Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms

Abstract

Chern numbers characterize the quantum Hall effect conductance—non-zero values are associated with topological phases. Previously only spotted in electronic systems, they have now been measured in ultracold atoms subject to artificial gauge fields. 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 metals1. A striking manifestation of this transverse transport was then revealed in the quantum Hall effect2 where the plateaux depicted by the Hall conductivity were attributed to a topological invariant characterizing the Bloch bands: the Chern number3. Until now, topological transport associated with non-zero Chern numbers has only been observed in electronic systems2,4,5. Here we use the transverse deflection of an atomic cloud in response to an optical gradient to measure the Chern number of artificially generated Hofstadter bands6. These topological bands are very flat and thus constitute good candidates for the realization of fractional Chern insulators7. Combining these deflection measurements with the determination of the band populations, we obtain an experimental value for the Chern number of the lowest band νexp = 0.99(5). This 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.