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During the last decade there has been remarkable progress in controlling and manipulating ensembles
of ultracold atoms. Using optical lattices and different types of atoms, a variety of non-trivial
many-body states can be 'engineered' that are very accurate realizations of Hubbard models. The
experimental observation of the Mott-Hubbard superfluid-insulator transition, of fermionic superfluids,
of the Tonks-Girardeau gas and other Luttinger liquids, the measurement of noise correlations, and
instabilities in Bose-Fermi mixtures, have created a great deal of excitement in the physics community.
These findings have prompted a large amount of theoretical work that study charge density wave order,
many-body states of composite particles, polaronic effects, and tunning of Feshbach resonances on lattices.
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