Colloquium : Anomalous statistics of laser-cooled atoms in dissipative optical lattices

The standard central limit theorem does not apply to sums of many random variables with heavy-tailed probability distributions. The anomalous statistics for such sums have exotic properties and they are applied phenomenologically across the natural sciences, economics, and the social sciences. This Colloquium reviews how anomalous statistics can be derived from first principles and how they govern the observed diffusive motion of ultracold atoms in laser fields.