Local density approximation for confined bosons in an optical lattice

TL;DR

This paper uses quantum Monte Carlo methods to validate a local-density approximation for the one-dimensional Bose-Hubbard model with confinement, revealing detailed insights into the system's properties and momentum distribution.

Contribution

It demonstrates the accuracy of the local-density approximation for confined bosons in an optical lattice and clarifies the origin of fine structures in the momentum distribution.

Findings

Local-density approximation is quantitatively accurate in most parameter regimes.

Identified the origin of fine structures in the momentum distribution.

Challenged claims of universal behavior in confined systems.

Abstract

We investigate local and global properties of the one-dimensional Bose-Hubbard model with an external confining potential, describing an atomic condensate in an optical lattice. Using quantum Monte Carlo techniques we demonstrate that a local-density approximation, which relates the unconfined and the confined model, yields quantitatively correct results in most of the interesting parameter range. We also examine claims of universal behavior in the confined system, and demonstrate the origin of a previously calculated fine structure in the experimentally accessible momentum distribution.