various geometries, varying lattice geometries can be created. These range from the simplest case of two counterpropagating beams forming a one-dimensional lattice, to more complex geometries like hexagonal lattices. The variety of geometries that can be produced in optical lattice systems allow the physical realization of different Hamiltonians, such as the Bose–Hubbard model, the Kagome lattice and Sachdev–Ye–Kitaev model, and the Aubry–André model. By studying the evolution of atoms under the influence of these Hamiltonians, insight about the solutions to the Hamiltonian can be gained. This is particularly relevant to complicated Hamiltonians which are not easily soluble using theoretical or numerical techniques, such as those for strongly correlated systems. Optical clocks 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. Quantum information They are also promising candidates for quantum information processing. Atom interferometry Shaken optical lattices – where the phase of the lattice is modulated, causing the lattice pattern to scan back and forth – can be used to control the momentum state of the atoms trapped in the lattice. This control is exercised to split the atoms into populations of different momenta, propagate them to accumulate phase differences between the populations, and recombine them to produce an interference pattern. Other uses 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. See also Bose–Hubbard model Ultracold atom List of laser articles Electromagnetically induced grating Magic wavelength References External links More about optical lattices Introduction to optical lattices Optical lattice on arxiv.org Quantum optics Atomic physics