  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.
