Bloch state tomography using Wilson lines

TL;DR

This paper demonstrates a method to perform Bloch state tomography by utilizing Wilson lines in ultracold Rb atoms within a honeycomb optical lattice, revealing detailed band geometry and topological invariants.

Contribution

It introduces a novel experimental technique to directly measure band eigenstates, Berry curvature, and topological invariants using Wilson lines in cold atom systems.

Findings

Successful realization of strong-force dynamics in Bloch bands

Direct observation of band population evolution revealing band geometry

Full determination of topological invariants including Chern and Z2 numbers

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.