Quasi-resonant van der Waals interaction between non-identical atoms

TL;DR

This paper presents a quantum calculation of van der Waals forces between two different atoms, revealing oscillatory behaviors influenced by their resonant frequencies and detuning, emphasizing the importance of causality.

Contribution

It provides a time-dependent quantum analysis of non-identical atoms' van der Waals interaction, highlighting the role of causality and oscillations, which was not fully addressed in prior stationary approaches.

Findings

Interaction exhibits temporal and spatial oscillations.

Spatial oscillations depend on both atoms' resonant frequencies.

Time oscillation frequency equals the atoms' detuning.

Abstract

We present a time-dependent quantum calculation of the van der Waals interaction between a pair of dissimilar atoms, one of which is initially excited while the other one is in its ground state. For small detuning, the interaction is predominantly mediated at all distances by the exchange of doubly resonant photons between the two atoms. We find that it presents both temporal and spatial oscillations. Spatially oscillating terms depend on the resonant frequencies of both atoms, while the frequency of the time oscillations is given by their detuning. We analyse the physical content of our findings and discuss to what extent previous conflicting stationary approaches provide compatible results. A proper account of causality is found essential in order to obtain the correct result.