Single-atom density of states of an optical lattice

C. Hooley, J. Quintanilla

Published 2003-12-02, updated 2004-05-14Version 3

We consider a single atom in an optical lattice, subject to a harmonic trapping potential. The problem is treated in the tight-binding approximation, with an extra parameter \kappa denoting the strength of the harmonic trap. It is shown that the \kappa \to 0 limit of this problem is singular, in the sense that the density of states for a very shallow trap (\kappa \to 0) is {\it qualitatively different} from that of a translationally invariant lattice (\kappa = 0). The physics of this difference is discussed, and densities of states and wave functions are exhibited and explained.