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Nat Commun. 2016 Jun 17;7:11994. doi: 10.1038/ncomms11994.

Interferometric measurements of many-body topological invariants using mobile impurities.

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Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, Kaiserslautern 67663, Germany.
Graduate School Materials Science in Mainz, Gottlieb-Daimler-Strasse 47, 67663 Kaiserslautern, Germany.
Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Department of Physics, University of California, Berkeley, California 94720, USA.
Department of Theoretical Physics, University of Geneva, 24 quai Ernest-Ansermet, 1207 Geneva, Switzerland.


Topological quantum phases cannot be characterized by Ginzburg-Landau type order parameters, and are instead described by non-local topological invariants. Experimental platforms capable of realizing such exotic states now include synthetic many-body systems such as ultracold atoms or photons. Unique tools available in these systems enable a new characterization of strongly correlated many-body states. Here we propose a general scheme for detecting topological order using interferometric measurements of elementary excitations. The key ingredient is the use of mobile impurities that bind to quasiparticles of a host many-body system. Specifically, we show how fractional charges can be probed in the bulk of fractional quantum Hall systems. We demonstrate that combining Ramsey interference with Bloch oscillations can be used to measure Chern numbers characterizing the dispersion of individual quasiparticles, which gives a direct probe of their fractional charges. Possible extensions of our method to other many-body systems, such as spin liquids, are conceivable.

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