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

Justin H. Wilson, Benjamin M. Fregoso, and Victor M. Galitski
Phys. Rev. B 85, 174304 – Published 22 May 2012

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 nonmonotonic 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.

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  • Received 21 February 2012

DOI:https://doi.org/10.1103/PhysRevB.85.174304

©2012 American Physical Society

Authors & Affiliations

Justin H. Wilson, Benjamin M. Fregoso, and Victor M. Galitski

  • Joint Quantum Institute and Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA

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Issue

Vol. 85, Iss. 17 — 1 May 2012

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