  We study several effects which lead to symmetry-broken momentum distributions
of quantum gases released from optical lattices. In particular, we demonstrate
that interaction within the first milliseconds of the time-of-flight expansion
can strongly alter the measurement of the initial atomic momentum distribution.
For bosonic mixtures in state-dependent lattices, inter-species scattering
processes lead to a symmetry breaking in momentum space. The underlying
mechanism is identified to be diffraction of the matter wave from the total
density lattice, which gives rise to a time-dependent interaction potential.
Our findings are of fundamental relevance for the interpretation of
time-of-flight measurements and for the study of exotic quantum phases such as
the twisted superfluid. Beyond that, the observed matter-wave diffraction can
also be used as an interferometric probe. In addition, we report on diffraction
from the state-dependent standing light field, which leads to the same
symmetry-broken momentum distributions, even for single component condensates.
