Markovian master equationsof the reduced density matrix for two different but related models of thecontinuous variable systems. The two models both consist of two interactingharmonic oscillators. In model A, each of the two oscillators is coupled to itsown independent thermal reservoir, while in model B the two oscillators arecoupled to a common reservoir. To quantify the degrees of entanglement for thebipartite continuous variable systems in Gaussian states, logarithmicnegativity is used. We find that the dynamics of the quantum entanglement issensitive to the initial states, the oscillator-oscillator interaction, theoscillator-environment interaction and the coupling to a common bath or todifferent, independent baths.

Non-Markovian entanglement dynamics of quantum continuous variable systems in thermal environments