  Optical lattices can be loaded with atoms which can have strong interactions,
such that the interaction of atoms at different lattice sites cannot be
neglected. Moreover, the intersite interactions can be so strong that it can
force the atoms to form a self-organized lattice, such that exists in crystals.
With increasing intersite interactions, there can appear several lattice
states, including conducting optical lattices, insulating optical lattices,
delocalized quantum crystals, and localized quantum crystals.
