Eur. Phys. J. Plus (2024) 139: 4
https://doi.org/10.1140/epjp/s13360-023-04800-w

Regular Article

About interaction potential of two ground-state atoms in circularly accelerated motion

Department of Physics, School of Physical Science and Technology, Ningbo University, 315211, Ningbo, Zhejiang, China

^b zhouwenting@nbu.edu.cn

Received: 30 August 2023
Accepted: 14 December 2023
Published online: 2 January 2024

Abstract

We study the interaction potential of two circularly accelerated atoms in interaction with a fluctuating massless scalar field in vacuum by separately calculating, in the ultrarelativistic limit, the contributions of vacuum fluctuations and those of the radiation reaction of the atoms. We show that, as compared with its counterpart of two inertial atoms in vacuum, the interaction potential of the two circularly accelerated atoms is only slightly modified in the two van der Waals (vdW) regions $L\ll \lambda \ll a^{-1}$ and $L\ll a^{-1}\ll \lambda$ and the Casimir–Polder (CP) region $\lambda \ll L\ll a^{-1}$, where L, $\lambda$, and a are, respectively, the interatomic separation, the atomic transition wavelength, and the proper acceleration. In contrast, it is severely altered in the third vdW region $a^{-1}\ll L\ll \lambda$ and the other two CP regions $\lambda \ll a^{-1}\ll L$ and $a^{-1}\ll \lambda \ll L$, in which it scales as $a^{-1}{L}^{-3}$, $a^{-\frac{1}{2}}{L}^{-\frac{7}{2}}$, and $a^{-1}{L}^{-3}$, respectively. Our results suggest that the interaction potential of two circularly accelerated atoms exhibits a universal behavior of $\sim a^{-1}{L}^{-3}$ in both the vdW and CP regions where both L and $\lambda$ are much greater than $a^{-1}$, the length scale characterizing the breakdown of the local inertial frame approximation. Similarities and distinctions between effects of the circularly accelerated motion and those of the uniformly accelerated motion are also analyzed.