The modern description of elementary particles, as formulated in the standard model of particle physics, is built on gauge theories1. Gauge theories implement fundamental laws of physics by local symmetry constraints. For example, in quantum electrodynamics Gauss's law introduces an intrinsic local relation between charged matter and electromagnetic fields, which protects many salient physical properties, including massless photons and a long-ranged Coulomb law. Solving gauge theories using classical computers is an extremely arduous task2, which has stimulated an effort to simulate gauge-theory dynamics in microscopically engineered quantum devices3-6. Previous achievements implemented density-dependent Peierls phases without defining a local symmetry7,8, realized mappings onto effective models to integrate out either matter or electric fields9-12, or were limited to very small systems13-16. However, the essential gauge symmetry has not been observed experimentally. Here we report the quantum simulation of an extended U(1) lattice gauge theory, and experimentally quantify the gauge invariance in a many-body system comprising matter and gauge fields. These fields are realized in defect-free arrays of bosonic atoms in an optical superlattice of 71 sites. We demonstrate full tunability of the model parameters and benchmark the matter-gauge interactions by sweeping across a quantum phase transition. Using high-fidelity manipulation techniques, we measure the degree to which Gauss's law is violated by extracting probabilities of locally gauge-invariant states from correlated atom occupations. Our work provides a way to explore gauge symmetry in the interplay of fundamental particles using controllable large-scale quantum simulators.

中文翻译：

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在 71 位 Bose-Hubbard 量子模拟器中观察规范不变性

在粒子物理学的标准模型中，对基本粒子的现代描述是建立在规范理论之上的。规范理论通过局部对称约束实现物理基本定律。例如，在量子电动力学中，高斯定律引入了带电物质和电磁场之间的内在局部关系，它保护了许多显着的物理特性，包括无质量光子和长程库仑定律。使用经典计算机解决规范理论是一项极其艰巨的任务2，这激发了在微观工程量子设备中模拟规范理论动力学的努力3-6。以前的成就在没有定义局部对称性的情况下实现了与密度相关的 Peierls 相7,8，实现映射到有效模型以整合物质或电场 9-12，或者仅限于非常小的系统 13-16。然而，基本规范对称性尚未通过实验观察到。在这里，我们报告了扩展 U(1) 格子规范理论的量子模拟，并通过实验量化了包含物质和规范场的多体系统中的规范不变性。这些场是在 71 个位点的光学超晶格中的无缺陷玻色原子阵列中实现的。我们展示了模型参数的完全可调性，并通过扫描量子相变来对物质-规范相互作用进行基准测试。使用高保真操纵技术，我们通过从相关原子占据中提取局部规范不变状态的概率来测量违反高斯定律的程度。