Topologically non-trivial Hamiltonians with periodic boundary
conditions are characterized by strictly quantized invariants. Open
questions and fundamental challenges concern their existence, and the
possibility of measuring them in systems with open boundary conditions
and limited spatial extension. Here, we consider transport in Hofstadter
strips, that is, two-dimensional lattices pierced by a uniform magnetic
flux which extend over few sites in one of the spatial dimensions. As we
show, an atomic wave packet exhibits a transverse displacement under the
action of a weak constant force. After one Bloch oscillation, this
displacement approaches the quantized Chern number of the periodic
system in the limit of vanishing tunneling along the transverse
direction. We further demonstrate that this scheme is able to map out
the Chern number of ground and excited bands, and we investigate the
robustness of the method in presence of both disorder and harmonic
trapping. Our results prove that topological invariants can be measured
in Hofstadter strips with open boundary conditions and as few as three
sites along one direction.
Measuring topology from dynamics by obtaining the Chern number from a linking number