The Spectral Backbone of Excitation Transport in Ultra-Cold Rydberg Gases

TL;DR

This paper investigates the spectral properties of excitation energy transfer in ultra-cold Rydberg gases, revealing a transition from localized to delocalized states influenced by the dipole blockade effect and spectral statistics.

Contribution

It introduces a detailed analysis of the spectral and eigenvector structure in Rydberg gases, highlighting a transition from localized to delocalized states and the impact of the dipole blockade on this transition.

Findings

Identification of a critical energy separating localized and delocalized eigenstates.

Observation of a spectral transition from Lévy to Gaussian statistics with increasing blockade radius.

Correlation effects cause deviations from standard random matrix theory predictions.

Abstract

The spectral structure underlying excitonic energy transfer in ultra-cold Rydberg gases is studied numerically, in the framework of random matrix theory, and via self-consistent diagrammatic techniques. Rydberg gases are made up of randomly distributed, highly polarizable atoms that interact via strong dipolar forces. Dynamics in such a system is fundamentally different from cases in which the interactions are of short range, and is ultimately determined by the spectral and eigenvector structure. In the energy levels' spacing statistics, we find evidence for a critical energy that separates delocalized eigenstates from states that are localized at pairs or clusters of atoms separated by less than the typical nearest-neighbor distance. We argue that the dipole blockade effect in Rydberg gases can be leveraged to manipulate this transition across a wide range: As the blockade radius increases, the relative weight of localized states is reduced. At the same time, the spectral statistics -- in particular, the density of states and the nearest neighbor level spacing statistics -- exhibits a transition from approximately a 1-stable L\'evy to a Gaussian orthogonal ensemble. Deviations from random matrix statistics are shown to stem from correlations between interatomic interaction strengths that lead to an asymmetry of the spectral density and profoundly affect localization properties. We discuss approximations to the self-consistent Matsubara-Toyozawa locator expansion that incorporate these effects.