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.[why?] Atoms are cooled and congregate in the locations of potential minima. 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.
There are two important parameters of an optical lattice: the well depth and the periodicity. The well depth of the optical lattice can be tuned in real time by changing the power of the laser, which is normally controlled by an AOM (acousto-optic modulator). 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. Because the wavelength of the laser cannot be varied over a large range in real time, 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. Continuous control of the periodicity of a one-dimensional optical lattice while maintaining trapped atoms in-situ was first demonstrated in 2005 using a single-axis servo-controlled galvanometer. This "accordion lattice" was able to vary the lattice periodicity from 1.30 to 9.3 μm. More recently, a different method of real-time control of the lattice periodicity was demonstrated, in which the center fringe moved less than 2.7 μm while the lattice periodicity was changed from 0.96 to 11.2 μm. Keeping atoms (or other particles) trapped while changing the lattice periodicity remains to be tested more thoroughly experimentally. Such accordion lattices are useful for controlling ultracold atoms in optical lattices, where small spacing is essential for quantum tunneling, and large spacing enables single-site manipulation and spatially resolved detection. Site-resolved detection of the occupancy of lattice sites of both bosons and fermions within a high tunneling regime is regularly performed in quantum gas microscopes.
Besides trapping cold atoms, optical lattices have been widely used in creating gratings and photonic crystals. They are also useful for sorting microscopic particles, and may be useful for assembling cell arrays.
Atoms in an optical lattice provide an ideal quantum system where all parameters can be controlled. Thus they can be used to study effects that are difficult to observe in real crystals. They are also promising candidates for quantum information processing. The best atomic clocks in the world use atoms trapped in optical lattices, to obtain narrow spectral lines that are unaffected by the Doppler effect and recoil. 
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