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.

 量子几何张量是一个刻画量子系统几何性质的重要物理量，它的虚部对应着人们熟知的贝里曲率，在凝聚态物理、量子物理和光学等领域中都有着十分重要的应用；它的实部则对应着黎曼度规，用来定义两个相邻的量子态在参数空间中的“距离”，与量子精密测量理论中的量子费舍信息关系密切。近些年来，随着研究的深入，量子几何张量的重要性正在逐渐显现。例如：它与平带中的超流效应，轨道磁性，受激兰姆位移和非绝热反常霍尔效应等都相关。由于量子几何张量在拓扑物理、量子信息处理以及精密测量等领域的重要应用，因此，实现对量子几何张量的完整测量在实验上是十分必要的。