Geometric phases acquired for a two-level atom coupled to fluctuating vacuum scalar fields due to linear acceleration and circular motion

TL;DR

This paper investigates how geometric phases of a two-level atom are affected by linear acceleration and circular motion in vacuum scalar fields, revealing conditions where these phases are equivalent and effects of boundaries.

Contribution

It provides a detailed comparison of geometric phases under different accelerations and motions, highlighting conditions for simulating linear acceleration effects via circular motion.

Findings

Geometric phase varies with acceleration and motion type.

Boundary presence increases geometric phase magnitude.

Linear and circular accelerations can produce equivalent phases under certain conditions.

Abstract

In open quantum systems, we study the geometric phases acquired for a two-level atom coupled to a bath of fluctuating vacuum massless scalar fields due to linear acceleration and circular motion without and with a boundary. In free space, as we amplify acceleration, the geometric phase acquired purely due to linear acceleration case firstly is smaller than the circular acceleration case in the ultrarelativistic limit for the initial atomic state $\theta\in(0,\frac{\pi}{2})\cup(\frac{\pi}{2},\pi)$, then equals to the circular acceleration case in a certain acceleration, and finally, is larger than the circular acceleration case. The spontaneous transition rates show a similar feature. This result is different from the case of a bath of fluctuating vacuum electromagnetic fields that has been studied. Considering the initial atomic state $\theta \in(0,\pi)$, we find that the geometric phase acquired purely due to linear acceleration always equals to the circular acceleration case for the certain acceleration. The feature implies that, in a certain condition, one can simulate the case of the uniformly accelerated two-level atom by studying the properties of the two-level atom in circular motion. Adding a reflecting boundary, we observe that a larger value of a geometric phase can be obtained compared to the absence of a boundary. Besides, the geometric phase fluctuates along $z$, and the maximum of geometric phase is closer to the boundary for a larger acceleration. We also find that geometric phases can be acquired purely due to the linear acceleration case and circular acceleration case with $\theta \in(0,\pi)$ for a smaller $z$.