Quantum spin ice in three-dimensional Rydberg atom arrays

TL;DR

This paper proposes a method to realize and study a three-dimensional $U(1)$ quantum spin liquid using Rydberg atom arrays on a pyrochlore lattice, enabling exploration of confinement and Higgs transitions in a controllable quantum simulator.

Contribution

It introduces a novel scheme to simulate a 3D $U(1)$ quantum spin liquid with Rydberg atoms, including phase diagram analysis and experimental detection strategies.

Findings

Access to confinement-deconfinement transition via Rabi frequency tuning

Identification of Higgs transition driven by electric charge proliferation

Proposed experimental probes to distinguish deconfined phase

Abstract

Quantum spin liquids are exotic phases of matter whose low-energy physics is described as the deconfined phase of an emergent gauge theory. With recent theory proposals and an experiment showing preliminary signs of $\mathbb{Z}_2$ topological order [G. Semeghini et al., Science 374, 1242 (2021)], Rydberg atom arrays have emerged as a promising platform to realize a quantum spin liquid. In this work, we propose a way to realize a $U(1)$ quantum spin liquid in three spatial dimensions, described by the deconfined phase of $U(1)$ gauge theory in a pyrochlore lattice Rydberg atom array. We study the ground state phase diagram of the proposed Rydberg system as a function of experimentally relevant parameters. Within our calculation, we find that by tuning the Rabi frequency, one can access both the confinement-deconfinement transition driven by a proliferation of "magnetic" monopoles and the Higgs transition driven by a proliferation of "electric" charges of the emergent gauge theory. We suggest experimental probes for distinguishing the deconfined phase from ordered phases. This work serves as a proposal to access a confinement-deconfinement transition in three spatial dimensions on a Rydberg-based quantum simulator.