Boundary Effects on Quantum Entanglement and its Dynamics in a Detector-Field System
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.
Cite
@article{arxiv.1301.0073,
title = {Boundary Effects on Quantum Entanglement and its Dynamics in a Detector-Field System},
author = {Rong Zhou and Ryan O. Behunin and Shih-Yuin Lin and B. L. Hu},
journal= {arXiv preprint arXiv:1301.0073},
year = {2015}
}
Comments
22 pages, 2 figures. An expanded version of arXiv:1201.0541 where the boundary effects are expounded in greater details