Light propagating in a resonant atomic vapor performs a Lévy flight random walk, in which rare long steps dominate the transport. In contrast to the ideal power-law step-length distributions usually assumed in the literature, the actual distribution in atomic vapors is characterized by a local Lévy index $\alpha \left(\ell \right)$ that varies smoothly with the step length $\ell$. Moreover, the walker alternates between two distinct step-length distributions, depending on whether an atomic collision occurs during each scattering event. In this work, we experimentally investigate which effective Lévy index is retrieved from diffuse transmission measurements in such a nonideal Lévy flight, and how the alternation between the two distributions influences the transmission. From measurements in a dense cesium vapor for different system sizes and atomic densities, we show that the measured Lévy index corresponds to the local exponent evaluated at the system size, ${\alpha }_T=\alpha (\ell =L)$. Surprisingly, the measured values are consistent with the step-length distribution associated with atomic collisions, that has heavier tails, even when the collision probability is small. Monte Carlo simulations of walkers alternating between two Lévy-like step-length distributions support the experimental findings. Our results extend the study of Lévy flights to a class of nonideal random walks, with length-dependent local exponents and alternating step-length distributions, that are likely to be relevant in other real physical systems.

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• Levy flights
• Lineshapes & shifts