Probing the Crossover between Dynamical Phases with Local Correlations in a Rydberg Atom Array

TL;DR

This paper shows that local correlations in a Rydberg atom array can effectively detect non-equilibrium quantum criticality, offering a practical alternative to global measurements.

Contribution

It introduces a method using local correlations and a Magnus expansion to probe dynamical phases, validated by numerical simulations.

Findings

Derived analytic expressions for local correlations capturing crossover behavior.

Validated analytic results against exact numerical simulations.

Demonstrated robustness of local correlation signals to finite-size effects.

Abstract

The experimental detection of non-equilibrium quantum criticality remains a challenge, as traditional signatures like dynamical quantum phase transitions rely on hard-to-measure global properties. Here, we demonstrate that local connected correlation functions provide a superior, practical means to directly probe the dynamics of magnetic order in a quenched Rydberg atom array. Using a Magnus expansion formalism, we derive analytic expressions for these correlations that capture a smooth crossover from antiferromagnetic to ferromagnetic dominance. Our analytic results, which reveal the critical parameter relationship $U_{c}(\delta)$, are validated against exact numerical simulations and exhibit robustness to finite-size effects. By shifting the focus from global singularities to local correlations, our protocol establishes a direct and feasible path to observe the rich critical dynamics in scalable quantum simulators.