Quantum Hall Physics with Cold Atoms in Cylindrical Optical Lattices

TL;DR

This paper proposes a method to realize and study quantum Hall physics using cold atoms in cylindrical optical lattices created by Laguerre-Gauss beams, enabling exploration of fractional quantum Hall effects.

Contribution

It introduces a novel experimental setup with optical lattices and synthetic gauge fields to simulate quantum Hall systems and probe their responses with cold atoms.

Findings

Design of a cylindrical optical lattice using Laguerre-Gauss beams

Implementation of synthetic magnetic fields and flux variation

Potential observation of fractional quantum Hall physics in cold atom systems

Abstract

We propose and study various realizations of a Hofstadter-Hubbard model on a cylinder geometry with fermionic cold atoms in optical lattices. The cylindrical optical lattice is created by copropagating Laguerre-Gauss beams, i.e.~light beams carrying orbital angular momentum. By strong focusing of the light beams we create a real space optical lattice in the form of rings, which are offset in energy. A second set of Laguerre-Gauss beams then induces a Raman-hopping between these rings, imprinting phases corresponding to a synthetic magnetic field (artificial gauge field). In addition, by rotating the lattice potential, we achieve a slowly varying flux through the hole of the cylinder, which allows us to probe the Hall response of the system as a realization of Laughlin's thought experiment. We study how in the presence of interactions fractional quantum Hall physics could be observed in this setup.