Environment-induced two-mode entanglement in quantum Brownian motion

TL;DR

This paper investigates how different environmental interactions affect the entanglement of two-mode continuous variable quantum states, revealing conditions under which entanglement persists or is lost due to non-Markovian effects and temperature.

Contribution

It extends the quantum Brownian motion model to analyze environment-induced entanglement in two-mode systems under various reservoir conditions.

Findings

Moderate non-Markovian effects prolong entanglement.

In two-reservoir models, initial entanglement is lost over time.

In a common reservoir, entanglement can be preserved below a critical temperature.

Abstract

The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir as well as two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Below a critical bath temperature entanglement between the two modes is preserved even in the steady state. A separability criterion is derived, which depends on the bath temperature and the response function of the open quantum system. Thus, the extended quantum Brownian motion model of a two-mode continuous variable system in a common reservoir provides an example of environment-induced entanglement.