Geometric phase for an accelerated two-level atom in AdS spacetime

TL;DR

This paper studies how the geometric phase of a uniformly accelerated two-level atom in AdS spacetime depends on acceleration, boundary conditions, and the AdS radius, revealing distinct behaviors for subcritical and supercritical accelerations.

Contribution

It introduces a detailed analysis of the geometric phase for an accelerated atom in AdS spacetime, highlighting boundary-condition effects and the distinction between subcritical and supercritical accelerations.

Findings

Geometric phase is independent of AdS radius and acceleration for subcritical accelerations.

Boundary conditions significantly influence phase corrections in supercritical accelerations.

Phase corrections exhibit a hierarchy Neumann > transparent > Dirichlet at large accelerations.

Abstract

We have investigated the geometric phase acquired by a uniformly accelerated two-level atom coupled to vacuum fluctuations of a massless conformal scalar field in Anti-de Sitter (AdS) spacetime. Using the open-quantum-system formalism, we calculate the phase under three boundary conditions (Dirichlet, transparent and Neumann) imposed on the field at the AdS boundary. Our findings reveal a sharp distinction between subcritical and supercritical accelerations. For subcritical accelerations, the atom evolves effectively as an isolated system, and the geometric phase is independent of both the AdS radius and the acceleration. For supercritical accelerations, however, topology-acceleration-induced phase corrections emerge and display pronounced boundary-condition dependence. When the AdS radius is smaller than the atomic proper wavelength, the magnitude of the correction at large accelerations follows the ordering Neumann$>$transparent$>$Dirichlet. Moreover, over a finite interval of the atomic weight parameter, both Dirichlet and Neumann boundary conditions produce a richer peak structure in the phase correction than the transparent case, with the detailed pattern governed by the competition between the acceleration and the atomic energy gap. Finally, for transparent boundary conditions in the supercritical regime, the AdS phase correction closely resembles its de Sitter (dS) counterpart.