title: Measuring the Second Chern Number from Nonadiabatic Effects.
abstract: The geometry and topology of quantum systems have deep connections to quantum dynamics. In this Letter, I show how to measure the non-Abelian Berry curvature and its related topological invariant, the second Chern number, using dynamical techniques. The second Chern number is the defining topological characteristic of the four-dimensional generalization of the quantum Hall effect and has relevance in systems from three-dimensional topological insulators to Yang-Mills field theory. I illustrate its measurement using the simple example of a spin-3/2 particle in an electric quadrupole field. I show how one can dynamically measure diagonal components of the Berry curvature in an overcomplete basis of the degenerate ground state space and use this to extract the full non-Abelian Berry curvature. I also show that one can accomplish the same ideas by stochastically averaging over random initial states in the degenerate ground state manifold. Finally, I show how this system can be manufactured and the topological invariant measured in a variety of realistic systems, from superconducting qubits to trapped ions and cold atoms.
authors.affiliation: Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA; Department of Physics, University of California, Berkeley, California 94720, USA; and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Kolodrubetz