Signatures of Le´vy flights with annealed disorder

Abstract

We present theoretical and experimental results of Le´vy 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 micro- scopic first principles including Doppler broadening we find anomalous Le´vy-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’s law [Tdiff ∝ L−α/2 ⵬= L−1], as expected for a Le´vy walk of independent steps. Furthermore, the spatial profile of the transmitted light develops power-law tails [Tdiff(r) ∝ r−3−α]. In an experiment using a slab geometry with hot Rb vapor, we measured the total diffuse transmission Tdiff and the spatial profile of the transmitted light Tdiff(r). We obtained the microscopic Le´vy parameter α under macroscopic multiple scattering conditions paving the way to investigation of Le´vy flights in different atomic physics and astrophysics systems.