Cold bosons in optical lattices

Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles of correct self-consistent description of arbitrary systems with Bose-Einstein condensate are formulated. Theoretical methods for describing regular periodic lattices are presented. A special attention is paid to the discussion of Bose-atom properties in the frame of the boson Hubbard model. Optical lattices with arbitrary strong disorder, induced by random potentials, are treated. Possible applications of cold atoms in optical lattices are discussed, with an emphasis of their usefulness for quantum information processing and quantum computing. An important feature of the present review article, distinguishing it from other review works, is that theoretical fundamentals here are not just mentioned in brief, but are thoroughly explained. This makes it easy for the reader to follow the principal points without the immediate necessity of resorting to numerous publications in the field.