Sub-Poissonian Statistics of Jamming Limits in Ultracold Rydberg Gases
We have submitted Sub-Poissonian Statistics of Jamming Limits in Ultracold Rydberg Gases, and it is currently under review. It is joint work between Jaron Sanders, Matthieu Jonckheere, and Servaas Kokkelmans.
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.It is accompanied by a technical report, titled Scaling Limits for Exploration Algorithms. The technical report rigorously establishes the results presented in Sub-Poissonian Statistics of Jamming Limits in Ultracold Rydberg Gases, and is joint work between Paola Bermolen, Matthieu Jonckheere, and Jaron Sanders.
We consider an exploration algorithm where at each step, a random number of items become active while related items get explored. Given an initial number of items $N$ growing to infinity and building on a strong homogeneity assumption, we study using scaling limits of Markovian processes statistical properties of the proportion of active nodes in time. This is a companion paper that rigorously establishes the claims and heuristics presented in Sub-Poissonian statistics of jamming limits in Rydberg gases.