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Register a new userLevy flights of photons in hot atomic vapours
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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.
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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.
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 inofensive systems, diffusion of light in dilute atomic vapours eludes this familiar interpretation, exhibiting a superdiffusive behavior. 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 centimeters), superdiffusion is characterized by sudden abnormally long steps (L{e}vy 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 L{e}vy statistics. Propagation of light in resonant atomic vapours is one of these systems that have been studied for decades and have only recently been shown to be the scene of L{e}vy flights.
Using data on the Berlin public transport network, the present study extends previous observations of fractality within public transport routes by showing that also the distribution of inter-station distances along routes displays non-trivial power law behaviour. This indicates that the routes may in part also be described as Levy-flights. The latter property may result from the fact that the routes are planned to adapt to fluctuating demand densities throughout the served area. We also relate this to optimization properties 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.
We report on the use of parametric excitation to coherently manipulate the collective spin state of an atomic vapour at room temperature. Signatures of the parametric excitation are detected in the ground-state spin evolution. These include the excitation spectrum of the atomic coherences, which contains resonances at frequencies characteristic of the parametric process. The amplitudes of the signal quadratures show amplification and attenuation, and their noise distribution is characterized by a strong asymmetry, similarly to those observed in mechanical oscillators. The parametric excitation is produced by periodic modulation of the pumping beam, exploiting a Bell-Bloom-like technique widely used in atomic magnetometry. Notably, we find that the noise-squeezing obtained by this technique enhances the signal-to-noise ratio of the measurements up to a factor of 10, and improves the performance of a Bell-Bloom magnetometer by a factor of 3.
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