Two-atom van-der-Waals forces with one atom excited: the identical atoms limit I

TL;DR

This paper investigates the time-dependent van-der-Waals forces between two identical atoms with one initially excited, revealing fully-resonant, linearly growing forces related to spontaneous emission and parity violation.

Contribution

It introduces a time-dependent approach to calculate van-der-Waals forces for identical atoms in the excited state, highlighting the importance of non-stationary effects.

Findings

Forces grow linearly in time at leading order.

Forces are fully-resonant and differ for each atom.

Net force relates to spontaneous emission directionality.

Abstract

We compute the conservative van-der-Waals forces between two atoms, one of which is initially excited, in the limit of identical atoms. Starting with the perturbative calculation of the interaction between two dissimilar atoms, we show that a time-dependent approach in the weak-interaction approximation is essential in considering the identical atoms limit in the perturbative regime. In this limit we find that, at leading order, the van-der-Waals forces are fully-resonant and grow linearly in time, being different upon each atom. The resultant net force upon the two-atom system is related to the directionality of spontaneous emission, which results from the violation of parity symmetry. In contrast to the usual stationary van-der-Waals forces, the time-dependent conservative forces cannot be written as the gradients of the expectation values of the interaction potentials, but as the expectation values of the gradients of the interaction potentials only.