Two-atom van der Waals forces with one atom excited: The identical-atom limit

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-atom 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. The strength of this force is much greater than that found in dissimilar atoms, raising the possibility of its experimental detection. In contrast to the usual stationary van der Waals forces, the timedependent 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.

Automated summary

The study investigates the conservative van der Waals forces between two atoms in the limit of identical atoms, revealing the importance of a time-dependent approach in the weak-interaction regime. The resultant force is significantly stronger than that found in dissimilar atoms, raising the possibility of experimental detection. The timedependent conservative forces cannot be expressed as the gradients of the expectation values of the interaction potentials, setting them apart from the usual stationary van der Waals forces.