We propose to observe many-body localization in cold atomic gases byrealizing a Bose-Hubbard chain with binary disorder and studying itsnon-equilibrium dynamics. In particular, we show that measuring the differencein occupation between even and odd sites, starting from a prepared density-wavestate, provides clear signatures of localization. As hallmarks of the many-bodylocalized phase we confirm, furthermore, a logarithmic increase of theentanglement entropy in time and Poissonian level statistics. Our numericaldensity-matrix renormalization group calculations for infinite system size arebased on a purification approach; this allows us to perform the disorderaverage exactly, thus producing data without any statistical noise and withmaximal simulation times of up to a factor 10 longer than in the clean case.
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