Quasiperiodically 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 Letter opens up the possibility of using driven qubits to design and study higher-dimensional topological insulators and semimetals in synthetic dimensions.

中文翻译：

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用准周期性驱动的量子位研究二维合成量子霍尔物理

预测准周期性驱动的量子系统将表现出量化的拓扑特性，类似于拓扑绝缘体的量化的传输特性。我们使用金刚石中的单个氮空位中心来实验研究带有两个音调的合成量子霍尔效应。我们测量了两个量子态轨迹的演化，这些量子态最初是在合成相空间中的邻近点准备的。我们通过在与基恩数成比例的量化基频上通过预测的重叠振荡来检测合成霍尔效应，这表征了系统的拓扑相位。我们进一步观察到在合成霍尔体系和平凡体系之间过渡处的切恩数的半量化，以及在合成相空间中相关的局部贝里曲率的集中。