Observation of gauge invariance in a 71-site Bose–Hubbard quantum simulator

Bing Yang, Hui Sun, Robert Ott, Han-Yi Wang, Torsten V. Zache, Jad C. Halimeh, Zhen-Sheng Yuan (), Philipp Hauke () and Jian-Wei Pan ()
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Bing Yang: University of Science and Technology of China
Hui Sun: University of Science and Technology of China
Robert Ott: Ruprecht-Karls-Universität Heidelberg
Han-Yi Wang: University of Science and Technology of China
Torsten V. Zache: Ruprecht-Karls-Universität Heidelberg
Jad C. Halimeh: Ruprecht-Karls-Universität Heidelberg
Zhen-Sheng Yuan: University of Science and Technology of China
Philipp Hauke: Ruprecht-Karls-Universität Heidelberg
Jian-Wei Pan: University of Science and Technology of China

Nature, 2020, vol. 587, issue 7834, 392-396

Abstract: Abstract 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.

Date: 2020
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DOI: 10.1038/s41586-020-2910-8

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