Observing the space- and time-dependent growth of correlations in dynamically tuned synthetic Ising antiferromagnets

TL;DR

This study investigates how correlations develop over space and time in synthetic Ising antiferromagnets using a Rydberg quantum simulator, revealing finite-range order, propagation delays, and agreement with analytical models.

Contribution

It introduces a detailed experimental and theoretical analysis of correlation dynamics in quantum antiferromagnets with tunable parameters and geometries.

Findings

Finite-range antiferromagnetic correlations observed.

Correlation build-up delays linked to finite propagation speed.

Analytical model accurately describes correlation dynamics.

Abstract

We explore the dynamics of artificial one- and two-dimensional Ising-like quantum antiferromagnets with different lattice geometries by using a Rydberg quantum simulator of up to 36 spins in which we dynamically tune the parameters of the Hamiltonian. We observe a region in parameter space with antiferromagnetic (AF) ordering, albeit with only finite-range correlations. We study systematically the influence of the ramp speeds on the correlations and their growth in time. We observe a delay in their build-up associated to the finite speed of propagation of correlations in a system with short-range interactions. We obtain a good agreement between experimental data and numerical simulations taking into account experimental imperfections measured at the single particle level. Finally, we develop an analytical model, based on a short-time expansion of the evolution operator, which captures the observed spatial structure of the correlations, and their build-up in time.