Atoms trapped in the optical lattice may move due to quantum tunneling, even if the potential well depth of the lattice points exceeds the kinetic energy of the atoms, which is similar to the electrons in a conductor. However, a superfluid–Mott insulator transition may occur, if the interaction energy between the atoms becomes larger than the hopping energy when the well depth is very large. In the Mott insulator phase, atoms will be trapped in the potential minima and cannot move freely, which is similar to the electrons in an insulator. In the case of Fermionic atoms, if the well depth is further increased the atoms are predicted to form an antiferromagnetic, i.e. Néel state at sufficiently low temperatures. Atoms in an optical lattice provide an ideal quantum system where all parameters