Expansion dynamics of interacting bosons in homogeneous lattices

Due to independent real-time control of Hamiltonian parameters in optical lattices, the non-equilibrium transport properties of interacting bosons and fermions can be studied in experiments with ultra-cold atomic gases (see [1] for a sudden expansion experiment with fermions). In this work, we experimentally and numerically investigate the expansion of initially localized bosons in homogeneous one- and two-dimensional optical lattices. Dimensionality has a crucial influence, since one-dimensional systems expand ballistically both in the non-interacting and the strongly interacting limit, separated by a pronounced minimum in the expansion velocity at intermediate interaction strengths. For two-dimensional and sufficiently strongly coupled one-dimensional systems, even weak interactions lead to a dramatic suppression of the expansion, indicative of diffusive dynamics. In the case of one dimension, we find an excellent agreement between the experimental results and time-dependent density-matrix renormalization group simulations. [1] Schneider et al. Nature Phys. 8, 213 (2012)