Detecting Chiral Edge States in the Hofstadter Optical Lattice

Nathan Goldman, Jérôme Beugnon, and Fabrice Gerbier
Phys. Rev. Lett. 108, 255303 – Published 19 June 2012
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Abstract

We propose a realistic scheme to detect topological edge states in an optical lattice subjected to a synthetic magnetic field, based on a generalization of Bragg spectroscopy sensitive to angular momentum. We demonstrate that using a well-designed laser probe, the Bragg spectra provide an unambiguous signature of the topological edge states that establishes their chiral nature. This signature is present for a variety of boundaries, from a hard wall to a smooth harmonic potential added on top of the optical lattice. Experimentally, the Bragg signal should be very weak. To make it detectable, we introduce a “shelving method,” based on Raman transitions, which transfers angular momentum and changes the internal atomic state simultaneously. This scheme allows us to detect the weak signal from the selected edge states on a dark background, and drastically improves the detectivity. It also leads to the possibility to directly visualize the topological edge states, using in situ imaging, offering a unique and instructive view on topological insulating phases.

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  • Received 6 March 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.255303

© 2012 American Physical Society

Authors & Affiliations

Nathan Goldman1,*, Jérôme Beugnon2, and Fabrice Gerbier2

  • 1Center for Nonlinear Phenomena and Complex Systems-Université Libre de Bruxelles (U.L.B.), B-1050 Brussels, Belgium
  • 2Laboratoire Kastler Brossel, CNRS, ENS, UPMC, 24 rue Lhomond, 75005 Paris

  • *ngoldman@ulb.ac.be

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Issue

Vol. 108, Iss. 25 — 22 June 2012

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