# Abelian gauge potentials on cubic lattices

## TL;DR

This paper reviews how to implement and analyze tunable Abelian gauge potentials in ultracold atom systems on cubic lattices, highlighting experimental schemes, theoretical models, and applications in ring geometries.

## Contribution

It provides a comprehensive overview of experimental methods and theoretical models for synthetic Abelian gauge fields in optical lattices, including applications in one-dimensional rings.

## Key findings

- Two main experimental schemes for synthetic gauge potentials are discussed.
- Cubic lattice tight-binding models with commensurate flux are analyzed.
- Applications in one-dimensional ring systems are examined.

## Abstract

The study of the properties of quantum particles in a periodic potential subject to a magnetic field is an active area of research both in physics and mathematics; it has been and it is still deeply investigated. In this review we discuss how to implement and describe tunable Abelian magnetic fields in a system of ultracold atoms in optical lattices. After discussing two of the main experimental schemes for the physical realization of synthetic gauge potentials in ultracold set-ups, we study cubic lattice tight-binding models with commensurate flux. We finally examine applications of gauge potentials in one-dimensional rings.