Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms

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M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, N. Goldman
Nature Physics 11, 162-166 (2015), published online AOP 3171 (2014)

The quantum Hall effect has led to a deeper understanding of topological (or geometrical) effects in physics and has found generalizations in the spin quantum Hall effect and topological insulators. The plateaux in conductivity in this effect are attributed to the Chern numbers, a topological invariant characterizing the Bloch bands.

In their work, Aidelsburger and co-workers report the first measurement of Chern numbers in a non- electronic system. They use the transverse deflection of an atomic cloud 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. The experiment is facilitated by an all-optical artificial gauge field scheme, generating uniform flux in optical super-lattices.