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arXiv:2008.03506 · Physical review. E

Lévy flights of photons with infinite mean free path

M. Araujo, Thierry Passerat de Silans, Robin Kaiser

Published Jan 6, 2021• 16 citations
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Abstract

Multiple scattering of light by resonant vapor is characterized by Lévy-type superdiffusion with a single-step size distribution p(x)∝1/x^{1+α}. We investigate Lévy flight of light in a hot rubidium vapor collisional-broadened by 50 torr of He gas. The frequent collisions produce Lorentzian absorptive and emissive profiles with α<1 and a corresponding divergent mean step size. We extract the Lévy parameter α≈0.5 in a multiple-scattering regime from radial profile of the transmission and from violation of the Ohm's law. The measured radial transmission profile and the total diffusive transmission curves are well reproduced by numerical simulations for Lorentzian line shapes.

DOI
10.1103/physreve.103.l010101

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Multiple scattering of light by resonant vapor is characterized by Lévy-type superdiffusion with a single-step size distribution p(x)∝1/x^{1+α}. We investigate Lévy flight of light in a hot rubidium vapor collisional-broadened by 50 torr of He gas. The frequent collisions produce Lorentzian absorptive and emissive profiles with α<1 and a corresponding divergent mean step size. We extract the Lévy parameter α≈0.5 in a multiple-scattering regime from radial profile of the transmission and from violation of the Ohm's law. The measured radial transmission profile and the total diffusive transmission curves are well reproduced by numerical simulations for Lorentzian line shapes.
Multiple scattering of light by resonant vapor is characterized by Lévy-type superdiffusion with a step size distribution P(x)∝1/x1+αP(x) \propto 1/x^{1+α}P(x)∝1/x1+α, with 0<α<20 < α< 20<α<2. The Lévy parameter ααα was measured from P(x)P(x)P(x), steady fluorescence, frequency-dependent fluorescence and time-resolved transmission, where the latter was observed for quenched disordered media, not yet for annealed disordered media. Here we report first measurements of this quantity from time-resolved fluorescence for photons that are forward diffused from light pulses exciting a hot rubidium vapor, a medium characterized by annealed disorder, where correlations between the photon steps are absent. Also, the vapor is contained in a three-dimensional geometry, a turned cylinder with respect of the incident photon direction. We show experimentally that ααα can be extracted from this setup, and the results are consistent with those given by the steady frequency-dependent forward fluorescence. Theoretical simulations are consistent with these results. Also, our simulations show the validity of the one-dimensional theories for our actual geometry and other three-dimensional ones, as thin and thick disks, and a measurement of the number of steps that the photon performed before leaving the medium.
We present theoretical and experimental results of Lflights 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 Lsuperdiffusion 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 L´ evy 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 L´ evy parameter α under macroscopic multiple scattering conditions paving the way to investigation of L´ evy flights in different atomic physics and astrophysics systems.
The propagation of light in a resonant atomic vapor can a priori be thought of as a multiple scattering process, in which each scattering event redistributes both the direction and the frequency of the photons. Particularly, the frequency redistribution may result in L\'evy flights of photons, directly affecting the transport properties of light in a resonant atomic vapor and turning this propagation into a superdiffusion process. Here, we report on a Monte Carlo simulation developed to study the evolution of the spectrum of the light in a resonant thermal vapor. We observe the gradual change of the spectrum and its convergence towards a regime of complete frequency redistribution as the number of scattering events increases. We also analyze the probability density function of the step length of photons between emissions and reabsorptions in the vapor, which governs the statistics of the light diffusion. We observe two different regimes in the light transport: superdiffusion when the vapor is excited near the line center and normal diffusion for excitation far from the line center. The regime of complete frequency redistribution is not reached for excitation far from resonance even after many absorption and reemission cycles due to correlations between emitted and absorbed frequencies.
Lévy flight superdiffusion consists of random walks characterized by very long jumps that dominate the transport. However, the finite size of real samples introduces truncation of long jumps and modifies the transport properties. We measure typical Levy flight parameters for photon diffusion in atomic vapor characterized by a Voigt absorption profile. We observe the change of Lévy parameter as a function of truncation length. We associate this variation with size-dependent contributions from different spectral regions of the emission profile with the Doppler core dominating the transport for thin samples and Lorentz wings for thick samples. Monte Carlo simulations are implemented to support the interpretation of results.