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Chern numbers hiding in time-of-flight images

TitleChern numbers hiding in time-of-flight images
Publication TypeJournal Article
Year of Publication2011
AuthorsE. Zhao, N. Bray-Ali, C. J. Williams, I. B. Spielman, and I. Satija
JournalPhys. Rev. A
Date Publisheddec
Keywords2011, Multiple Fellows

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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