Bloch State Tomography Using Wilson Lines
Fig. 1b: Wilson lines and effectively degenerate Bloch bands.* [Reprinted with permission from AAAS ©2016.]
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.
In a new issue of Science*, Prof. Eugene Demler and colleagues from several institutions in Germany, as well as Caltech, and Stanford, described a new technique for measuring the detailed structure of the band wave functionsby using an ultracold gas of rubidium atoms loaded in a honeycomb optical lattice. This technique enables a full determination of band eigenstates, Berry curvature, and topological invariants, including single- and multiband Chern and Z2 numbers.
* Read T. Li, L. Duca, M. Reitter, F. Grusdt, E. Demler, M.l Endres, M. Schleier-Smith, I. Bloch, and U. Schneider, "Bloch state tomography using Wilson lines," Science 352: 6289 (27 May 2016) DOI: 10.1126/science.aad5812.