Bloch state tomography using Wilson lines

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 multi-band systems. Using an ultracold gas of Rb 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 multi-band Chern and $Z_2$ numbers.

5+9 pages, final ublished version

References in corpus (9)

• The electronic properties of graphene
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Wannier representation of Z_2 topological insulators
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Optical Flux Lattices for Ultracold Atomic Gases
• Interferometric approach to measuring band topology in 2D optical lattices
• Geometric phase in Stückelberg interferometry

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