Quantized energy pumping in quasi-periodically driven Nitrogen Vacancy Centres

A spin strongly driven by two incommensurate tones can exhibit a topological class of dynamics in which it (i) pumps energy from one drive to the other at a quantized average rate, in precise relationship with the quantum Hall effect, and (ii) exhibits an oscillatory response to a perturbation to the phases of the drives. We show these remarkable signatures to be realized in experiments in Nitrogen Vacancy centres. We further provide an experimental demonstration of half-integer quantization of various responses at the transition between the topological and trivial classes of dynamics.