  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.
