Concepts from topology provide insight into wide ranging areas from fluid mechanics to quantum condensed matter physics. We studied the topology of ultracold 87Rb atoms in a highly tunable bipartite optical lattice, using a form of quantum state tomography, to measure the full pseudospin state throughout the Brillouin zone. We used this capability to follow the evolution of two topological quantities: the Zak phase and chiral winding number, after changing the lattice configuration. We observed continuous time evolution of the Zak phase and discontinuous changes in the winding number, depending on the symmetries of the initial state and evolution Hamiltonian. Next, we studied a topological Floquet system with a linear (Dirac) dispersion created by periodically changing the lattice configuration. We measured the underlying Floquet topological invariant from the time resolved pseudospin micromotion.

(Pizza and refreshments will be served after the talk.)