Quasi-one-dimensional Bose-Einstein condensates in nonlinear lattices

TL;DR

This paper investigates the stability of three-dimensional Bose-Einstein condensate solitons in a nonlinear lattice with sign-changing nonlinearity, using variational and 1D NPSE methods, revealing stability regions and unique dynamical effects.

Contribution

It introduces a combined variational and NPSE approach to identify stable 3D solitons in nonlinear lattices with sign-changing nonlinearity, highlighting differences from 1D models.

Findings

Stable soliton regions identified in parameter space.

Kicked solitons cannot be set in motion but can be stabilized.

Unique wave packet emission observed in dynamics.

Abstract

We consider the three-dimensional (3D) mean-field model for the Bose-Einstein condensate (BEC), with a 1D nonlinear lattice (NL), which periodically changes the sign of the nonlinearity along the axial direction, and the harmonic-oscillator trapping potential applied in the transverse plane. The lattice can be created as an optical or magnetic one, by means of available experimental techniques. The objective is to identify stable 3D solitons supported by the setting. Two methods are developed for this purpose: The variational approximation, formulated in the framework of the 3D Gross-Pitaevskii equation, and the 1D nonpolynomial Schr\"{o}dinger equation (NPSE) in the axial direction, which allows one to predict the collapse in the framework of the 1D description. Results are summarized in the form of a stability region for the solitons in the plane of the NL strength and wavenumber. Both methods produce a similar form of the stability region. Unlike their counterparts supported by the NL in the 1D model with the cubic nonlinearity, kicked solitons of the NPSE cannot be set in motion, but the kick may help to stabilize them against the collapse, by causing the solitons to shed excess norm. A dynamical effect specific to the NL is found in the form of freely propagating small-amplitude wave packets emitted by perturbed solitons.