 Optical lattice

An optical lattice is formed by the interference of counterpropagating 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 in the locations of potential minima. The resulting arrangement of trapped atoms resembles a crystal lattice.^{[1]}
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.^{[citation needed]} However, superfluid–Mott insulator transition^{[2]} 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.^{[3]} 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.^{[4]}
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 (acoustooptic 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 realtime 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.^{[5]} 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 onedimensional optical lattice while maintaining trapped atoms insitu was first demonstated in 2005 using a singleaxis servocontrolled galvanometer.^{[6]} This "accordion lattice" was able to vary the lattice periodicity from 1.30 to 9.3 μm. More recently, a different method of realtime control of the lattice periodicity was demonstrated,^{[7]} 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 singlesite manipulation and spatially resolved detection.
Besides trapping cold atoms, optical lattices have been widely used in creating gratings and photonic crystals. They are also useful for sorting microscopic particles,^{[8]} and may be useful for assembling cell arrays.
See also
 Bose–Hubbard model
References
 ^ Bloch, Immanuel (April 10, 2004). "Quantum gases in optical lattices". IOP. http://physicsworld.com/cws/article/print/19273.
 ^ Greiner, Markus; Mandel, Olaf; Esslinger, Tilman; Hänsch, Theodor W.; Bloch, Immanuel (January 3, 2002). "Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms". Nature 415 (6867): 39–44. Bibcode 2002Natur.415...39G. doi:10.1038/415039a. PMID 11780110.
 ^ Koetsier, Arnaud; Duine, R. A.; Bloch, Immanuel; Stoof, H. T. C. (2008). "Achieving the Néel state in an optical lattice". Phys. Rev. A 77: 023623. Bibcode 2008PhRvA..77b3623K. doi:10.1103/PhysRevA.77.023623.
 ^ Brennen, Gavin K.; Caves, Carlton; Jessen, Poul S.; Deutsch, Ivan H. (1999). "Quantum logic gates in optical lattices". Phys. Rev. Lett. 82 (5): 1060–1063. arXiv:quantph/9806021. Bibcode 1999PhRvL..82.1060B. doi:10.1103/PhysRevLett.82.1060.
 ^ Fallani, Leonardo; Fort, Chiara; Lye, Jessica; Inguscio, Massimo (May 2005). "BoseEinstein condensate in an optical lattice with tunable spacing: transport and static properties". Optics Express 13 (11): 4303–4313. arXiv:condmat/0505029. Bibcode 2005OExpr..13.4303F. doi:10.1364/OPEX.13.004303. PMID 19495345.
 ^ Huckans, J. H. (December 2006). "Optical Lattices and Quantum Degenerate Rb87 in Reduced Dimensions". University of Maryland doctoral dissertation.
 ^ Li, T. C.; Kelkar,H.; Medellin, D.; Raizen, M. G. (April 3, 2008). "Realtime control of the periodicity of a standing wave: an optical accordion". Optics Express 16 (8): 5465–5470. Bibcode 2008OExpr..16.5465L. doi:10.1364/OE.16.005465. PMID 18542649.
 ^ MacDonald, M. P.; Spalding, G. C.; Dholakia, K. (November 27, 2003). "Microfluidic sorting in an optical lattice". Nature 426 (6965): 421–424. Bibcode 2003Natur.426..421M. doi:10.1038/nature02144. PMID 14647376.
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