Dynamical behavior and geometric phase for a circularly accelerated two-level atom

TL;DR

This paper investigates the quantum dynamics and geometric phase of a circularly accelerated two-level atom, revealing differences from linear acceleration and dependence on initial states, with implications for understanding quantum effects in accelerated frames.

Contribution

It provides a detailed analysis of the spontaneous transition rates and geometric phase for a circularly accelerated atom, highlighting differences from linear acceleration and the influence of initial states.

Findings

Transition rates and effective temperature are higher in circular acceleration than linear.

Geometric phase depends on initial atomic state and differs between circular and linear acceleration.

In the ultrarelativistic limit, circular motion yields larger geometric phases than linear acceleration for certain initial states.

Abstract

We study, in the framework of open quantum systems, the time evolution of a circularly accelerated two-level atom coupled in the multipolar scheme to a bath of fluctuating vacuum electromagnetic fields. We find that both the spontaneous transition rates and the geometric phase for a circularly accelerated atom do not exhibit a clear sign of thermal radiation characterized by the Planckian factor in contrast to the linear acceleration case. The spontaneous transition rates and effective temperature of the atom are examined in detail in the ultrarelativistic limit and are shown to be always larger than those in the linear acceleration case with the same proper acceleration. Unlike the effective temperature, the geometric phase is dependent on the initial atomic states. We show that when the polar angle in Bloch sphere, $\theta$, that characterizes the initial state of the atom equals $\pi/{2}$, the geometric phases acquired due to circular and linear acceleration are the same. However, for a generic state with an arbitrary $\theta$, the phase will be in general different, and then we demonstrate in the ultrarelativistic limit that the geometric phase acquired for the atom in circular motion is always larger than that in linear acceleration with same proper acceleration for $\theta\in(0,\frac{\pi}{2})\cup(\frac{\pi}{2},\pi)$.