  We investigate the behavior of ultracold bosons in optical lattices with a
disorder potential generated via a secondary species frozen in random
configurations. The statistics of disorder is associated with the physical
state in which the secondary species is prepared. The resulting random
potential, albeit displaying algebraic correlations, is found to lead to
localization of all single-particle states. We then investigate the real-time
dynamics of localization for a hardcore gas of mobile bosons which are brought
into sudden interaction with the random potential. Regardless of their initial
state and for any disorder strength, the mobile particles are found to reach a
steady state characterized by exponentially decaying off-diagonal correlations
and by the absence of quasi-condensation; when the mobile particles are
initially confined in a tight trap and then released in the disorder potential,
their expansion is stopped and the steady state is exponentially localized in
real space, clearly revealing Anderson localization.
