Atomic soliton transmission and induced collapse in scattering from a narrow barrier

TL;DR

This paper uses numerical simulations to study how bright matter-wave solitons scatter from a narrow barrier, revealing conditions for transmission and collapse, and compares three-dimensional results with effective one-dimensional models.

Contribution

It introduces a modified nonpolynomial Schrödinger equation that accurately predicts soliton transmission and collapse, improving upon existing models.

Findings

Transmission depends on impact velocity and barrier height.

Collapse occurs in specific parameter regions during collision.

Modified 1D model accurately predicts transmission even near collapse regions.

Abstract

We report systematic numerical simulations of the collision of a bright matter-wave soliton made of Bose-condensed alkali-metal atoms through a narrow potential barrier by using the three-dimensional Gross-Pitaevskii equation. In this way, we determine how the transmission coefficient depends on the soliton impact velocity and the barrier height. Quite remarkably, we also obtain the regions of parameters where there is the collapse of the bright soliton induced by the collision. We compare these three-dimensional results with the ones obtained by three different one-dimensional nonlinear Schr\"odinger equations. We find that a specifically modified nonpolynomial Schr\"odinger equation is able to accurately assess the transmission coefficient even in a region in which the usual nonpolynomial Schr\"odinger equation does collapse. In particular, this simplified but very effective one-dimensional model takes into account the transverse width dynamics of the soliton with an ordinary differential equation coupled to the partial differential equation of the axial wave function of the Bose-Einstein condensate.