Experimental investigation of L\'evy flights for step-length distributions with a length-dependent local power exponent

Abstract

We experimentally investigate the transmission of light by dense atomic vapor. The light propagating in dense atomic vapor can be modeled as a L\'evy flight random walk. For such system, the step-length distribution can be modeled as $P(\ell)\sim \ell^{-1-\alpha(\ell)}$, with the L\'evy index $\alpha(\ell)$ varying smoothly with the step length. Moreover, the walkers alternate between two distinct distributions depending on the occurrence of collisions between atoms in the light scattering. We obtain the L\'evy index from transmission measurements for different system sizes and atomic densities. The measured L\'evy index is determined by the system size $\alpha=\alpha(\ell=L)$. Simulations are made for walkers alternating between two L\'evy like step-length