Chern numbers hiding in time-of-flight images

Details Chern numbers hiding in time-of-flight images Chern numbers hiding in time-of-flight images

2011-05-16

arxiv.org/abs/1105.3100v3

Phys. Rev. A 84, 063629 (2011)

Physics

Condensed Matter

Quantum Gases

Published version

Scientific paper

10.1103/PhysRevA.84.063629

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.

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