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

TL;DR

This paper reports the experimental measurement of a topological invariant, the Chern number, in a superconducting qubit system, demonstrating a topological transition by manipulating the Hamiltonian parameters.

Contribution

First measurement of a topological transition in a superconducting qubit system using nonadiabatic response to determine the Chern number.

Findings

Quantized Chern number measurement within 2% accuracy

Observation of a topological transition from C=1 to C=0

Controlled manipulation of Hamiltonian parameters to induce topological change

Abstract

We present measurements of a topological property, the Chern number ($C_\mathrm{1}$), 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 $C_\mathrm{1}$ from the nonadiabitic 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 $C_\mathrm{1} = 1 \rightarrow 0$. Our measurement of $C_\mathrm{1}$ is quantized to within 2 percent on either side of the transition.