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

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.