Voos de Lévy de fótons em vapores atômicos

Abstract

When the variance of a particle's displacement increases linearly in time, the Central Limit Theorem (TCL) is obeyed, and the distribution of probabilities of the particle's position will be Gaussian. On some systems, nonetheless, the probability of the particle performing a large step during the random walk, is not negligible, and the variance of the displacement grows faster than linearly in time. A particular mechanism for such superdi usive random walk are the Lévy ights, which has the step length probability distribution decaying asymptotically as |x|−1−α , with 0 < α < 2 a typical parameter of the system, which gives the slope of the "wings"of this distribution. When radiation (laser) focuses on one resonant atomic vapor, the incident radiation photons perform a walk random inside the vapor, through successive reabsorption and spontaneous remissions events called radiation trapping. This random walk is a superdifusion of the Lévy ight type, where the α parameter value depends on the absorption spectral pro le of sample, and can be measured from modi cation of Ohm's law, through the relationship between the di usive transmission, related to radiation trapping, with the opacity of the sample, a dimensionless quantity related to step size. For a Doppler pro le, the value α = 1.0 was theoretically obtained, and the value α = 1.47 was measured experimentally, while for a Lorentz pro le, the value α = 0.5 was theoretically obtained and con rmed experimentally. In the latter case, the random walk is quasi-ballistic, with an indeterminate average step size. In turn, for Voigt pro le, the α parameter was theoretically obtained in agreement with the Lorentz pro- le. However, the experimental con rmation has not been veri ed. Therefore, in this work, we measured Lévy's α parameter for the hot alkaline vapor absorption pro le, what is a Voigt pro le, that is, Gaussian around the line center and Lorentzian in the "wings"(in great detuning). The value of α parameter depends on the portion of the spectral pro le accessible for the photon that performs the random walk. For instance, for low opacity vapor (or low atomic density), the steps size in the Lorentzian wings are much longer than the sample length, and only photons emitted in the central gaussian portion perform a random walk in the cell, resulting in a parameter α = 1.2 ± 0.2. For higher densities, photons emitted in the lorentzian wings are reabsorbed and perform random walk resulting in a parameter α = 0.5 ± 0.04. In particular, we observed for di use light transmission TD as a function of the opacity r, a crossover in rc = 103 of the photonic transport, which divides the random walk in two regimes: bellow rc = 103, where only photons emitted in the Doppler nucleus are scattered by the vapour, while photons emitted in the lorentzian wings are not; and above rc = 103, where the photons emitted in the lorentzian wings are scattered by the vapour, resulting in large step that dominate the transport. Our results con rm that radiation trapping is characterized by an superdi usion of the Lévy ights type. Furthermore, given the nite size of the system, the characteristics of photonic transport for the Voigt absorption pro le are determined by a truncation in the system.