Levy flights of photons in hot atomic vapours

The properties of random and fluctuating systems are often studied through the use of Gaussian distributions. However, in a number of situations, rare events have drastic consequences, which cannot be explained by Gaussian statistics. Considerable efforts have thus been devoted to the study of non-Gaussian fluctuations such as Levy statistics, generalizing the standard description of random walks. Unfortunately, only macroscopic signatures, obtained by averaging over many random steps, are usually observed in physical systems. We present experimental results investigating the elementary process of anomalous diffusion of photons in hot atomic vapours. We measure the step-size distribution of the random walk and show that it follows a power-law characteristic of Levy flights.