  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.

Quantum Physics