Two-atom interaction energies with one atom in an excited state: van der Waals potentials vs. level shifts

TL;DR

This paper clarifies the relationships between various interaction energies and level shifts in two-atom systems with one atom excited, resolving conflicting results and analyzing effects of dissipation and excitation rates.

Contribution

It demonstrates the equivalence of different interaction quantities under certain approximations and clarifies their physical distinctions, especially for identical excited atoms.

Findings

Equivalent expressions for phase-shift rate, van der Waals potential, and level shifts in quasistationary approximation.

Identifies non-equivalence of these quantities for identical excited atoms.

Shows that spatial oscillations are due to different physical quantities, not reversible or irreversible processes.

Abstract

I revisit the problem of the interaction between two dissimilar atoms with one atom in an excited state, recently addressed by the authors of Refs.[1-3], and for which precedent approaches have given conflicting results. In the first place, I discuss to what extent Refs.[1], [2] and [3] provide equivalent results. I show that the phase-shift rate of the two-atom wave function computed in Ref.[1], the van der Waals potential of the excited atom in Ref.[2] and the level shift of the excited atom in Ref.[3] possess equivalent expressions in the quasistationary approximation. In addition, I show that the level shift of the ground state atom computed in Ref.[3] is equivalent to its van der Waals potential. A diagrammatic representation of all those quantities is provided. The equivalences among them are however not generic. In particular, it is found that for the case of the interaction between two identical atoms excited, the phase-shift rate and the van der Waals potentials differ. Concerning the conflicting results of previous approaches in regards to the spatial oscillation of the interactions, I conclude in agreement with Refs.[1,3] that they refer to different physical quantities. The impacts of free-space dissipation and finite excitation rates on the dynamics of the potentials are analyzed. In contrast to Ref.[3], the oscillatory versus monotonic spatial forms of the potentials of each atom are found not to be related to the reversible versus irreversible nature of the excitation transfer involved.