Quantum Numbers for Excitations of Bose-Einstein Condensates in 1D Optical Lattices

TL;DR

This paper investigates the excitation spectrum and band structure of Bose-Einstein condensates in 1D optical lattices, comparing finite and periodic systems, and introduces new methods to analyze their spectral properties.

Contribution

It provides a detailed comparison of excitation spectra in finite and periodic 1D Bose-Einstein condensates using new definitions of effective wavenumber and phase-slip number.

Findings

Two excitation branches in finite 1D models.

Good agreement of band edges between finite and periodic systems.

Finite-size effects cause additional spectral branches.

Abstract

The excitation spectrum and the band structure of a Bose-Einstein condensate in a periodic potential are investigated. Analyses within full 3D systems, finite 1D systems, and ideal periodic 1D systems are compared. We find two branches of excitations in the spectra of the finite 1D model. The band structures for the first and (part of) the second band are compared between a finite 1D and the fully periodic 1D systems, utilizing a new definition of a effective wavenumber and a phase-slip number. The upper and lower edges of the first gap coincide well between the two cases. The remaining difference is explained by the existence of the two branches due to the finite-size effect.