title: Measuring a topological transition in an artificial spin-1/2 system.
abstract: We present measurements of a topological property, the Chern number (C_{1}), of a closed manifold in the space of two-level system Hamiltonians, where the two-level system is formed from a superconducting qubit. We manipulate the parameters of the Hamiltonian of the superconducting qubit along paths in the manifold and extract C_{1} from the nonadiabatic response of the qubit. By adjusting the manifold such that a degeneracy in the Hamiltonian passes from inside to outside the manifold, we observe a topological transition C_{1}=1→0. Our measurement of C_{1} is quantized to within 2% on either side of the transition.
authors.affiliation: JILA, National Institute of Standards and Technology and The University of Colorado, Boulder, Colorado 80309, USA.
authors.forename: M D
authors.initials: MD
authors.lastname: Schroer
authors.affiliation: Physics Department, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: M H
authors.initials: MH
authors.lastname: Kolodrubetz
authors.affiliation: JILA, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA.
authors.forename: W F
authors.initials: WF
authors.lastname: Kindel
authors.affiliation: National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
authors.forename: M
authors.initials: M
authors.lastname: Sandberg
authors.affiliation: National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
authors.forename: J
authors.initials: J
authors.lastname: Gao
authors.affiliation: National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
authors.forename: M R
authors.initials: MR
authors.lastname: Vissers
authors.affiliation: National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
authors.forename: D P
authors.initials: DP
authors.lastname: Pappas
authors.affiliation: Physics Department, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Anatoli
authors.initials: A
authors.lastname: Polkovnikov
authors.affiliation: JILA, National Institute of Standards and Technology and The University of Colorado, Boulder, Colorado 80309, USA and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA.
authors.forename: K W
authors.initials: KW
authors.lastname: Lehnert