Abstract
Similarities between alkali gases in optical lattices with non-integer occupation of the lattice sites and quantum crystals are explored. The analogy with the vacancy liquid provides an alternative explanation to the Mott transition for the recent experiment on the phase transition in the lattice. The vacancy liquid can undergo BEC with T c within experimental reach. Direct and vacancy-assisted mechanisms of the band motion for hyperfine impurities are discussed. The presence of vacancies can result in the spatial decomposition of the system into pure hyperfine components. Below BEC for the vacancies, the impurity component resembles 3 He in 3 He - Hell mixtures.
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