Sub-Poissonian Statistics of Jamming Limits in Ultracold Rydberg Gases

TL;DR

This paper models the sub-Poissonian statistics of Rydberg excitations in ultracold gases caused by the blockade effect, providing explicit formulas and confirming strong agreement with experimental data.

Contribution

It introduces random-graph models to analytically describe the blockade-induced jamming limits and relates the Mandel Q parameter to the blockade effect.

Findings

Derived formulas for mean and variance of Rydberg excitations.

Established explicit relationship between Mandel Q parameter and blockade.

Confirmed strong agreement between theoretical predictions and experimental data.

Abstract

Several recent experiments have established by measuring the Mandel Q parameter that the number of Rydberg excitations in ultracold gases exhibits sub-Poissonian statistics. This effect is attributed to the Rydberg blockade that occurs due to the strong interatomic interactions between highly-excited atoms. Because of this blockade effect, the system can end up in a state in which all particles are either excited or blocked: a jamming limit. We analyze appropriately constructed random-graph models that capture the blockade effect, and derive formulae for the mean and variance of the number of Rydberg excitations in jamming limits. This yields an explicit relationship between the Mandel Q parameter and the blockade effect, and comparison to measurement data shows strong agreement between theory and experiment.