Abstract
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 diffusion1,2,3. 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 ergodicity4. 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 ergodicity5, in perfect agreement with an analytical continuous-time random-walk model6,7,8. Our experimental system offers an ideal testbed for the detailed investigation of complex diffusion processes.
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Acknowledgements
This work was partially funded by the ERC Starting Grant No. 278208, the Collaborative Project TherMiQ (Grant Agreement 618074) and the SFB/TRR49. T.L. acknowledges funding by Carl Zeiss Stiftung. D.M. is a recipient of a DFG-fellowship through the Excellence Initiative by the Graduate School Materials Science in Mainz (GSC 266). F.S. acknowledges funding by the Studienstiftung des deutschen Volkes.
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A.W. and F.K. conceived the experiment. F.K., M.H., T.L., D.M. and F.S. took experimental data, F.K. analysed the data. A.D. and E.L. developed the theoretical model and performed numerical simulations. All authors contributed in interpretation, discussion and writing of the manuscript.
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Kindermann, F., Dechant, A., Hohmann, M. et al. Nonergodic diffusion of single atoms in a periodic potential. Nature Phys 13, 137–141 (2017). https://doi.org/10.1038/nphys3911
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DOI: https://doi.org/10.1038/nphys3911
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