Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms

TL;DR

This paper demonstrates the first measurement of the Chern number in a non-electronic system using ultracold atoms, revealing topological properties of Hofstadter bands through transverse deflection experiments.

Contribution

It introduces an all-optical method to measure the Chern number of Hofstadter bands in ultracold atoms, bridging a gap between electronic topological phenomena and atomic systems.

Findings

Measured Chern number of the lowest band as 0.99(5)

First Chern-number measurement in a non-electronic system

Utilized an all-optical scheme to generate uniform flux

Abstract

Sixty years ago, Karplus and Luttinger pointed out that quantum particles moving on a lattice could acquire an anomalous transverse velocity in response to a force, providing an explanation for the unusual Hall effect in ferromagnetic metals. A striking manifestation of this transverse transport was then revealed in the quantum Hall effect, where the plateaus depicted by the Hall conductivity were attributed to a topological invariant characterizing Bloch bands: the Chern number. Until now, topological transport associated with non-zero Chern numbers has only been revealed in electronic systems. Here we use studies of an atomic cloud's transverse deflection in response to an optical gradient to measure the Chern number of artificially generated Hofstadter bands. These topological bands are very flat and thus constitute good candidates for the realization of fractional Chern insulators. Combining these deflection measurements with the determination of the band populations, we obtain an experimental value for the Chern number of the lowest band $\nu_{\mathrm{exp}} =0.99(5)$. This result, which constitutes the first Chern-number measurement in a non-electronic system, is facilitated by an all-optical artificial gauge field scheme, generating uniform flux in optical superlattices.