Single-atom density of states of an optical lattice
arXiv:cond-mat/0312079 · doi:10.1103/PhysRevLett.93.080404
Abstract
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 κdenoting the strength of the harmonic trap. It is shown that the κ\to 0 limit of this problem is singular, in the sense that the density of states for a very shallow trap (κ\to 0) is {\it qualitatively different} from that of a translationally invariant lattice (κ= 0). The physics of this difference is discussed, and densities of states and wave functions are exhibited and explained.
4 pages, 3 figures, REVTEX 4. Three typos corrected and minor textual modifications
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