Abstract 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.
Abstract 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.
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.
Towards 2+1D quantum electrodynamics on a cold-atom quantum simulator
Cold atoms have become a powerful platform for quantum-simulating lattice gauge theories in higher spatial dimensions. However, such realizations have been restricted to the lowest possible truncations of the gauge field, which limit the connections one can make to lattice quantum electrodynamics. Here, we propose a feasible cold-atom quantum simulator of a (2+1)-dimensional U(1) lattice gauge theory in a spin S=1 truncation, featuring dynamical matter and gauge fields. We derive a mapping of this theory onto a bosonic computational basis, stabilized by an emergent gauge-protection mechanism through quantum Zeno dynamics. The implementation is based on a single-species Bose--Hubbard model realized in a tilted optical superlattice. This approach requires only moderate experimental resources already available in current ultracold-atom platforms. Using infinite matrix product state simulations, we benchmark real-time dynamics under global quenches. The results demonstrate faithful evolution of the target gauge theory and robust preservation of the gauge constraints. Our work significantly advances the experimental prospects for simulating higher-dimensional lattice gauge theories using larger gauge-field truncations.
Abstract Quantum link models (QLMs) offer the realistic prospect for the practical implementation of lattice quantum electrodynamics (QED) on modern quantum simulators, and they provide a venue for exploring various nonergodic phenomena relevant to quantum many-body physics. In these models, gauge and electric fields are represented by spin- S operators. So far, large-scale realizations of QLMs have been restricted to S = 1/2 representations, whereas the lattice-QED limit is approached at S → ∞ . Here, we present a bosonic mapping for the representation of gauge and electric fields with effective spin- S operators for arbitrarily large values of S . Based on this mapping, we then propose an experimental scheme for the realization of a large-scale spin-1 U(1) QLM using spinless bosons in an optical superlattice. Using perturbation theory and infinite matrix product state calculations, which work directly in the thermodynamic limit, we demonstrate the faithfulness of the mapping and stability of gauge invariance throughout all accessible evolution times. We further demonstrate the potential of our proposed quantum simulator to address relevant high-energy physics by probing the (de)confinement of an electron–positron pair by tuning the gauge coupling. Our work provides an essential step towards gauge-theory quantum simulators in the quantum-field-theory limit.
Spin-SU(1) Quantum Link Models with Dynamical Matter on a Quantum Simulator
Quantum link models (QLMs) offer the realistic prospect for the practical implementation of lattice quantum electrodynamics (QED) on modern quantum simulators, and they provide a venue for exploring various nonergodic phenomena relevant to quantum many-body physics. In these models, gauge and electric fields are represented by spin-S operators. So far, large-scale realizations of QLMs have been restricted to S=1/2 representations, whereas the lattice-QED limit is approached at S→∞. Here, we present a bosonic mapping for the representation of gauge and electric fields with effective spin-S operators for arbitrarily large values of S. Based on this mapping, we then propose an experimental scheme for the realization of a large-scale spin-1U(1) QLM using spinless bosons in an optical superlattice. Using perturbation theory and infinite matrix product state calculations, which work directly in the thermodynamic limit, we demonstrate the faithfulness of the mapping and stability of gauge invariance throughout all accessible evolution times. We further demonstrate the potential of our proposed quantum simulator to address relevant high-energy physics by probing the (de)confinement of an electron--positron pair by tuning the gauge coupling. Our work provides an essential step towards gauge-theory quantum simulators in the quantum-field-theory limit.
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.
Scalable cold-atom quantum simulator of a 3+1D U(1) lattice gauge theory with dynamical matter
The stated overarching goal of the highly active field of quantum simulation of high-energy physics (HEP) is to achieve the capability to study \textit{ab-initio} real-time microscopic dynamics of 3+1D quantum chromodynamics (QCD). However, existing experimental realizations and theoretical proposals for future ones have remained restricted to one or two spatial dimensions. Here, we take a big step towards this goal by proposing a concrete experimentally feasible scalable cold-atom quantum simulator of a U(1) quantum link model of quantum electrodynamics (QED) in three spatial dimensions, employing \textit{linear gauge protection} to stabilize gauge invariance. Using tree tensor network simulations, we benchmark the performance of this quantum simulator through near- and far-from-equilibrium observables, showing excellent agreement with the ideal gauge theory. Additionally, we introduce a method for \textit{analog quantum error mitigation} that accounts for unwanted first-order tunneling processes, vastly improving agreement between quantum-simulator and ideal-gauge-theory results. Our findings pave the way towards realistic quantum simulators of 3+1D lattice gauge theories that can probe regimes well beyond classical simulability.