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

TL;DR

This paper presents an exact solution to a non-Markovian quantum model involving two oscillators, revealing how memory effects influence entanglement dynamics, including phenomena like sudden death and rebirth.

Contribution

It introduces Lie algebraic and functional integral methods to solve a two-oscillator non-Markovian model analytically, detailing entanglement behavior under memory effects.

Findings

Non-monotonic evolution of uncertainties with long bath correlations

Identification of entanglement 'sudden death' and 'rebirth' phenomena

Memory effects modulate entanglement dynamics via noisy energy levels

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.