Ultracold atoms confined in an optical lattice plus parabolic potential: A closed-form approach

We discuss interacting and noninteracting one dimensional atomic systems trapped in an optical lattice plus a parabolic potential. We show that, in the tight-binding approximation, the noninteracting problem is exactly solvable in terms of Mathieu functions. We use the analytic solutions to study th...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2005-09, Vol.72 (3), Article 033616
Main Authors: Rey, Ana Maria, Pupillo, Guido, Clark, Charles W., Williams, Carl J.
Format: Article
Language:English
Subjects:
ANALYTICAL SOLUTION
ATOMIC AND MOLECULAR PHYSICS
ATOMS
BOSE-EINSTEIN CONDENSATION
BOSE-EINSTEIN GAS
EXACT SOLUTIONS
EXCITATION
FERMIONS
HAMILTONIANS
INTERACTING BOSON MODEL
ONE-DIMENSIONAL CALCULATIONS
OPTICS
OSCILLATIONS
POTENTIALS
SUPERFLUIDITY
TRAPPING
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We discuss interacting and noninteracting one dimensional atomic systems trapped in an optical lattice plus a parabolic potential. We show that, in the tight-binding approximation, the noninteracting 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.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.72.033616