Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:physics/0311113 · Physical Review Letters

Photon Trajectories in Incoherent Atomic Radiation Trapping as Lévy Flights

Eduardo J. Nunes-Pereira, José M. G. Martinho, Mário Nuno Berberan-Santos

Published Sep 13, 2004• 51 citations
arXivHTMLPDF

Abstract

Photon trajectories in incoherent radiation trapping for Doppler, Lorentz, and Voigt line shapes under complete frequency redistribution are shown to be Lévy flights. The jump length (r) distributions display characteristic long tails. For the Lorentz line shape, the asymptotic form is a strict power law r(-3/2), while for Doppler the asymptotic is r(-2)(ln(r)(-1/2). For the Voigt profile, the asymptotic form always has a Lorentz character, but the trajectory is a self-affine fractal with two characteristic Hausdorff scaling exponents.

DOI
10.1103/physrevlett.93.120201

Related papers

Photonic superdiffusive motion in resonance radiation trapping

Mário Nuno Berberan-Santos, Eduardo J. Nunes-Pereira, José M. G. Martinho

In this work we consider the relation between the jump length probability density function and the line shape function in resonance radiation trapping in atomic vapors. The two-sided jump length probability density function suitable for a unidimensional formulation of radiative transfer is also derived. As a side result, a procedure to obtain the Maxwell distribution of velocities from the Maxwell-Boltzmann distribution of speeds was obtained. General relations that give the asymptotic jump length behavior and the Levy flight parameter mu for any line shape are obtained. The results are applied to generalized Doppler, generalized Lorentz, and Voigt line shape functions. It is concluded that the lighter the tail of the line shape function, the less heavy the tail of the jump length probability density function, although this tail is always heavy, with mu < or =1.

The Journal of Chemical Physics•Nov 7, 2006•7 citations

Sample size effects for Lévy flight of photons in atomic vapors

A. S. M. Macedo, J. P. Lopez, Thierry Passerat de Silans

Lévy flight superdiffusion consists of random walks characterized by very long jumps that dominate the transport. However, the finite size of real samples introduces truncation of long jumps and modifies the transport properties. We measure typical Levy flight parameters for photon diffusion in atomic vapor characterized by a Voigt absorption profile. We observe the change of Lévy parameter as a function of truncation length. We associate this variation with size-dependent contributions from different spectral regions of the emission profile with the Doppler core dominating the transport for thin samples and Lorentz wings for thick samples. Monte Carlo simulations are implemented to support the interpretation of results.

Physical review. E•Nov 30, 2021•5 citations

Microscopic characterization of Lévy flights of light in atomic vapors

Nicolas Mercadier, Martine Chevrollier, William Guerin +1 more

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 (L\'evy flights) dominate the transport properties.

arXiv:1305.1714•Physical Review A•Jun 24, 2013•20 citations

Dependence of Lévy-flight transmission on the starting point for photons propagating in atomic vapors

J. P. Lopez, A. S. M. Macedo, M. Araujo +1 more

The propagation of a photon in an atomic medium can be seen as a L\'evy-flight random walk where the probability distribution $P(z)$ for the photon step length $z$ scales with ${z}^{\ensuremath{-}(\ensuremath{\alpha}+1)}$, with $0<\ensuremath{\alpha}<2$. In atomic vapors, previous work reported the value of $\ensuremath{\alpha}$ obtained from direct measurement of $P(z)$ and also from the dependence of transmission on sample opacity, both for Doppler and Lorentz profiles. In this work, we report the measurement of $\ensuremath{\alpha}$ in a Cs cell from the scaling of transmission with starting point, i.e., the average penetration depth of the photon in the medium before the first scattering event. We show that the parameter $\ensuremath{\alpha}$ depends on the size of the system and on the probability that an atom suffers a collision before spontaneous emission. The measured $\ensuremath{\alpha}$ parameter corresponds to the expectation value for $P(z=L)$, with $L$ the size of the system, which is consistent with the so-called single-big-jump principle that states that a single jump rules the transport.

Physical Review A•Jan 3, 2023•2 citations

Lévy flights of photons with infinite mean free path

M. Araujo, Thierry Passerat de Silans, Robin Kaiser

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.

arXiv:2008.03506•Physical review. E•Jan 6, 2021•16 citations

Radiation trapping and Lévy flights in atomic vapours: an introductory review

Martine Chevrollier

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.

arXiv:1311.0253•Contemporary Physics•May 1, 2012•22 citations
Photon trajectories in incoherent radiation trapping for Doppler, Lorentz, and Voigt line shapes under complete frequency redistribution are shown to be Lévy flights. The jump length (r) distributions display characteristic long tails. For the Lorentz line shape, the asymptotic form is a strict power law r(-3/2), while for Doppler the asymptotic is r(-2)(ln(r)(-1/2). For the Voigt profile, the asymptotic form always has a Lorentz character, but the trajectory is a self-affine fractal with two characteristic Hausdorff scaling exponents.
In this work we consider the relation between the jump length probability density function and the line shape function in resonance radiation trapping in atomic vapors. The two-sided jump length probability density function suitable for a unidimensional formulation of radiative transfer is also derived. As a side result, a procedure to obtain the Maxwell distribution of velocities from the Maxwell-Boltzmann distribution of speeds was obtained. General relations that give the asymptotic jump length behavior and the Levy flight parameter mu for any line shape are obtained. The results are applied to generalized Doppler, generalized Lorentz, and Voigt line shape functions. It is concluded that the lighter the tail of the line shape function, the less heavy the tail of the jump length probability density function, although this tail is always heavy, with mu < or =1.
Lévy flight superdiffusion consists of random walks characterized by very long jumps that dominate the transport. However, the finite size of real samples introduces truncation of long jumps and modifies the transport properties. We measure typical Levy flight parameters for photon diffusion in atomic vapor characterized by a Voigt absorption profile. We observe the change of Lévy parameter as a function of truncation length. We associate this variation with size-dependent contributions from different spectral regions of the emission profile with the Doppler core dominating the transport for thin samples and Lorentz wings for thick samples. Monte Carlo simulations are implemented to support the interpretation of results.
The propagation of a photon in an atomic medium can be seen as a L\'evy-flight random walk where the probability distribution P(z)P(z)P(z) for the photon step length zzz scales with ${z}^{\ensuremath{-}(\ensuremath{\alpha}+1)}$, with $0<\ensuremath{\alpha}<2$. In atomic vapors, previous work reported the value of $\ensuremath{\alpha}$ obtained from direct measurement of P(z)P(z)P(z) and also from the dependence of transmission on sample opacity, both for Doppler and Lorentz profiles. In this work, we report the measurement of $\ensuremath{\alpha}$ in a Cs cell from the scaling of transmission with starting point, i.e., the average penetration depth of the photon in the medium before the first scattering event. We show that the parameter $\ensuremath{\alpha}$ depends on the size of the system and on the probability that an atom suffers a collision before spontaneous emission. The measured $\ensuremath{\alpha}$ parameter corresponds to the expectation value for P(z=L)P(z=L)P(z=L), with LLL the size of the system, which is consistent with the so-called single-big-jump principle that states that a single jump rules the transport.
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.