Proposal for direct measurement of topological invariants in optical lattices
Lei Wang, Alexey A. Soluyanov, and Matthias Troyer
Accepted
We propose an experimental technique for classifying the topology of band structures realized in optical lattices, based on a generalization of topological charge pumping in quantum Hall systems to cold atoms in optical lattices. Time-of-flight measurement along one spatial direction combined with in situ detection along the transverse direction provide a direct measure of the system's Chern number, as we illustrate by calculations for the Hofstadter lattice. Based on an analogy with Wannier functions techniques of topological band theory, the method is very general and also allows the measurement of other topological invariants, such as the \mathbbZ2 topological invariant of time-reversal symmetric insulators.