Accurate mapping of multilevel Rydberg atoms on interacting spin-$1/2$ particles for the quantum simulation of Ising models

TL;DR

This paper demonstrates how to accurately map laser-driven Rydberg atom systems onto spin-1/2 models for simulating Ising magnets, emphasizing parameter selection and validating with experiments and large-scale simulations.

Contribution

It provides a detailed non-perturbative analysis of Rydberg interactions and benchmarks the mapping accuracy against experiments, enabling scalable quantum simulations.

Findings

Good agreement between experimental dynamics and spin-1/2 Ising model simulations.

Identification of optimal parameters to maintain Rydberg blockade.

Successful simulation of systems with up to 49 spins.

Abstract

We study a system of atoms that are laser-driven to $nD_{3/2}$ Rydberg states and assess how accurately they can be mapped onto spin-$1/2$ particles for the quantum simulation of anisotropic Ising magnets. Using non-perturbative calculations of the pair interaction potentials between two atoms in the presence of both electric and magnetic fields, we emphasize the importance of a careful selection of the experimental parameters in order to maintain the Rydberg blockade and avoid excitation of unwanted Rydberg states. We then benchmark these theoretical observations against experiments using two atoms. Finally, we show that in these conditions, the experimental dynamics observed after a quench is in good agreement with numerical simulations of spin-1/2 Ising models in systems with up to 49 spins, for which direct numerical simulations become intractable.