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Radiation trapping and L{e}vy flights in atomic vapours: an introductory review

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 Publication date 2013
  fields Physics
and research's language is English




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Multiple scattering is a process in which a particle is repeatedly deflected by other particles. In an overwhelming majority of cases, the ensuing random walk can successfully be described through Gaussian, or normal, statistics. However, like a (growing) number of other apparently inofensive systems, diffusion of light in dilute atomic vapours eludes this familiar interpretation, exhibiting a superdiffusive behavior. As opposed to normal diffusion, whereby the particle executes steps in random directions but with lengths slightly varying around an average value (like a drunkard whose next move is unpredictable but certain to within a few tens of centimeters), superdiffusion is characterized by sudden abnormally long steps (L{e}vy flights) interrupting sequences of apparently regular jumps which, although very rare, determine the whole dynamics of the system. The formal statistics tools to describe superdiffusion already exist and rely on stable, well understood distributions. As scientists become aware of, and more familiar with, this non-orthodox possibility of interpretation of random phenomena, new systems are discovered or re-interpreted as following L{e}vy statistics. Propagation of light in resonant atomic vapours is one of these systems that have been studied for decades and have only recently been shown to be the scene of L{e}vy flights.

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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 can not 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.
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