Bose-Einstein Condensates in Optical Lattices: Band-Gap Structure and Solitons

TL;DR

This paper investigates the band-gap structure and stability of localized and extended states of Bose-Einstein condensates in optical lattices, revealing the existence of stable matter-wave gap solitons under various interactions.

Contribution

It provides a comprehensive analysis of the existence and stability of gap solitons in BECs within optical lattices, including both linear and nonlinear regimes.

Findings

Existence of spatially localized matter-wave gap solitons.

Stability of gap solitons varies across different band gaps.

Both repulsive and attractive interactions support stable solitons.

Abstract

We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions.