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Lévy 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 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.


  1. Lévy, P. Theorie de l’Addition des Variables Aleatoires (Gauthier-Villiers, 1937).

    MATH  Google Scholar 

  2. Bouchaud, J.-P. & Georges, A. Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications. Phys. Rep. 195, 127–293 (1990).

    ADS  MathSciNet  Article  Google Scholar 

  3. Shlesinger, M., Zaslavsky, G. & Frisch, U. Lévy Flights and Related Topics in Physics (Springer, 1995).

    Book  Google Scholar 

  4. Metzler, R. & Klafter, J. The random walk’s guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339, 1–77 (2000).

    ADS  MathSciNet  Article  Google Scholar 

  5. Bouchaud, J.-P. & Potters, M. Theory of Financial Risk and Derivative Pricing (Cambridge Univ. Press, 2003).

    Book  Google Scholar 

  6. Botet, R. & Ploszajczak, M. Universal Fluctuations (World Scientific, 2002).

    Book  Google Scholar 

  7. Goldenfeld, N. D. Lectures on Phase Transitions and the Renormalisation Group (Addison, 1992).

    MATH  Google Scholar 

  8. Barthelemy, P., Bertolotti, J. & Wiersma, D. S. A Lévy flight for light. Nature 453, 495–498 (2008).

    ADS  Article  Google Scholar 

  9. Springmann, U. Multiple resonance line scattering and the momentum problem in Wolf-Rayet star winds. Astron. Astrophys. 289, 505–523 (1994).

    ADS  Google Scholar 

  10. Molisch, A. F. & Oehry, B. P. Radiation Trapping in Atomic Vapours (Oxford Univ., 1998).

    Google Scholar 

  11. Holstein, T. Imprisonment of resonance radiation in gases. Phys. Rev. 72, 1212–1233 (1947).

    ADS  Article  Google Scholar 

  12. Kenty, C. On radiation diffusion and the rapidity of escape of resonance radiation from a gas. Phys. Rev. 42, 823–842 (1932).

    ADS  Article  Google Scholar 

  13. Fioretti, A., Molisch, A. F., Mutter, J. H., Verkerk, P. & Allegrini, M. Observation of radiation trapping in a dense Cs magneto-optical trap. Opt. Commun. 149, 415–422 (1998).

    ADS  Article  Google Scholar 

  14. Labeyrie, G. et al. Slow diffusion of light in a cold atomic cloud. Phys. Rev. Lett. 91, 223904 (2003).

    ADS  Article  Google Scholar 

  15. Labeyrie, G., Kaiser, R. & Delande, D. Radiation trapping in a cold atomic gas. Appl. Phys. B 81, 1001–1008 (2005).

    ADS  Article  Google Scholar 

  16. Pereira, E., Martinho, J. M. G. & Berberan-Santos, M. N. Photon trajectories in incoherent atomic radiation trapping as Lévy flights. Phys. Rev. Lett. 93, 120201 (2004).

    ADS  Article  Google Scholar 

  17. Alves-Pereira, A. R., Nunes-Pereira, E. J., Martinho, J. M. G. & Berberan-Santos, M. N. Photonic superdiffusive motion in resonance line radiation trapping partial frequency redistribution effects. J. Chem. Phys. 126, 154505 (2007).

    ADS  Article  Google Scholar 

  18. Mantegna, R. N. & Stanley, H. E. Stochastic process with ultraslow convergence to a Gaussian: The truncated Lévy flight. Phys. Rev. Lett. 73, 2946–2949 (1994).

    ADS  MathSciNet  Article  Google Scholar 

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

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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.

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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).

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