Signatures of Lévy flights with annealed disorder

Abstract

We present theoretical and experimental results of Lévy flights of light originating from a random walk of photons in a hot atomic vapor. In contrast to systems with quenched disorder, this system does not present any correlations between the position and the step length of the random walk. In an analytical model based on microscopic first principles including Doppler broadening we find anomalous Lévy-type superdiffusion corresponding to a single-step size distribution P (x) ∝ x −(1+α) , with α ≈ 1. We show that this step size distribution leads to a violation of Ohm', as expected for a Lévy walk of independent steps. Furthermore the spatial profile of the transmitted light develops power law tails [T diff (r) ∝ r −3−α ]. In an experiment using a slab geometry with hot rubidium vapor, we measured the total diffuse transmission T diff and the spatial profile of the transmitted light T diff (r). We obtained the microscopic Lévy parameter α under macroscopic multiple scattering conditions paving the way to investigation of Lévy flights in different atomic physics and astrophysics systems.

Temporal intensity correlation of light scattered by a hot atomic vapor

“…However, at high b, the contrast decreases to values lower than expected. We have checked that the stray light (e.g., from the laser diode amplified spontaneous emission), or the level of fluorescence, as well as the increase of the source size with b due to diffusion [25], are not responsible for the anomalous decrease of contrast. It should be mentioned that the same phenomena has been predicted [8] and observed in a cold atom experiment [9] where radiation trapping (with optical thicknesses as ( g (2) () -1)/(g (2) (0) -1)…”

Walk dimension for light in complex disordered media

“…Similarly to massive objects, multiply scattered waves in disordered media may also propagate anomalously [6,17], in which case the experimental retrieval of d w is particularly challenging. In recent years superdiffusion of light has been investigated in disordered photonics materials dubbed Lévy glasses [18,19] and in hot atomic vapors [20,21]. However, neither experiments on the dynamics of anomalous transport have been performed nor the walk dimension d w has been measured.…”

Microscopic characterization of Lévy flights of light in atomic vapors

“…This work shows that the microscopic element constituted by the step-length distribution is as experimentally accessible as macroscopic quantities characteristic of the transport, such as the diffuse transmission through a sample [27,28].…”