Measurement of the quantum geometric tensor and of the anomalous Hall drift
Measurement of the quantum geometric tensor and of the anomalous Hall drift
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DOI：
10.1038/s41586-020-1989-2
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发表时间：
2020-02-20
期刊：
影响因子：
64.8
通讯作者：
Malpuech, G.
中科院分区：
文献类型：
--
作者：
Gianfrate, A.;Bleu, O.;Malpuech, G.
拓扑物理学依赖于哈密顿算符本征态的结构。本征态的几何被编码在量子几何张量（1）中-包括Berry曲率（2）（对拓扑物质至关重要）（3）和量子度量（4），它定义了本征态之间的距离。量子度规的知识对于理解许多现象是必不可少的，例如平带中的超流性（5），轨道磁化率（6，7），激子兰姆位移（8）和非绝热异常霍尔效应（6，9）。然而，能带的量子几何结构还没有被测量。在这里，我们报告的Berry曲率和量子度规的直接测量在一个二维连续介质-高精细度平面微腔（10）-连同相关的异常霍尔漂移。微腔容纳强耦合的激子-光子模式（激子极化激元），其经受光子自旋-轨道耦合（11），狄拉克锥从光子自旋-轨道耦合（12）出现，并且经受激子塞曼分裂，破坏时间反演对称性。单极和半skyrmion赝自旋织构测量使用偏振分辨光致发光。相关的量子几何的频带提取，使预测的异常霍尔漂移，我们独立测量使用高分辨率的空间分辨epifluorescence。我们的结果揭示了光子模式的固有手性，拓扑光子学的基石（13-15）。这些结果也验证了几何非平凡带中波包运动的半经典描述（9，16）。激子极化激元（相互作用光子）的使用为拓扑系统中量子流体物理的未来研究开辟了可能性。
Topological physics relies on the structure of the eigenstates of the Hamiltonians. The geometry of the eigenstates is encoded in the quantum geometric tensor(1)-comprising the Berry curvature(2) (crucial for topological matter)(3) and the quantum metric(4), which defines the distance between the eigenstates. Knowledge of the quantum metric is essential for understanding many phenomena, such as superfluidity in flat bands(5), orbital magnetic susceptibility(6,7), the exciton Lamb shift(8) and the non-adiabatic anomalous Hall effect(6,9). However, the quantum geometry of energy bands has not been measured. Here we report the direct measurement of both the Berry curvature and the quantum metric in a two-dimensional continuous medium-a high-finesse planar microcavity(10)-together with the related anomalous Hall drift. The microcavity hosts strongly coupled exciton-photon modes (exciton polaritons) that are subject to photonic spin-orbit coupling(11) from which Dirac cones emerge(12), and to exciton Zeeman splitting, breaking time-reversal symmetry. The monopolar and half-skyrmion pseudospin textures are measured using polarization-resolved photoluminescence. The associated quantum geometry of the bands is extracted, enabling prediction of the anomalous Hall drift, which we measure independently using high-resolution spatially resolved epifluorescence. Our results unveil the intrinsic chirality of photonic modes, the cornerstone of topological photonics(13-15). These results also experimentally validate the semiclassical description of wavepacket motion in geometrically non-trivial bands(9,16). The use of exciton polaritons (interacting photons) opens up possibilities for future studies of quantum fluid physics in topological systems.