Measurement of the topological Chern number by continuous probing of a qubit subject to a slowly varying Hamiltonian

Abstract

We analyze a measurement scheme that allows determination of the Berry curvature and the topological Chern number of a Hamiltonian with parameters exploring a two-dimensional closed manifold. Our method uses continuous monitoring of the gradient of the Hamiltonian with respect to one parameter during a quasi-adiabatic quench of the other. Measurement back-action leads to disturbance of the system dynamics, but we show that this can be compensated by a feedback Hamiltonian. As an example, we analyze the implementation with a superconducting qubit subject to time varying, near resonant microwave fields; equivalent to a spin 1/2 particle in a magnetic field.

Revised version with new analytic results, numerical simulations and figures. Accepted for Rapid Publication in PRA. 6 pages, 2 figures, Supplemental material included (4 pages). Journal reference added and figures updated for better grayscale appearance