Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles

TL;DR

This study demonstrates that fractional Chern insulators can be identified in small cold-atom systems through center-of-mass Hall drift measurements and static density profiles, providing practical detection methods for experiments.

Contribution

It introduces a numerical approach to detect fractional Chern insulators in small bosonic ensembles via Hall drift and density profiles, linking topological properties to observable signatures.

Findings

Hall conductivity approaches fractional values consistent with topological invariants

Hall plateaus are observable through center-of-mass drift measurements

Density profiles can be used to identify topological phases via Streda's formula

Abstract

Realizing strongly-correlated topological phases of ultracold gases is a central goal for ongoing experiments. And while fractional quantum Hall states could soon be implemented in small atomic ensembles, detecting their signatures in few-particle settings remains a fundamental challenge. In this work, we numerically analyze the center-of-mass Hall drift of a small ensemble of hardcore bosons, initially prepared in the ground state of the Harper-Hofstadter-Hubbard model in a box potential. By monitoring the Hall drift upon release, for a wide range of magnetic flux values, we identify an emergent Hall plateau compatible with a fractional Chern insulator state: the extracted Hall conductivity approaches a fractional value determined by the many-body Chern number, while the width of the plateau agrees with the spectral and topological properties of the prepared ground state. Besides, a direct application of Streda's formula indicates that such Hall plateaus can also be directly obtained from static density-profile measurements. Our calculations suggest that fractional Chern insulators can be detected in cold-atom experiments, using available detection methods.