Entangling detectors in anti-de Sitter space

TL;DR

This paper investigates how entanglement harvesting by particle detectors in (2+1)-dimensional anti-de Sitter space depends on their motion, separation, and boundary conditions, revealing conditions where entanglement extraction is inhibited.

Contribution

It provides a detailed analysis of entanglement harvesting in AdS space, highlighting the influence of spacetime curvature and boundary conditions on entanglement extraction capabilities.

Findings

Identifies an island of separability where entanglement harvesting fails.

Shows the dependence of detector transition probability on curvature and boundary conditions.

Compares entanglement harvesting phenomena in AdS$_3$ and AdS$_4$.

Abstract

We examine in $(2+1)$-dimensional anti-de Sitter (AdS) space the phenomena of entanglement harvesting - the process in which a pair of detectors (two-level atoms) extract entanglement from a quantum field through local interactions with the field. We begin by reviewing the Unruh-DeWitt detector and its interaction with a real scalar field in the vacuum state, as well as the entanglement harvesting protocol in general. We then examine how the entanglement harvested by a pair of such detectors depends on their spacetime trajectory, separation, spacetime curvature, and boundary conditions satisfied by the field. The harvested entanglement is interpreted as an indicator of field entanglement between the localized regions where the detectors interact with the field, and thus this investigation allows us to probe indirectly the entanglement structure of the AdS vacuum. We find an island of separability for specific values of the detectors' energy gap and separation at intermediate values of the AdS length for which entanglement harvesting is not possible; an analogous phenomena is observed in AdS$_4$, to which we compare and contrast our results. In the process we examine how the transition probability of a single detector, as a proxy for local fluctuations of the field, depends on spacetime curvature, its location in AdS space, and boundary conditions satisfied by the field.