Ultracold Atoms Confined in an Optical Lattice Plus Parabolic Potential: A Closed-Form Approach

Published

September 22, 2005

Author(s)

G Pupillo, A M. Rey, Charles W. Clark, Carl J. Williams

Abstract

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”S 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.

Citation

Physical Review A (Atomic, Molecular and Optical Physics)

Volume

72

Issue

033616

Pub Type

Journals

Keywords

Bose-Hubbard Hamiltonian, bosons in optical lattices, dipole oscillations

Citation

Pupillo, G. , Rey, A. , Clark, C. and Williams, C. (2005), Ultracold Atoms Confined in an Optical Lattice Plus Parabolic Potential: A Closed-Form Approach, Physical Review A (Atomic, Molecular and Optical Physics) (Accessed October 27, 2025)