Bloch state tomography using Wilson lines

Tracy Li; Lucia Duca; Martin Reitter; Fabian Grusdt; Eugene Demler; Manuel Endres; Monika Schleier-Smith; Immanuel Bloch; Ulrich Schneider

doi:10.1126/science.aad5812

Bloch state tomography using Wilson lines

Science. 2016 May 27;352(6289):1094-7. doi: 10.1126/science.aad5812.

Authors

Tracy Li¹, Lucia Duca¹, Martin Reitter¹, Fabian Grusdt², Eugene Demler³, Manuel Endres⁴, Monika Schleier-Smith⁵, Immanuel Bloch¹, Ulrich Schneider⁶

Affiliations

¹ Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany.
² Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, Germany. Graduate School Materials Science in Mainz, Gottlieb-Daimler-Strasse 47, 67663 Kaiserslautern, Germany. Department of Physics, Harvard University, Cambridge, MA 02138, USA.
³ Department of Physics, Harvard University, Cambridge, MA 02138, USA.
⁴ Department of Physics, Harvard University, Cambridge, MA 02138, USA. Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA.
⁵ Department of Physics, Stanford University, Stanford, CA 94305, USA.
⁶ Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany. Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK. uws20@cam.ac.uk.

PMID: 27230376
DOI: 10.1126/science.aad5812

Abstract

Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high-energy theories, quantum information, and condensed-matter physics. In condensed-matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multiband systems. Using an ultracold gas of rubidium atoms loaded in a honeycomb optical lattice, we realize strong-force dynamics in Bloch bands that are described by Wilson lines and observe an evolution in the band populations that directly reveals the band geometry. Our technique enables a full determination of band eigenstates, Berry curvature, and topological invariants, including single- and multiband Chern and Z₂ numbers.

Publication types

Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.