Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to topological states predicted in dimensions D > 3. We report the realization of an atomic quantum Hall system evolving in four dimensions (4D), with two spatial dimensions and two synthetic ones encoded in the large spin of dysprosium atoms. We measure the nontrivial topological index of the ground band through a full characterization of the nonlinear electromagnetic response and observe the associated anisotropic hyperedge modes. We also excite nonplanar cyclotron motion, in contrast to the planar orbits in D ≤ 3. Our work may enable the investigation of strongly correlated topological liquids in 4D, generalizing fractional quantum Hall states.

中文翻译：

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四维原子量子霍尔系统的实现


现代凝聚态物理学依靠拓扑概念对物质进行分类，从量子霍尔系统到拓扑绝缘体。受益于合成维度的工程系统有可能获得维度预测的拓扑状态D > 3. 我们报告了在四个维度 (4D) 中演化的原子量子霍尔系统的实现，其中两个空间维度和两个合成维度编码在镝原子的大自旋中。我们通过非线性电磁响应的完整表征来测量地带的非平凡拓扑指数，并观察相关的各向异性超边缘模式。我们还激发非平面回旋运动，与平面轨道相反D ≤ 3。我们的工作可能能够研究 4D 中的强相关拓扑液体，推广分数量子霍尔态。