We investigate the expansion of bosons and fermions in a homogeneous lattice after a sudden removal of the trapping potential using exact numerical methods. As a main result, we show that in one dimension, both bosonic and fermionic Mott insulators expand with the same velocity, irrespective of the interaction strength, provided the expansion starts from the ground state of the trapped gas. Furthermore, their density profiles become identical during the expansion: The asymptotic density dynamics is identical to that of initially localized, non-interacting particles, and the asymptotic velocity distribution is flat. The expansion velocity for initial correlated Mott insulating states is therefore independent of the interaction strength and particle statistics. Interestingly, this non-equilibrium dynamics is sensitive to the interaction driven quantum phase transition in the Bose-Hubbard model: While being constant in the Mott phase, the expansion velocity decreases in the superfluid phase and vanishes for large systems in the non-interacting limit. These results are compared to the set-up of a recent experiment [PRL 110, 205301 (2013)], where the trap opening was combined with an interaction quench from infinitely strong interactions to finite values. We carry out an analogous analysis for a two-component Fermi gas, with similar observations. In addition, we study the effect of breaking the integrability of hard-core bosons in different ways: While the fast ballistic expansion from the ground state of Mott insulators in one dimension remains unchanged for finite interactions, we observe strong deviations from this behavior on a two-leg ladder even in the hard-core case. This change in dynamics bares similarities with the dynamics in the dimensional crossover from one to two dimensions observed in the aformentioned experimental study.
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