It is shown how to map the quantum states of a system of free Bose particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group.
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.
Large-Scale 2+1D U(1) Gauge Theory with Dynamical Matter in a Cold-Atom Quantum Simulator
A major driver of quantum-simulator technology is the prospect of probing high-energy phenomena in synthetic quantum matter setups at a high level of control and tunability. Here, we propose an experimentally feasible realization of a large-scale 2+1D U(1) gauge theory with dynamical matter and gauge fields in a cold-atom quantum simulator with spinless bosons. We present the full mapping of the corresponding Gauss's law onto the bosonic computational basis. We then show that the target gauge theory can be faithfully realized and stabilized by an emergent gauge protection term in a two-dimensional single-species Bose--Hubbard optical Lieb superlattice with two spatial periods along either direction, thereby requiring only moderate experimental resources already available in current cold-atom setups. Using infinite matrix product states, we calculate numerical benchmarks for adiabatic sweeps and global quench dynamics that further confirm the fidelity of the mapping. Our work brings quantum simulators of gauge theories a significant step forward in terms of investigating particle physics in higher spatial dimensions, and is readily implementable in existing cold-atom platforms.