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

The propagation of a photon in an atomic medium can be seen as a Levy-flight random walk where the probability distribution P(z) for the photon step length z scales with z-(alpha +1), with 0 < alpha < 2. In atomic vapors, previous work reported the value of 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 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 alpha depends on the size of the system and on the probability that an atom suffers a collision before spontaneous emission. The measured 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.