Starts 5 May 2016 14:30
Ends 5 May 2016 16:00
Central European Time
Topology and geometry are fundamental 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, the most prominent examples being the Quantum Hall Effect and Topological Insulators, which are governed by the Berry curvature of isolated bands. For general multi-band systems, the geometry of Hilbert space is encoded in the matrix-valued Wilson line, giving rise to more intricate transport phenomena and holding the potential for holonomic quantum computing. I will start with an introduction into these concepts and then present interferometric measurements of Bloch band geometry using ultracold atoms in optical lattices. In analogy to an Aharonov-Bohm interferometer that measures magnetic flux, we realized an atomic interferometer measureing Berry curvature in momentum space. For our graphene-type hexagonal optical lattice, this interferometer enabled us to directly observe the singular pi-Berry flux localized at each Dirac point. We furthermore engineered strong-force dynamics in Bloch bands that are described by Wilson lines and observed an evolution in the band populations that directly reveals band geometry. Our techniques enable a full determination of the dispersion relations, band eigenstates, Berry curvature distributions, and topological invariants, including single- and multi-band Chern and Z2 numbers. Time permitting, I'll also present a short update on our activities regarding Many-Body Localization (MBL).