Single-atom density of states of an optical lattice

Details Single-atom density of states of an optical lattice Single-atom density of states of an optical lattice

2003-12-02

arxiv.org/abs/cond-mat/0312079v3

Phys. Rev. Lett. 93, 080404 (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures, REVTEX 4. Three typos corrected and minor textual modifications

Scientific paper

10.1103/PhysRevLett.93.080404

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.

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