Defect modes of a Bose-Einstein condensate in an optical lattice with a localized impurity

TL;DR

This paper investigates defect modes in a Bose-Einstein condensate within an optical lattice containing a localized impurity, using theoretical modeling and numerical simulations to analyze their properties and stability.

Contribution

It introduces a method to describe defect modes via Wannier functions and coupled nonlinear Schrödinger equations with a delta-impurity, advancing understanding of impurity effects in BECs.

Findings

Defect modes can be accurately modeled by Wannier function expansion.

The stability of defect modes is confirmed through numerical simulations.

Potential methods for experimental generation of defect modes are discussed.

Abstract

We study defect modes of a Bose-Einstein condensate in an optical lattice with a localized defect within the framework of the one-dimensional Gross-Pitaevskii equation. It is shown that for a significant range of parameters the defect modes can be accurately described by an expansion over Wannier functions, whose envelope is governed by the coupled nonlinear Schr\"{o}dinger equation with a delta-impurity. The stability of the defect modes is verified by direct numerical simulations of the underlying Gross-Pitaevskii equation with a periodic plus defect potentials. We also discuss possibilities of driving defect modes through the lattice and suggest ideas for their experimental generation.