Abelian and non-Abelian gauge fields in dipole-dipole interacting Rydberg atoms

TL;DR

This paper demonstrates how dipole-dipole interactions in Rydberg atoms generate both Abelian and non-Abelian gauge fields, leading to synthetic magnetic fields and spin-orbit coupling effects in atomic motion.

Contribution

It introduces a method to evaluate gauge fields in Rydberg atom systems and shows their effects on atomic states, including synthetic spin-orbit coupling.

Findings

Gauge fields cause Zeeman splitting of rotational states

Ground state is the first excited rotational state in a potential well

System realizes non-Abelian gauge fields and spin-orbit coupling

Abstract

We show that the dipole-dipole interaction between two Rydberg atoms can lead to substantial Abelian and non-Abelian gauge fields acting on the relative motion of the two atoms. We demonstrate how the gauge fields can be evaluated by numerical techniques. In the case of adiabatic motion in a single internal state, we show that the gauge fields give rise to a magnetic field that results in a Zeeman splitting of the rotational states. In particular, the ground state of a molecular potential well is given by the first excited rotational state. We find that our system realises a synthetic spin-orbit coupling where the relative atomic motion couples to two internal two-atom states. The associated gauge fields are non-Abelian.