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

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.

Figures (4)

• Figure 1: The magnitude of the topology-acceleration geometric phase correction, $|\delta|/\mu^2$, is plotted as a function of the parameter $a\ell$ ($a\ell\geq1$) in AdS spacetime with $\theta=\pi/4,\ell\omega_0=0.1$ in (a) and $\theta=\pi/4,\ell\omega_0=10$ in (b). Notice that for $\theta=\pi/4$ the subscript acceleration case ($a\ell<1$) under all boundary conditions, according to Eq. (\ref{['deltasub']}), then yields a constant phase correction : $|\delta|/\mu^2\approx1.06$.
• Figure 2: The magnitude of the topology-acceleration geometric phase correction versus the weight parameter for supercritical accelerations in AdS spacetime. Top: $\ell\omega_0=0.5$ with $a\ell=\{5,10\}$ in the left-to-right order. Bottom: $\ell\omega_0=5$ with $a\ell=\{5,10\}$ in the left-to-right order.
• Figure 3: The topology-acceleration geometric phase corrections in AdS (under different boundary conditions) and dS spacetimes are respectively plotted as a function of $a\ell$ with $\theta=\pi/4,\ell\omega_0=0.2$ in (a)(b)(c) and with $\theta=\pi/4,\ell\omega_0=5$ in(d)(e)(f).
• Figure 4: The topology-acceleration geometric phase corrections in AdS (under different boundary conditions) and dS spacetimes versus the parameter with $a\ell=1.5$ in (a)(b)(c) and $a\ell=10$ in (d)(e)(f). Here, we assume $\ell\omega_0=1$ for all plots.