Effective Quantum Dynamics of two Brownian particles

TL;DR

This paper investigates how a common environment can induce entanglement between two quantum particles by extending the traditional bath model, analyzing different regimes based on particle separation and system-reservoir interactions.

Contribution

It introduces a nonlinear, translationally invariant bath model with a spectral density-dependent coupling, providing a criterion for environment-induced entanglement based on particle distance.

Findings

Identifies three regimes: short, long, and intermediate distances.

Derives conditions under which the environment induces entanglement.

Provides a model linking spectral density to effective interaction strength.

Abstract

We use the system-plus-reservoir approach to study the quantum dynamics of a bipartite continuous variable system (two generic particles). We present an extension of the traditional model of a bath of oscillators which is capable of inducing an effective coupling between the two parts of the system depending on the choice made for the spectral density of the bath. The coupling is nonlinear in the system variables and an exponential dependence on these variables is imposed in order to guarantee the translational invariance of the model if the two particles are not subject to any external potential. The reduced density operator is obtained by the functional integral method. The dynamical susceptibility of the reservoir is modelled in order to introduce, besides a characteristic frequency, a characteristic length that determines if the effective interaction potential is strong enough to induce entanglement between the particles. Our model provides a criterion of distance for identifying in which cases a common environment can induce entanglement. Three regimes are found: the short distance regime, equivalent to a bilinear system-reservoir coupling, the long distance regime in which the particles act like coupled to independent reservoirs and the intermediate regime suitable for the competition between decoherence and induced-entanglement.