Topological gauge theories describe the low-energy properties of certain strongly correlated quantum systems through effective weakly interacting models^1,2. A prime example is the Chern–Simons theory of fractional quantum Hall states, where anyonic excitations emerge from the coupling between weakly interacting matter particles and a density-dependent gauge field³. Although in traditional solid-state platforms such gauge theories are only convenient theoretical constructions, engineered quantum systems enable their direct implementation and provide a fertile playground to investigate their phenomenology without the need for strong interactions⁴. Here, we report the quantum simulation of a topological gauge theory by realizing a one-dimensional reduction of the Chern–Simons theory (the chiral BF theory^5,6,7) in a Bose–Einstein condensate. Using the local conservation laws of the theory, we eliminate the gauge degrees of freedom in favour of chiral matter interactions^8,9,10,11, which we engineer by synthesizing optically dressed atomic states with momentum-dependent scattering properties. This allows us to reveal the key properties of the chiral BF theory: the formation of chiral solitons and the emergence of an electric field generated by the system itself. Our results expand the scope of quantum simulation to topological gauge theories and open a route to the implementation of analogous gauge theories in higher dimensions¹².

^{拓扑规范理论通过有效的弱相互作用模型1,2}描述了某些强相关量子系统的低能特性。一个典型的例子是分数量子霍尔态的 Chern-Simons 理论，其中任意子激发来自弱相互作用物质粒子与密度相关的规范场³之间的耦合。尽管在传统的固态平台中，这种规范理论只是方便的理论构造，但工程量子系统可以直接实现它们，并为研究其现象学提供了一个肥沃的游乐场，而无需强相互作用⁴. 在这里，我们通过在玻色-爱因斯坦凝聚体中实现 Chern-Simons 理论（手性 BF 理论^5,6,7 ）的一维简化来报告拓扑规范理论的量子模拟。^{使用该理论的局部守恒定律，我们消除了有利于手性物质相互作用8,9,10,11}的规范自由度，我们通过合成具有动量相关散射特性的光学修饰原子态来进行设计。这使我们能够揭示手性 BF 理论的关键特性：手性孤子的形成和系统本身产生的电场的出现。我们的结果将量子模拟的范围扩展到拓扑规范理论，并开辟了在更高维度上实现类比规范理论的途径¹² .