Superdiffusive comb: Application to experimental observation of anomalous diffusion in one dimension

TL;DR

This paper proposes a fractal comb model to explain superdiffusive behavior observed in ultra-cold atoms within a one-dimensional optical lattice, linking anomalous diffusion to fractal geometry and Levy flights.

Contribution

It introduces a superdiffusive comb model based on fractal geometry to explain experimental observations of anomalous diffusion in cold atoms.

Findings

Transport exponent is dictated by fractal geometry.

Recoil distributions lead to Levy flights.

Model aligns with experimental superdiffusion data.

Abstract

A possible mechanism of superdiffusion of ultra-cold atoms in a one-dimensional polarization optical lattice, observed experimentally in [Phys. Rev. Lett. \textbf{108}, 093002 (2012)], is suggested. The analysis is based on a consideration of anomalous diffusion in a fractal comb [Phys. Rev. E \textbf{83}, 052106 (2011)]. It is shown that the transport exponent is determined by the fractal geometry of the comb due to recoil distributions resulting in L\'evy flights of atoms.