Quantum Simulation of Two-Dimensional $\mathrm{U(1)}$ Gauge Theory in Rydberg and Rydberg-Dressed Atom Arrays

TL;DR

This paper proposes an experimentally feasible method to simulate two-dimensional U(1) gauge theories using Rydberg atom arrays, capturing key phenomena like topological sectors and deconfinement.

Contribution

It introduces a simple, practical realization of 2D U(1) gauge theories on triangular Rydberg arrays, enabling exploration of complex gauge phenomena.

Findings

Effective model simulates U(1) gauge features

Observation of topological sectors and incommensurability

Pronounced quantum dynamics compared to previous proposals

Abstract

Simulating $\mathrm{U(1)}$ quantum gauge theories with spatial dimension greater than one is of great physical significance yet has not been achieved experimentally. Here we propose a simple realization of $\mathrm{U(1)}$ gauge theory on triangular lattice Rydberg atom arrays. Within experimentally accessible range, we find that the effective model well simulates various aspects of the $\mathrm{U(1)}$ gauge theory, such as emergence of topological sectors, incommensurability, and the deconfined Rokhsar-Kivelson point. Our proposal is easy to implement experimentally and exhibits pronounced quantum dynamics compared with previous proposals realizing $\mathrm{U(1)}$ and $\mathbb Z_2$ gauge theories.