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Register a new userMicroscopic characterization of Levy flights of light in atomic vapors
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Authors
Nicolas Mercadier
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We investigate multiple scattering of near-resonant light in a Doppler-broadened atomic vapor. We experimentally characterize the length distribution of the steps between successive scattering events. The obtained power law is characteristic of a superdiffusive behavior, where rare but very long steps (Levy flights) dominate the transport properties.
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Properties of random and fluctuating systems are often studied through the use of Gaussian distributions. However, in a number of situations, rare events have drastic consequences, which can not be explained by Gaussian statistics. Considerable efforts have thus been devoted to the study of non Gaussian fluctuations such as Levy statistics, generalizing the standard description of random walks. Unfortunately only macroscopic signatures, obtained by averaging over many random steps, are usually observed in physical systems. We present experimental results investigating the elementary process of anomalous diffusion of photons in hot atomic vapours. We measure the step size distribution of the random walk and show that it follows a power law characteristic of Levy flights.
It is shown that a quantum Levy process in a box leads to a problem involving topological constraints in space, and its treatment in the framework of the path integral formalism with the Levy measure is suggested. The eigenvalue problem for the infinite potential well is properly defined and solved. An analytical expression for the evolution operator is obtained in the path integral presentation, and the path integral takes the correct limit of the local quantum mechanics with topological constraints. An example of the Levy process in oscillating walls is also considered in the adiabatic approximation.
Cooperative scattering has been the subject of intense research in the last years. In this article, we discuss the concept of cooperative scattering from a broad perspective. We briefly review the various collective effects that occur when light interacts with an ensemble of atoms. We show that some effects that have been recently discussed in the context of single-photon superradiance, or cooperative scattering in the linear-optics regime, can also be explained by standard optics, i.e., using macroscopic quantities such as the susceptibility or the diffusion coefficient. We explain why some collective effects depend on the atomic density, and others on the optical depth. In particular, we show that, for a large and dilute atomic sample driven by a far-detuned laser, the decay of the fluorescence, which exhibits superradiant and subradiant dynamics, depends only on the on-resonance optical depth. We also discuss the link between concepts that are independently studied in the quantum-optics community and in the mesoscopic-physics community. We show that the coupled-dipole model predicts a departure from Ohms law for the diffuse light, that incoherent multiple scattering can induce a saturation of fluorescence and we also show the similarity between the weak-localization correction to the diffusion coefficient and the inaccuracy of Lorentz local field correction to the susceptibility.
The multiple scattering of photons in a hot, resonant, atomic vapor is investigated and shown to exhibit a Levy Flight-like behavior. Monte Carlo simulations give insights into the frequency redistribution process that originates the long steps characteristic of this class of random walk phenomena.
Levy flights for light have been demonstrated in disordered systems with and without optical gain, and remained unobserved in ordered ones. In the present letter, we investigate, numerically and experimentally, Levy flights for light in ordered systems due to an ordered (conventional) laser. The statistical analysis was performed on the intensity fluctuations of the output spectra upon repeated identical experimental realizations. We found out that the optical gain and the mirrors reflectivity are critical parameters governing the fluctuation statistics. We identified Levy regimes for gain around the laser threshold, and Gaussian-Levy-Gaussian crossovers were unveiling when increasing the gain from below to above the threshold. The experimental results were corroborated by Monte Carlo simulations, and the fluctuations were associated to a Langevin noise source that takes into account the randomness of the spontaneous emission, which seeds the laser emission and can cause large fluctuations of the output spectra from shot-to-shot under identical experimental realizations.
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