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Bloch state tomography using Wilson lines.

Tracy Li1, Lucia Duca1, Martin Reitter1

  • 1Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany.

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Researchers used ultracold atoms in a honeycomb lattice to directly observe the geometry of electronic band structures. This method reveals band eigenstates and topological invariants, advancing condensed-matter physics.

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Area of Science:

  • Condensed-matter physics
  • Quantum information science
  • Atomic physics

Background:

  • Topology and geometry are fundamental to modern physics, influencing high-energy theories, quantum information, and condensed-matter systems.
  • The geometry of band eigenstates, encoded in Wilson lines, governs phenomena in condensed-matter systems.

Purpose of the Study:

  • To experimentally probe and visualize the geometric properties of Bloch bands in a tunable system.
  • To demonstrate a method for fully characterizing band eigenstates and topological invariants.

Main Methods:

  • Utilizing an ultracold gas of rubidium atoms in a honeycomb optical lattice.
  • Implementing strong-force dynamics within Bloch bands described by Wilson lines.
  • Observing the evolution of band populations to infer band geometry.

Main Results:

  • Direct observation of band geometry through the evolution of band populations.
  • Successful determination of band eigenstates and Berry curvature.
  • Measurement of topological invariants, including single- and multiband Chern and Z₂ numbers.

Conclusions:

  • The experimental technique provides a powerful tool for exploring band geometry and topology in condensed-matter systems.
  • This work bridges the gap between theoretical concepts of band geometry and experimental observation.
  • Enables a deeper understanding of topological phenomena in quantum materials.