Entanglement dynamics in a non-Markovian environment: an exactly solvable model

Abstract

We study the non-Markovian effects on the dynamics of entanglement in an exactly-solvable model that involves two independent oscillators each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time-correlations, we see non-monotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of `sudden death' and `rebirth' of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.

11 pages, 4 figures; revision for PRB

References in corpus (12)

• Finite-Time Disentanglement via Spontaneous Emission
• An Atomic-resolution nanomechanical mass sensor
• Non-Markovian effects on the dynamics of entanglement
• Heralded Entanglement between Atomic Ensembles: Preparation, Decoherence, and Scaling
• Sudden Death of Entanglement: Classical Noise Effects
• Sudden Death of Entanglement of Two Jaynes-Cummings Atoms
• Dynamics of the entanglement between two oscillators in the same environment
• Pairwise Concurrence Dynamics: A Four-Qubit Model
• Non-Markovian entanglement dynamics of noisy continuous variable quantum channels
• Non-Markovian entanglement dynamics of quantum continuous variable systems in thermal environments
• Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach
• Entanglement oscillation and survival induced by non-Markovian decoherence dynamics of entangled squeezed-state

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• Overview on the phenomenon of two-qubit entanglement revivals in classical environments
• Rabi oscillations, decoherence, and disentanglement in a qubit-spin-bath system: exact dynamics
• NonMarkovian Abraham--Lorentz--Dirac Equation: Radiation Reaction without Pathology
• Solving quantum trajectories for systems with linear Heisenberg-picture dynamics and Gaussian measurement noise
• Entanglement dynamics of coupled quantum oscillators in independent nonMarkovian baths
• Dynamics of noisy quantum systems in the Heisenberg picture: application to the stability of fractional charge
• Thermally isolated Luttinger liquids with noisy Hamiltonians
• Hot entanglement? -- Parametrically coupled quantum oscillators in two heat baths: instability, squeezing and driving
• Probing the structure of entanglement with entanglement moments
• Phase Space Entanglement Spectrum