Observation of anomalous diffusion and fractional self-similarity in one dimension

TL;DR

This paper experimentally investigates anomalous diffusion of ultra-cold atoms in a one-dimensional optical lattice, revealing fractional self-similarity and Levy distribution characteristics with depth-dependent exponents.

Contribution

It provides the first experimental observation of fractional self-similarity and anomalous diffusion in ultra-cold atoms within a 1D optical lattice, including analysis of distribution shapes and correlations.

Findings

Cloud width follows a power-law time dependence with depth-dependent exponent.

Distribution exhibits fractional self-similarity with a specific characteristic exponent.

Distribution fits Levy distribution but with a different exponent from the temporal one.

Abstract

We experimentally study anomalous diffusion of ultra-cold atoms in a one dimensional polarization optical lattice. The atomic spatial distribution is recorded at different times and its dynamics and shape are analyzed. We find that the width of the cloud exhibits a power-law time dependence with an exponent that depends on the lattice depth. Moreover, the distribution exhibits fractional self-similarity with the same characteristic exponent. The self-similar shape of the distribution is found to be well-fitted by a L\'{e}vy distribution, but with a characteristic exponent that differs from the temporal one. Numerical simulations suggest that this may be due to correlations between the atoms' velocity and flight duration.