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arXiv:1506.05683 · Physical Review A

Redistribution of light frequency by multiple scattering in a resonant atomic vapor

J. C. de Aquino Carvalho, Marcos Oriá, Martine Chevrollier, Hugo L. D. de S. Cavalcante, Thierry Passerat de Silans

Published May 22, 2015• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.91.053846

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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.
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 is a process in which a particle is repeatedly deflected by other particles. In an overwhelming majority of cases, the ensuing random walk can successfully be described through Gaussian, or normal, statistics. However, like a (growing) number of other apparently inoffensive systems, diffusion of light in dilute atomic vapours eludes this familiar interpretation, exhibiting a superdiffusive behaviour. As opposed to normal diffusion, whereby the particle executes steps in random directions but with lengths slightly varying around an average value (like a drunkard whose next move is unpredictable but certain to within a few tens of centimetres), superdiffusion is characterised by sudden abnormally long steps (Lévy flights) interrupting sequences of apparently regular jumps which, although very rare, determine the whole dynamics of the system. The formal statistics tools to describe superdiffusion already exist and rely on stable, well understood distributions. As scientists become aware of, and more familiar with, this non-orthodox possibility of interpretation of random phenomena, new systems are discovered or re-interpreted as following Lévy statistics. Propagation of light in resonant atomic vapours is one of these systems which have been studied for decades and have only recently been shown to be the scene of Lévy flights.
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.
Abstract The problem of transfer of line radiation in sodium vapor under photoexcitation by laser radiation of a resonance line with wavelength λ = 589.6 nm is numerically solved. The influence of Doppler frequency shifts on photon emission coherent in the atomic reference system is taken into account in the formation of an emission line profile using the model of partial frequency redistribution. In the case of a small optical thickness of a medium τ0 ≤ 1, the Doppler frequency redistribution in the laboratory reference system yields higher intensity values in the emission line profile core in comparison with the model of complete frequency redistribution. For an optically dense medium, thermal motion of atoms leads to an increase of reabsorption in the emission line core, and intensity increases in the line wings as compared to the complete redistribution model. The dependence of the Holstein trapping factor on optical thickness is closer to the analytic dependence than the complete redistribution model. This is explained by the fact that the frequencies of emitted photons in the laboratory reference system fall into the spectral profile core, which increases the effects of resonance radiation trapping in a dense medium.