Lévy flights of light in hot vapors

In many diffusive media, light is scattered with a frequency shift. In some cases this can change the transport properties of light in the medium. That is what happens in hot vapors, where the Doppler effect induces a frequency redistribution during multiple scattering. Since the mean-free path between scattering events is strongly dependent on the frequency, it can have a dramatic effect of the diffusion coefficient, which is given by the second moment of the step-length distribution. If this distribution is a power law x-a, the diffusion coefficient is infinite if a < 3. The transport is then said to be "superdiffusive", dominated by the very long steps, the "Lévy flights".
In a first experiment [1-3], we have directly measured the step-length distribution and found an exponent a ~ 2.3, in agreement with theoretical predictions. In a second, more recent experiment [5], we have characterized the macroscopic consequences (superdiffusive transport) of the Lévy flights, which allowed us to develop a very simple way to measure the exponent a.
Several questions remain open. For example, we would like to investigate the possibility of changing the exponent a of the power law of the step-size distribution. Different spectral broadening mechanisms should be tested. It would be especially interesting to find a regime where even the mean-free path is not defined (a < 2).


People currently involved in this topic:

Robin Kaiser, William Guerin


People involved in the past:

Quentin Baudouin (PhD, 2010-2013), Nicolas Mercadier (PhD, 2008-2011)

External collaborators: Romain Pierrat (Paris), Edouardo Peireira (Braga, Portugal), Martine Chevrollier (João Pessoa, Brazil)




  1. Lévy flights of photons in hot atomic vapours
    N. Mercadier, W. Guerin, M. Chevrollier and R. Kaiser
    Nature Phys. 5, 602 (2009), preprint : physics/0904.2454
    Press : CNRS INP News, Le Journal du CNRS
  2. Anomalous photon diffusion in atomic vapors
    M. Chevrollier, N. Mercadier, W. Guerin, R. Kaiser
    Eur. Phys. J. D 58, 161 (2010), preprint : physics/1001.0320
    EPJD Highlight; press : Europhysics News 41 (4), 10 (2010)
  3. Microscopic characterization of Lévy flights of light in atomic vapors
    N. Mercadier, M. Chevrollier, W. Guerin, R. Kaiser
    Phys. Rev. A 87, 063837 (2013), preprint : physics/1305.1714
  4. Cold and hot atomic vapors: a testbed for astrophysics?
    Q. Baudouin, W. Guerin, R. Kaiser
    in Annual Review of Cold Atoms and Molecules, vol. 2, edited by K. Madison, K. Bongs, L. D. Carr, A. M. Rey, and H. Zhai
    World Scientific, Singapour, 2014
    Preprint: hal-00968233
  5. Signatures of Lévy flights with annealed disorder
    Q. Baudouin, R. Pierrat, A. Eloy, E. J. Nunes-Pereira, P.-A. Cuniasse, N. Mercadier, R. Kaiser
    Phys. Rev. E 90, 052114 (2014), preprint: physics/1402.6200


See also the  Master and PhD thesis: