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Journal of Nanophotonics

Levy distribution of time delay in emission of resonantly trapped light in ferrodispersions

Rajesh Patel, Rasbindu V. Mehta

Published Sep 12, 2012• 5 citations
Publisher

Abstract

Time delays in emission of resonantly trapped light in magnetite microspheres dispersed in a ferrofluid were measured for three different sphere sizes. The time delay was found to vary randomly. The effect of the size of microspheres on the probability distribution was determined. Analysis of the data showed that the statistics of the time delay is best described by a Levy distribution.

DOI
10.1117/1.jnp.6.069503

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Time delays in emission of resonantly trapped light in magnetite microspheres dispersed in a ferrofluid were measured for three different sphere sizes. The time delay was found to vary randomly. The effect of the size of microspheres on the probability distribution was determined. Analysis of the data showed that the statistics of the time delay is best described by a Levy distribution.
The effects of light absorption and amplification on the transition rates of the electric-dipole emission of atoms or molecules embedded in micrometer-sized dielectric spheres are investigated in the framework of classical electrodynamics. The expression for the form factor of a resonant emission line is derived. Its dependence on the imaginary part of the light’s refractive index is investigated. It is discovered that the active sphere does not act as an optical resonator if light amplification is strong.
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.
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.
The propagation of a band-limited light pulse through an atomic medium under a Λ excitation scheme is theoretically analyzed in this paper. We consider in particular the case where the light pulse is detected through the coherent microwave emission of the atomic ensemble (coherent population trapping maser). Significant differences are predicted with respect to the more usual optical detection (electromagnetically induced transparency signal) and found in agreement with the experimental results. Higher signal delays were observed in the microwave emission than in the optical signal with an equivalent group velocity of 6 m/s as well as highly superluminal propagation under a proper modulation scheme. The experiments were performed with a thermal 87Rb vapor in buffer gas.
We have analyzed the statistical distribution of the fluorescence signal levels in a magneto-optical trap containing a few atoms and observed that it strongly depends on the relative size of the bin time with respect to the trap decay time. We derived analytic expressions for the signal distributions in two limiting cases, long and short bin time limits, and found good agreement with numerical simulations performed regardless of the size of the bin time. We found an optimal size of the bin time for minimizing the probability of indeterminate atom numbers while providing accurate information on the instantaneous number of atoms in the trap. These theoretical results are compared with actual experimental data. We observed super-Poisson counting statistics for the fluorescence from trapped atoms, which might be attributed to uncorrelated motion of trapped atoms in the inhomogeneous magnetic field in the trap.