Resonance energy transfer between two atoms in a conducting cylindrical waveguide

TL;DR

This paper analyzes how a perfectly conducting cylindrical waveguide modifies the energy transfer between two atoms, showing suppression in the far zone and variable effects depending on dipole orientation and distance.

Contribution

It provides an analytical framework for energy transfer in waveguides using Green's tensors and evaluates the effects of waveguide geometry on atomic interactions.

Findings

Energy transfer is suppressed in the far zone within the waveguide.

Radial dipoles experience larger modifications than axial dipoles.

Waveguide presence significantly alters the resonance interaction energy.

Abstract

We consider the energy transfer process between two identical atoms placed inside a perfectly conducting cylindrical waveguide. We first introduce a general analytical expression of the energy transfer amplitude in terms of the electromagnetic Green's tensor; we then evaluate it in the case of a cylindrical waveguide made of a perfect conductor, for which analytical forms of the Green's tensor exist. We numerically analyse the energy transfer amplitude when the radius of the waveguide is such that the transition frequency of both atoms is below the lower cutoff frequency of the waveguide, so that the resonant photon exchange is strongly suppressed. We consider both cases of atomic dipoles parallel and orthogonal to the axis of the guide. In both cases, we find that the energy transfer is modified by the presence of the waveguide. In the near zone, that is when the atomic separation is smaller than the atomic transition wavelength, the change, with respect to the free-space case, is small for axial dipoles, while it is larger for radial dipoles; it grows when the intermediate region between near and far zone is approached. In the far zone, we find that the energy transfer amplitude is strongly suppressed by the waveguide, becoming virtually zero. A physical interpretation of these results is discussed. Finally, we discuss the resonance interaction energy and force between two identical correlated atoms in the waveguide, one excited and the other in the ground state, prepared in their symmetric or antisymmetric superposition.