L\'evy statistics of interacting Rydberg gases

TL;DR

This paper demonstrates that the distribution of energy level shifts in interacting Rydberg gases follows Le9vy statistics, and develops a statistical model for probe light transmission that aligns well with experimental data.

Contribution

It introduces the first demonstration of Le9vy statistics in energy level shifts of Rydberg gases and develops a new statistical approach for modeling light transmission.

Findings

Energy level shifts follow Le9vy distribution in any dimension and for certain interactions.

Monte Carlo simulations confirm the Le9vy distribution in 3D for p=6 interactions.

The statistical model accurately reproduces experimental light transmission results.

Abstract

A statistical analysis of the laser excitation of cold and randomly distributed atoms to Rydberg states is developed. We first demonstrate with a hard ball model that the distribution of energy level shifts in an interacting gas obeys L\'evy statistics, in any dimension $d$ and for any interaction $-C_p/R^p$ under the condition $d/p<1$. This result is confirmed with a Monte Carlo rate equations simulation of the actual laser excitation in the particular case $p=6$ and $d=3$. With this finding, we develop a statistical approach for the modeling of probe light transmission through a cold atom gas driven under conditions of electromagnetically induced transparency involving a Rydberg state. The simulated results are in good agreement with experiment.