Boundary Effects on Quantum Entanglement and its Dynamics in a Detector-Field System

TL;DR

This paper presents an exactly solvable model analyzing how a boundary affects quantum entanglement dynamics between an inertial detector and a quantum field, revealing that entanglement decreases as the detector approaches the boundary.

Contribution

It introduces a solvable model for detector-field entanglement near a boundary, deriving exact expressions and comparing boundary effects with detector-detector interactions.

Findings

Entanglement decreases as the detector gets closer to the boundary.

Exact solutions for the detector's covariance matrix are obtained.

The boundary effect is qualitatively explained using a mirror image analogy.

Abstract

In this paper we analyze an exactly solvable model consisting of an inertial Unruh-DeWitt detector which interacts linearly with a massless quantum field in Minkowski spacetime with a perfectly reflecting flat plane boundary. Firstly a set of coupled equations for the detector's and the field's Heisenberg operators are derived. Then we introduce the linear entropy as a measure of entanglement between the detector and the quantum field under mirror reflection, and solve the early-time detector-field entanglement dynamics. After coarse-graining the field, the dynamics of the detector's internal degree of freedom is described by a quantum Langevin equation, where the dissipation and noise kernels respectively correspond to the retarded Green's functions and Hadamard elementary functions of the free quantum field in a half space. At late times when the combined system is in a stationary state, we obtain exact expressions for the detector's covariance matrix and show that the detector-field entanglement decreases for smaller separation between the detector and the mirror. We explain the behavior of detector-field entanglement qualitatively with the help of a detector's mirror image, compare them with the case of two real detectors and explain the differences.