An optical lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift. Atoms are cooled and congregate at the potential extrema (at maxima for blue-detuned lattices, and minima for red-detuned lattices). The resulting arrangement of trapped atoms resembles a crystal lattice and can be used for quantum simulation. 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. Parameters There are two important parameters of an optical lattice: the potential well depth and the periodicity. Control of potential depth The potential experienced by the atoms is related to the intensity of the laser used to generate the optical lattice. The potential depth of the optical lattice can be tuned in real time by changing the power of the laser, which is normally controlled by an acousto-optic modulator (AOM). The AOM is tuned to deflect a variable amount of the laser power into the optical lattice. Active power stabilization of the lattice laser can be accomplished by feedback of a photodiode signal to the AOM. Control of periodicity The periodicity of the optical lattice can be tuned by changing the wavelength of the laser or by changing the relative angle between the two laser beams. The real-time control of the periodicity of the lattice is still a challenging task. The wavelength of the laser cannot easily be varied over a large range in real time, and so the periodicity of the lattice is normally controlled by the relative angle between the laser beams. However, it is difficult to keep the lattice stable while changing the relative angles, since the interference is sensitive to the relative phase between the laser beams. Titanium-sapphire lasers, with their