Entanglement of remote quantum systems by environmental modes

TL;DR

This paper models how two remote quantum oscillators can become entangled through a shared bosonic environment, revealing conditions for effective entanglement and the impact of boundary conditions on entanglement enhancement.

Contribution

It provides an exact Langevin equation framework for analyzing entanglement dynamics in remote oscillators coupled to a common bath, including boundary effects.

Findings

Entanglement is significant only at microscopic distances.

Boundary conditions like wave-guide geometries enhance entanglement.

An analytical model supports numerical results.

Abstract

We investigate the generation of quantum mechanical entanglement of two remote oscillators that are locally coupled to a common bosonic bath. Starting with a Lagrangian formulation of a suitable model, we derive two coupled Quantum Langevin Equations that exactly describe the time evolution of the two local oscillators in presence of the coupling to the bosonic bath. Numerically obtained solutions of the Langevin Equations allow us to study the entanglement generation between the oscillators in terms of the time evolution of the logarithmic negativity. Our results confirm and extend our previously obtained findings, namely that significant entanglement between oscillators embedded in a free bosonic bath can only be achieved if the system are within a microscopic distance. We also consider the case where the bosonic spectral density is substantially modified by imposing boundary conditions on the bath modes. For boundary conditions corresponding to a wave-guide like geometry of the bath we find significantly enlarged entanglement generation. This phenomenon is additionally illustrated within an approximative model that allows for an analytical treatment.