Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit*

Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties, in analogy with the quantized transport properties of topological insulators. We use a single nitrogen-vacancy center in diamond to experimentally study a synthetic quantum Hall effect with a two-tone drive. We measure the evolution of trajectories of two quantum states, initially prepared at nearby points in synthetic phase space. We detect the synthetic Hall effect through the predicted overlap oscillations at a quantized fundamental frequency proportional to the Chern number, which characterizes the topological phases of the system. We further observe half-quantization of the Chern number at the transition between the synthetic Hall regime and the trivial regime, and the associated concentration of local Berry curvature in synthetic phase space. Our work opens up the possibility of using driven qubits to design and study higher-dimensional topological insulators and semi-metals in synthetic dimensions.