Distance and Coupling Dependence of Entanglement in the Presence of a Quantum Field

TL;DR

This paper investigates how the entanglement between two harmonic oscillator detectors depends on their separation and direct coupling when interacting with a quantum field, revealing complex late-time behaviors and the importance of direct coupling for sustained entanglement.

Contribution

It introduces a detailed analysis of the combined effects of finite separation and direct coupling on entanglement dynamics, extending prior work that neglected these factors.

Findings

Entanglement can be sustained over finite distances with direct coupling.

Previous no-separation results are transient and not representative of late-time behavior.

Direct coupling enhances the robustness of entanglement at larger separations.

Abstract

We study the entanglement between two coupled detectors, whose internal degrees of freedom are modeled by harmonic oscillators, interacting with a common quantum field, paying special attention to two less studied yet important features: finite separation and direct coupling. Distance dependence is essential in quantum teleportation and relativistic quantum information considerations. The presence of a quantum field as the environment accords an indirect interaction between the two oscillators at finite separation of a non-Markovian nature which competes with the direct coupling between them. The interplay between these two factors results in a rich variety of interesting entanglement behaviors at late times. We show that the entanglement behavior reported in prior work assuming no separation between the detectors can at best be a transient effect at very short times, and claims that such behaviors represent late time entanglement are misplaced. Entanglement between the detectors with direct coupling enters in the consideration of macroscopic quantum phenomena and other frontline issues. We find that with direct coupling entanglement between the two detectors can sustain over a finite distance, in contrast to the no-direct coupling case reported before, where entanglement can not survive at separation more than a few inverse high frequency cutoff scales. This work provides a solid platform necessary for further systematic investigations into the entanglement behavior of continuous variable quantum systems.