On the entanglement of a quantum field with a dispersive medium

TL;DR

This paper investigates how a quantum radiation field becomes entangled with a dispersive dielectric medium, analyzing different models and their effects on entanglement entropy, including a Casimir-like distance dependence and a toy model of plate interactions.

Contribution

It provides a detailed comparison of plasma and Drude models on field-medium entanglement and introduces a formula for Casimir entanglement entropy with implications for quantum field interactions.

Findings

Different models produce distinct entanglement behaviors.

Distance-dependent entanglement entropy is finite and decreases with separation.

Field entanglement entropy can diverge, but its distance-dependent part remains finite.

Abstract

In this Letter we study the entanglement of a quantum radiation field interacting with a dielectric medium. In particular, we describe the quantum mixed state of a field interacting with a dielectric through plasma and Drude models and show that these generate very different entanglement behavior, as manifested in the entanglement entropy of the field. We also present a formula for a "Casimir" entanglement entropy, i.e., the distance dependence of the field entropy. Finally, we study a toy model of the interaction between two plates. In this model, the field entanglement entropy is divergent; however, as in the Casimir effect, its distance-dependent part is finite, and the field matter entanglement is reduced when the objects are far.