Multipole blackbody radiation shift in Rydberg atoms

TL;DR

This paper investigates the impact of retardation effects on the thermal radiation-induced energy shifts in Rydberg atoms, emphasizing the importance of non-dipole contributions at high temperatures.

Contribution

It provides a detailed analysis of multipole and retardation effects on Rydberg atom energy shifts due to thermal radiation, extending previous electric-dipole approximations.

Findings

Retardation effects become significant at temperatures above a specific threshold related to the principal quantum number.

Non-dipole shifts can dominate electric-dipole shifts at about 2.5 times the characteristic temperature.

Electric-quadrupole thermal shifts are comparable to diamagnetic shifts and should be considered in relevant scenarios.

Abstract

We study the role of retardation in the energy shift of Rydberg states induced by thermal radiation, focusing on the case of temperatures higher than those for which the electric-dipole approximation is expected to apply. As anticipated by Farley and Wing [Phys. Rev. A {\bf 23}, 2397 (1981)], retardation needs to be taken into account in calculations of this energy shift at and above the temperature $\alpha\, mc^2/(3k_{\rm B}\,n^2)$, where $n$ is the principal quantum number of the state considered, $m$ is the mass of the electron and $k_{\rm B}$ is Boltzmann constant.The corresponding non-dipole shift dominates the electric-dipole shift at about 2.5 times that characteristic temperature. We also show that the electric-quadrupole thermal shift is of the same order of magnitude as the diamagnetic thermal shift and would thus need to be taken into account in the circumstances where the latter is relevant.