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Topologically non-trivial Hamiltonians with periodic boundary conditions arecharacterized by strictly quantized invariants. Open questions and fundamentalchallenges concern their existence, and the possibility of measuring them insystems with open boundary conditions and limited spatial extension. Here, weconsider transport in Hofstadter strips, that is, two-dimensional latticespierced by a uniform magnetic flux which extend over few sites in one of thespatial dimensions. As we show, an atomic wavepacket exhibits a transversedisplacement under the action of a weak constant force. After one Blochoscillation, this displacement approaches the quantized Chern number of theperiodic system in the limit of vanishing tunneling along the transversedirection. We further demonstrate that this scheme is able to map out the Chernnumber of ground and excited bands, and we investigate the robustness of themethod in presence of both disorder and harmonic trapping. Our results provethat topological invariants can be measured in Hofstadter strips with openboundary conditions and as few as three sites along one direction.

Measuring Chern numbers in Hofstadter strips