Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2005-03-18
Phys. Rev. A 72, 033616 (2005)
Physics
Condensed Matter
Other Condensed Matter
19 pages, 15 figures Minor modification were done and new references were added
Scientific paper
10.1103/PhysRevA.72.033616
We discuss interacting and non-interacting one dimensional atomic systems trapped in an optical lattice plus a parabolic potential. We show that, in the tight-binding approximation, the non-interacting problem is exactly solvable in terms of Mathieu functions. We use the analytic solutions to study the collective oscillations of ideal bosonic and fermionic ensembles induced by small displacements of the parabolic potential. We treat the interacting boson problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From analysis of the dependence upon lattice depth of the low-energy excitation spectrum of the interacting system, we consider the problems of "fermionization" of a Bose gas, and the superfluid-Mott insulator transition. The spectrum of the noninteracting system turns out to provide a useful guide to understanding the collective oscillations of the interacting system, throughout a large and experimentally relevant parameter regime.
Clark Charles W.
Pupillo Guido
Rey Ana Maria
Williams Carl J.
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