  Large-deviations theory deals with tails of probability distributions and the
rare events of random processes, for example spreading packets of particles.
Mathematically, it concerns the exponential fall-of of the density of
thin-tailed systems. Here we investigate the spatial density $P_t(x)$ of laser
cooled atoms, where at intermediate length scales the shape is fat-tailed. We
focus on the rare events beyond this range, which dominate important
statistical properties of the system. Through a novel friction mechanism
induced by the laser fields, the density is explored with the recently proposed
nonnormalized infinite-covariant density approach. The small and large
fluctuations give rise to a bi-fractal nature of the spreading packet.
