Entanglement Dynamics of Detectors in an Einstein Cylinder

TL;DR

This paper explores how the topology of an Einstein cylinder influences entanglement dynamics between detectors and quantum fields, revealing unique beat patterns and the role of zero modes in entanglement evolution.

Contribution

It introduces a derivative-coupling Unruh-DeWitt-like detector model in an Einstein cylinder to analyze topology-induced effects on entanglement dynamics, highlighting differences from Minkowski space.

Findings

Beat patterns differ between normal and twisted fields due to mode spectra.

Zero mode contributions are qualitatively similar to nonzero modes in entanglement dynamics.

Topology significantly affects entanglement evolution and field mode behavior.

Abstract

We investigate how nontrivial topology affects the entanglement dynamics between a detector and a quantum field and between two detectors mediated by a quantum field. Nontrivial topology refers to both that of the base space and that of the bundle. Using a derivative-coupling Unruh-DeWitt-like detector model interacting with a quantum scalar field in an Einstein cylinder S1 (space) x R1 (time), we see the beating behaviors in the dynamics of the detector-field entanglement and the detector-detector entanglement, which distinguish from the results in the non-compact (1+1) dimensional Minkowski space. The beat patterns of entanglement dynamics in a normal and a twisted field with the same parameter values are different because of the difference in the spectrum of the field modes. In terms of the kinetic momentum of the detectors, we find that the contribution by the zero mode in a normal field to entanglement dynamics has no qualitative difference from those by the nonzero modes.