Realizing the Harper model with Ultracold Atoms in a Ring Lattice

TL;DR

This paper demonstrates how ultracold atoms in a ring lattice can emulate the Harper-Hofstadter model, revealing critical spectral features, localization transitions, and edge-like states through realistic potentials and experimental conditions.

Contribution

It provides a practical implementation of the Harper model with ultracold atoms, analyzing deviations from ideal models and introducing methods to observe key phenomena.

Findings

Realization of the Harper spectrum in a ring lattice with ultracold atoms.

Observation of the Aubry-André localization transition in a finite, commensurate ring.

Generation of edge-like localized states with minimal perturbations.

Abstract

We demonstrate that all of the salient features of the Harper-Hofstadter model can be implemented with ultracold atoms trapped in a bichromatic ring-shaped lattice. Using realistic sinusoidal lattice potentials rather than assume the idealized tight-binding picture, we determine the optimal conditions necessary to realize the critical point where the spectrum becomes fractal, and identify the nature and cause of the departures from the discrete model predictions. We also show that even with a commensurate ring with a few lattice sites, the Aubry-Andr\'e localization transition can be realized. Localized states that behave like edge states with energies that reside in the band gaps can be generated by introducing a surprisingly small local perturbation within the ring. Spectrum oscillation arising from complex coupling can be implemented by uniform rotation of the ring, but with certain significant differences that are explained