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

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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. This model is related to proposed mirror-field superposition
and relevant experiments in macroscopic quantum phenomena, as well as
atomic fluctuation forces near a conducting surface. Firstly a coupled
set of equations for the detector’s and the field’s Heisenberg operators
are derived. After coarse graining the field, the dynamics of the
detector’s internal degreeof 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 half space. We use the linear
entropy as measures of entanglement between the detector and the quantum
field under mirror reflection, then solve the early-time
detector-fieldentanglement dynamics. 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.