  Correlations between particles can lead to subtle and sometimes
counterintuitive phenomena. We analyze one such case, occurring during the
sudden expansion of fermions in a lattice when the initial state has a strong
admixture of double occupancies. We promote the notion of quantum distillation:
during the expansion, and in the presence of strongly repulsive interactions,
doublons group together, forming a nearly ideal band insulator, which is
metastable with a low entropy. We propose that this effect could be used for
cooling purposes in experiments with two-component Fermi gases.
