Going beyond the first Chern number Topological properties of physical systems are reflected in so-called Chern numbers: A nonzero Chern number typically means that a system is topologically nontrivial. Sugawa et al. engineered a cold atom system with a nonzero second Chern number, in contrast to condensed matter physics, where only the first Chern number is usually invoked. The exotic topology relates to the emergence of a type of magnetic monopole called the Yang monopole (known from theoretical high-energy physics) in a five-dimensional space of internal degrees of freedom in a rubidium Bose-Einstein condensate. The results illustrate the potential of cold atoms physics to simulate high-energy phenomena. Science, this issue p. 1429 A cold atom system supports an exotic topological object with a nonzero second Chern number. Topological order is often quantified in terms of Chern numbers, each of which classifies a topological singularity. Here, inspired by concepts from high-energy physics, we use quantum simulation based on the spin degrees of freedom of atomic Bose-Einstein condensates to characterize a singularity present in five-dimensional non-Abelian gauge theories—a Yang monopole. We quantify the monopole in terms of Chern numbers measured on enclosing manifolds: Whereas the well-known first Chern number vanishes, the second Chern number does not. By displacing the manifold, we induce and observe a topological transition, where the topology of the manifold changes to a trivial state.

中文翻译：

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量子模拟非阿贝尔杨单极子的第二陈数


超越第一个陈数 物理系统的拓扑性质反映在所谓的陈数中：非零陈数通常意味着系统在拓扑上是非平凡的。菅川等人。设计了一个具有非零第二陈数的冷原子系统，这与通常只调用第一陈数的凝聚态物理相反。这种奇特的拓扑结构与铷玻色-爱因斯坦凝聚态内部自由度五维空间中一种称为杨单极子（从理论高能物理学中已知）的磁单极子的出现有关。结果说明了冷原子物理学模拟高能现象的潜力。科学，本期第 14 页。第1429章 冷原子系统支持具有非零第二陈数的奇异拓扑对象。拓扑序通常用陈数来量化，每个陈数都分类一个拓扑奇点。在这里，受到高能物理学概念的启发，我们使用基于原子玻色-爱因斯坦凝聚态自旋自由度的量子模拟来表征五维非阿贝尔规范理论中存在的奇点——杨单极子。我们用在封闭流形上测量的陈数来量化单极子：众所周知的第一个陈数消失了，但第二个陈数却没有。通过置换流形，我们诱导并观察到拓扑转变，其中流形的拓扑变为平凡状态。