Measuring a topological transition in an artificial spin-1/2 system

Phys Rev Lett. 2014 Aug 1;113(5):050402. doi: 10.1103/PhysRevLett.113.050402. Epub 2014 Jul 30.


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.