Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully captured by the quantum geometric tensor. Using a qubit formed by an NV center in diamond, we perform the first experimental measurement of the complete quantum geometric tensor. Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states. We then apply our method to a system of two interacting qubits, by exploiting the coupling between the NV center spin and a neighboring ¹³C nuclear spin. Our results establish coherent dynamical responses as a versatile probe for quantum geometry, and they pave the way for the detection of novel topological phenomena in solid state.

中文翻译：

---

使用金刚石中的耦合量子位对量子几何张量进行实验测量

几何学和拓扑学是基本概念，它们构成了各种引人入胜的物理现象的基础，例如物质的拓扑状态和拓扑缺陷。在量子力学中，量子态的几何形状完全被量子几何张量所捕获。使用由金刚石中的 NV 中心形成的量子位，我们对完整的量子几何张量进行了第一次实验测量。我们的方法建立在参数调制的相干 Rabi 振荡与基础状态的量子几何之间的紧密联系之上。然后，我们通过利用 NV 中心自旋和相邻的¹³C 核自旋。我们的结果建立了相干动力学响应，作为量子几何的通用探针，它们为检测固态中的新拓扑现象铺平了道路。