The electric field intensity of a standing-wave laser field is periodic in space. Due to the ac Stark effect, this gives rise to a spatially periodic potential acting on an atom, as explained in Chapter 4 (see, e.g., Eq. (4.31)). This is the physical principle behind the generation of optical lattices. By superimposing a number of different laser beams it is possible to generate potentials which are periodic in one, two or three dimensions. The suggestion that standing light waves may be used to confine the motion of atoms dates back to 1968 and is due to Letokhov. The first experimental realization of an optical lattice was achieved in 1987 for a classical gas of cesium atoms.

The study of atoms in such potentials has many different facets. At the simplest level, it is possible to study the energy band structure of atoms moving in these potentials and to explore experimentally a number of effects that are difficult to observe for electrons in the periodic lattice of a solid. Interactions between atoms introduce qualitatively new effects. Within mean-field theory, which applies when the number of atoms in the vicinity of a single minimum of the potential is sufficiently large, one finds that interatomic interactions give rise to novel features in the band structure. These include multivaluedness of the energy for a given band and states possessing a periodicity different from that of the optical lattice.