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Ultracold molecules on optical lattices = molecular crystals with unusual properties: Intermolecular interactions are very weak, much weaker than the energy of rotational splitting in molecules Molecules are held in the crystal by optical field forces, not intermolecular interactions Is rotational excitation of a molecule a single-particle or collective excitation? What can we do with molecules on a lattice that cannot be done with conventional crystals? Frenkel exciton φn = |00〉1|00〉2...|10〉n|00〉n+1...|00〉N ψk = n eik·rn