Universal time-evolution of a Rydberg lattice gas with perfect blockade

TL;DR

This paper studies the universal time-evolution of Rydberg lattice gases with perfect blockade, showing that small systems can predict long-term behavior in the thermodynamic limit for certain observables.

Contribution

It introduces a method to analyze the universal dynamics of Rydberg gases and proves finite systems follow this behavior up to a calculable time.

Findings

Expectations converge logarithmically to universal functions

Finite systems exhibit universal behavior up to a size-dependent time

Small systems can predict long-term dynamics in the thermodynamic limit

Abstract

We investigate the dynamics of a strongly interacting spin system that is motivated by current experimental realizations of strongly interacting Rydberg gases in lattices. In particular we are interested in the temporal evolution of quantities such as the density of Rydberg atoms and density-density correlations when the system is initialized in a fully polarized state without Rydberg excitations. We show that in the thermodynamic limit the expectation values of these observables converge at least logarithmically to universal functions and outline a method to obtain these functions. We prove that a finite one-dimensional system follows this universal behavior up to a given time. The length of this universal time period depends on the actual system size. This shows that already the study of small systems allows to make precise predictions about the thermodynamic limit provided that the observation time is sufficiently short. We discuss this for various observables and for systems with different dimensions, interaction ranges and boundary conditions.