Hairy Ball Theorem

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APS » Journals » Phys. Rev. A » Volume 84 » Issue 6

Phys. Rev. A 84, 063629 (2011) [5 pages]

Chern numbers hiding in time-of-flight images

Erhai Zhao1,2, Noah Bray-Ali2,, Carl J. Williams2, I. B. Spielman2, and Indubala I. Satija1,2
1School of Physics, Astronomy, and Computational Sciences, George Mason University, Fairfax, Virginia 22030, USA
2Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA

Received 19 May 2011; revised 8 July 2011; published 21 December 2011

We present a technique for detecting topological invariants—Chern numbers—from time-of-flight images of ultracold 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 nontrivial topology.
©2011 American Physical Society
DOI: 10.1103/PhysRevA.84.063629
PACS: 67.85.-d, 03.75.Mn, 03.75.Ss, 05.30.