Towards $2+1$D quantum electrodynamics on a cold-atom quantum simulator

TL;DR

This paper proposes a feasible cold-atom quantum simulator for a (2+1)D U(1) lattice gauge theory with dynamical matter, using a spin 1 truncation and existing ultracold-atom technology, enabling more realistic simulations.

Contribution

It introduces a new method to simulate higher-dimensional lattice gauge theories with larger gauge-field truncations using cold atoms and quantum Zeno stabilization.

Findings

Simulated real-time dynamics faithfully reproduce the target gauge theory.

Gauge constraints are robustly preserved during evolution.

Implementation requires only moderate resources available in current ultracold-atom experiments.

Abstract

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.