Modeling Rydberg Gases using Random Sequential Adsorption on Random Graphs

TL;DR

This paper compares quantum and classical models of Rydberg gases, introducing a new graph-based RSA model that accurately predicts atom statistics and highlights the dominant effects at different time scales.

Contribution

It introduces a novel Decomposed Random Intersection Graph model for Rydberg gases and provides rigorous analysis and accurate predictions of their statistical behavior.

Findings

The new graph model accurately predicts Rydberg atom statistics across densities.

Geometrical blockade effects dominate long-term statistics.

Quantum effects influence short-term statistical behavior.

Abstract

The statistics of strongly interacting, ultracold Rydberg gases are governed by the interplay of two factors: geometrical restrictions induced by blockade effects, and quantum mechanical effects. To shed light on their relative roles in the statistics of Rydberg gases, we compare three models in this paper: a quantum mechanical model describing the excitation dynamics within a Rydberg gas, a Random Sequential Adsorption (RSA) process on a Random Geometric Graph (RGG), and a RSA process on a Decomposed Random Intersection Graph (DRIG). The latter model is new, and refers to choosing a particular subgraph of a mixture of two other random graphs. Contrary to the former two models, it lends itself for a rigorous mathematical analysis; and it is built specifically to have particular structural properties of a RGG. We establish for it a fluid limit describing the time-evolution of number of Rydberg atoms, and show numerically that the expression remains accurate across a wider range of particle densities than an earlier approach based on an RSA process on an Erdos-Renyi Random Graph (ERRG). Finally, we also come up with a new heuristic using random graphs that gives a recursion to describe a normalized pair-correlation function of a Rydberg gas. Our results suggest that even without dissipation, on long time scales the statistics are affected most by the geometrical restrictions induced by blockade effects, while on short time scales the statistics are affected most by quantum mechanical effects.