van der Waals Interaction Energy Between Two Atoms Moving With Uniform Acceleration

TL;DR

This paper investigates how uniform acceleration affects the van der Waals interaction between two atoms, revealing new distance dependencies and time-dependent effects that could be observable without extreme accelerations.

Contribution

It introduces a model for van der Waals interaction between accelerating atoms, showing modified distance laws and time-dependent corrections related to acceleration and the Unruh effect.

Findings

Near zone interaction includes a $R^{-5}$ term instead of $R^{-6}$.

Far zone interaction includes a $R^{-6}$ term instead of $R^{-7}$.

Interaction energy becomes time-dependent with acceleration-related corrections.

Abstract

We consider the interatomic van der Waals interaction energy between two neutral ground-state atoms moving in the vacuum space with the same uniform acceleration. We assume the acceleration orthogonal to their separation, so that their mutual distance remains constant. Using a model for the van der Waals dispersion interaction based on the interaction between the instantaneous atomic dipole moments, which are induced and correlated by the zero-point field fluctuations, we evaluate the interaction energy between the two accelerating atoms in terms of quantities expressed in the laboratory reference frame. We find that the dependence of the van der Waals interaction between the atoms from the distance is different with respect to the case of atoms at rest, and the relation of our results with the Unruh effect is discussed. We show that in the near zone a new term proportional to $R^{-5}$ adds to the usual $R^{-6}$ behavior, and in the far zone a term proportional to $R^{-6}$ adds to the usual $R^{-7}$ behavior, making the interaction of a longer range. We also find that the interaction energy is time-dependent, and the physical meaning of this result is discussed. In particular, we find acceleration-dependent corrections to the $R^{-7}$ (far zone) and $R^{-6}$ (near zone) proportional to $a^2t^2/c^2$; this suggests that significant changes to the van der Waals interaction between the atoms could be obtained if sufficiently long times are taken, without necessity of the extremely high accelerations required by other known manifestations of the Unruh effect.