Nonergodic diffusion of single atoms in a periodic potential

Drawing microscopic information out of the diffusive dynamics of complex processes often requires an assumption of ergodicity. Precision experiments on a single atom in a periodic potential suggest that this may be too simplistic in many cases. Diffusion can be used to infer the microscopic features of a system from the observation of its macroscopic dynamics. Brownian motion accurately describes many diffusive systems, but non-Brownian and nonergodic features are often observed on short timescales. Here, we trap a single ultracold caesium atom in a periodic potential and measure its diffusion 1 , 2 , 3 . We engineer the particle–environment interaction to fully control motion over a broad range of diffusion constants and timescales. We use a powerful stroboscopic imaging method to detect single-particle trajectories and analyse both non-equilibrium diffusion properties and the approach to ergodicity 4 . Whereas the variance and two-time correlation function exhibit apparent Brownian motion at all times, higher-order correlations reveal strong non-Brownian behaviour. We additionally observe the slow convergence of the exponential displacement distribution to a Gaussian and—unexpectedly—a much slower approach to ergodicity 5 , in perfect agreement with an analytical continuous-time random-walk model 6 , 7 , 8 . Our experimental system offers an ideal testbed for the detailed investigation of complex diffusion processes.