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

Abstract

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.