Phys. Rev. Lett. 93, 080404 (2004) [4 pages]Single-Atom Density of States of an Optical LatticeReceived 11 December 2003; published 19 August 2004 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 κ denoting the strength of the harmonic trap. It is shown that the κ→0 limit of this problem is singular, in the sense that the density of states for a very shallow trap (κ→0) is 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. © 2004 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.93.080404
DOI:
10.1103/PhysRevLett.93.080404
PACS:
03.75.Lm, 03.65.Sq, 39.25.+k
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