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Lévy flights of photons in hot atomic vapours

Abstract

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 Lévy 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 Lévy flights.

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Figure 1: The experimental set-up.
Figure 2: Fluorescence images.
Figure 3: Single-step-size distributions P(x) plotted in a log–log scale.
Figure 4: Evolution of the power-law exponent.

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Acknowledgements

We acknowledge financial support from the program ANR-06-BLAN-0096 and financial support for N.M. by DGA.

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Contributions

N.M. contributed to planning of the project, laboratory measurements, data analysis and analytical calculations. W.G. contributed to planning of the project and data interpretation. M.C. contributed to numerical simulations. R.K. contributed to the conception and coordination of the project and to interpretation of results.

Corresponding author

Correspondence to R. Kaiser.

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Mercadier, N., Guerin, W., Chevrollier, M. et al. Lévy flights of photons in hot atomic vapours. Nature Phys 5, 602–605 (2009). https://doi.org/10.1038/nphys1286

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