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We investigate the dynamics of neutral atoms in a 2D optical lattice whichtraps two distinct internal states of the atoms in different columns. Two Ramanlasers are used to coherently transfer atoms from one internal state to theother, thereby causing hopping between the different columns. By adjusting thelaser parameters appropriately we can induce a non vanishing phase of particlesmoving along a closed path on the lattice. This phase is proportional to theenclosed area and we thus simulate a magnetic flux through the lattice. Thissetup is described by a Hamiltonian identical to the one for electrons on alattice subject to a magnetic field and thus allows us to study this equivalentsituation under very well defined controllable conditions. We consider thelimiting case of huge magnetic fields -- which is not experimentally accessiblefor electrons in metals -- where a fractal band structure, the Hofstadterbutterfly, characterizes the system.Comment: 6 pages, RevTe

Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms