Chern numbers hiding in time-of-flight images

We present a technique for detecting topological invariants -- Chern numbers
-- from time-of-flight images of ultra-cold atoms. We show that the Chern
numbers of integer quantum Hall states of lattice fermions leave their
fingerprints in the atoms' momentum distribution. We analytically demonstrate
that the number of local maxima in the momentum distribution is equal to the
Chern number in two limiting cases, for large hopping anisotropy and in the
continuum limit. In addition, our numerical simulations beyond these two limits
show that these local maxima persist for a range of parameters. Thus, an
everyday observable in cold atom experiments can serve as a useful tool to
characterize and visualize quantum states with non-trivial topology.