Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states

TL;DR

This paper demonstrates how adiabatic motion of ultra-cold atoms in specially configured laser fields can produce non-Abelian gauge potentials, enabling the simulation of complex gauge fields including monopole-like magnetic fields.

Contribution

It introduces a method to generate non-Abelian gauge fields in ultra-cold atoms using degenerate dark states in a tripod scheme, expanding quantum simulation capabilities.

Findings

Non-Abelian gauge potentials can be realized with degenerate dark states.

Orthogonal laser beams with orbital angular momentum create effective magnetic fields.

A monopole component in the gauge field is achievable.

Abstract

We show that the adiabatic motion of ultra-cold, multi-level atoms in spatially varying laser fields can give rise to effective non-Abelian gauge fields if degenerate adiabatic eigenstates of the atom-laser interaction exist. A pair of such degenerate dark states emerges e.g. if laser fields couple three internal states of an atom to a fourth common one under pairwise two--photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component.