Great advances in precision quantum measurement have been achieved with trapped ions and atomic gases at the lowest possible temperatures [1-3]. These successes have inspired ideas to merge the two systems [4]. In this way one can study the unique properties of ionic impurities inside a quantum fluid [5][6][7][8][9][10][11] or explore buffer gas cooling of the trapped ion quantum computer [12]. Remarkably, in spite of its importance, experiments with atom-ion mixtures remained firmly confined to the classical collision regime [13]. We report a collision energy of 1.15(0.23) times the s-wave energy (or 9.9(2.0) µK) for a trapped ytterbium ion in an ultracold lithium gas. We observed a deviation from classical Langevin theory by studying the spin-exchange dynamics, indicating quantum behavior in the atom-ion collisions. Our results open up numerous opportunities, such as the exploration of atom-ion Feshbach resonances [14,15], in analogy to neutral systems [16].

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Dynamical properties of two bosonic quantum walkers in a one-dimensional lattice are studied theoretically. Depending on the initial state, interactions, lattice tilting, and lattice disorder, whole plethora of different behaviors are observed. Particularly, it is shown that two bosons system manifests the many-body localization like behavior in the presence of a quenched disorder. The whole analysis is based on a specific decomposition of the temporal density profile into different contributions from singly and doubly occupied sites. In this way, the role of interactions is extracted. Since the contributions can be directly measured in experiments with ultra-cold atoms in optical lattices, the predictions presented may have some importance for upcoming experiment.

The impact of geometry on many-body localization is studied on simple, exemplary systems amenable to exact diagonalization treatment. The crossover between ergodic and MBL phase for uniform as well as quasi-random disorder is analyzed using statistics of energy levels. It is observed that the transition to many-body localized phase is correlated with the number of nearest coupled neighbors. The crossover from extended to localized systems is approximately described by the so called plasma model. arXiv:1805.07383v2 [cond-mat.dis-nn]