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Diffusion occurs in numerous physical systems throughout nature, drawing itsgenerality from the universality of the central limit theorem. Around a centuryago it was realized that an extension to this type of dynamics can be obtainedin the form of ``anomalous" diffusion where distributions are allowed to haveheavy, power-law tails. Due to a unique feature of its momentum-dependantdissipative friction force, laser-cooled atomic ensembles can be used as a testbed for such dynamics. The interplay between laser cooling and anomalousdynamics bears deep, predictive implications for fundamental concepts in bothequilibrium and non-equilibrium statistical physics. The high degree of controlavailable in cold-atom experiments allows for tuning of the parameters of thefriction force, revealing transitions in the dynamical properties of thesystem. Rare events, in both the momentum and spatial distributions, aredescribed by non-normalized states using tools adapted from infinite ergodictheory. This leads to new experimental and theoretical results, illuminatingthe various features of the system.

Anomalous statistics of laser-cooled atoms in dissipative optical lattices