Measurement of distance and orientation of two atoms in arbitrary geometry

TL;DR

This paper presents a method to accurately measure the distance and orientation of two nearby atoms with arbitrary relative geometry, using a realistic model that accounts for all Zeeman states and dipole couplings.

Contribution

It introduces a comprehensive approach to determine atomic distance and orientation without prior knowledge, considering arbitrary configurations and including complex atomic interactions.

Findings

Distance can be measured independently of orientation for close atoms.

Orientation of atoms can be inferred in waveguide and surface configurations.

Complete Zeeman and dipole interactions are essential for accurate measurements.

Abstract

Accurate measurement of relative distance and orientation of two nearby quantum particles is discussed. We are in particular interested in a realistic description requiring as little prior knowledge about the system as possible. Thus, unlike in previous studies, we consider the case of an arbitrary relative orientation of the two atoms. For this, we model the atom with complete Zeeman manifolds, and include parallel as well as orthogonal dipole-dipole couplings between all states of the two atoms. We find that it is possible to determine the distance of the two atoms independent of the orientation, as long as the particles are sufficiently close to each other. Next, we discuss how in addition the alignment of the atoms can be measured. For this, we focus on the two cases of atoms in a two-dimensional waveguide and of atoms on a surface.