Autangle: A case of Quantum Narcissism?

TL;DR

This paper investigates how a quantum harmonic oscillator's entanglement with a quantum field is affected by the presence of a mirror, revealing that entanglement decreases as the oscillator approaches the mirror, with implications for macroscopic quantum phenomena.

Contribution

The study provides an exact analysis of oscillator-field entanglement near a mirror, introducing a novel approach to understanding boundary effects on quantum entanglement in macroscopic systems.

Findings

Entanglement decreases as the oscillator gets closer to the mirror.

Exact expressions for the oscillator's covariance matrix are derived.

Comparison with free space and two-oscillator cases highlights boundary effects.

Abstract

In this paper we ask a common psychological question and provide a physics answer: "Looking into a mirror can one get entangled with one's image?" This is not a frivolous question; rather, it bears on the effect of boundaries on the behavior of quantum entanglement between a harmonic oscillator and a quantum field, a basic problem of interest in proposed mirror-field superposition and related experiments in macroscopic quantum phenomena, as well as atomic fluctuation forces near a conducting surface. The object's internal degree of freedom is modeled by a harmonic oscillator and the presence of a perfectly reflecting mirror enforces the Dirichlet boundary conditions on the quantum field, restricting the latter to a half space. By assuming a bilinear oscillator-field interaction, we derive a coupled set of equations for the oscillator's and the field's Heisenberg operators. The former can be cast in the form of a quantum Langevin equation, where the dissipation and noise kernels respectively correspond to the retarded and Hadamard functions of the free quantum field in half space. We use the linear entropy as measures of entanglement between the oscillator and the quantum field under mirror reflection, then solve the early-time oscillator-field entanglement dynamics and compare it with that between two inertial oscillators in free space. At late times when the combined system is in a stationary state, we obtain exact expressions for the oscillator's covariance matrix and show that the oscillator-field entanglement decreases as the oscillator moves closer to the mirror. We explain this behavior qualitatively with the help of a mirror image and provide an answer to the question raised above. We also compare this situation with the case of two real oscillators and explain the differences.