Quantum corrections to the classical electrostatic interaction between induced dipoles

TL;DR

This paper investigates quantum corrections to classical electrostatic interactions between induced dipoles under an external field, revealing higher-order quantum effects that modify the interaction potential beyond classical predictions.

Contribution

It demonstrates that higher-order quantum corrections, including two-photon and three-photon exchange processes, alter the classical dipole-dipole interaction in the presence of an external electrostatic field.

Findings

Classical dipole-dipole interaction is valid up to fourth order.

Quantum corrections appear at sixth and eighth orders, modifying the interaction.

Quantum corrections are much smaller than Casimir-Polder interactions.

Abstract

We study, in the presence of an external electrostatic field, the interatomic interaction between two ground-state atoms coupled with vacuum electromagnetic fluctuations within the dipole coupling approximation based on the perturbation theory. We show that, up to the fourth order, the electrostatic-field-induced interatomic interaction is just the classical dipole-dipole interaction, which disagrees with the recent result from Fiscelli et al. [G. Fiscelli et al., Phys. Rev. Lett. 124, 013604 (2020)]. However, to higher orders, there exist external-field-related quantum corrections to the induced classical electrostatic dipole-dipole interaction. In the sixth order, the external field effectively modifies the atomic polarizability to give rise to a two-photon-exchange quantum correction, while in the eighth order, the external field enables an additional process of three-photon exchange which is not allowed in the absence of the external field, and this process generates an $r^{-11}$ term in the interaction potential in the far regime, where $r$ is the interatomic separation. Numerical estimations show that these external-field-related quantum corrections are much smaller than the two-photon-exchange Casimir-Polder interaction.