Nonergodic Diffusion of Single Atoms in a Periodic Potential
  Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic potential. We engineer microscopic particle-environment interaction to control the ensuing diffusion over a broad range of diffusion constants and from normal to subdiffusion. While one- and two-point properties extracted from single particle trajectories, such as variance or position correlations, indicate apparent Brownian motion, the step size distribution, however, shows exponentially decaying tails. Furthermore non-ergodic dynamics is observed on long time scales. We demonstrate excellent agreement with a model of continuous time random walk with exponential distribution, which applies to various transport phenomena in condensed or soft matter with periodic potentials. 
Farina Kindermann, Andreas Dechant, Michael Hohmann, Tobias Lausch,   Daniel Mayer, Felix Schmidt, Eric Lutz and Artur Widera
physics.atom-ph cond-mat.stat-mech physics.bio-ph