Collapse instability of solitons in the nonpolynomial Schr\"{o}dinger equation with dipole-dipole interactions

TL;DR

This paper investigates how dipole-dipole interactions influence the stability and collapse of solitons in a dipolar Bose-Einstein condensate modeled by a 1D nonpolynomial Schrödinger equation, revealing conditions that prevent collapse.

Contribution

It introduces a detailed analysis of dipole-dipole effects on soliton collapse in BECs within the 1D NPSE framework, including stability diagrams for various interaction types.

Findings

Attractive DD interactions can prevent collapse in attractive contact BECs.

Stability diagrams map collapse and stability regions in parameter space.

Both attractive and repulsive interactions are considered in the analysis.

Abstract

A model of the Bose-Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial Schr\"{o}dinger equation (NPSE) with additional terms describing long-range dipole-dipole (DD) interactions. The NPSE makes it possible to describe the collapse of localized modes, which was experimentally observed in the self-attractive BEC confined in tight traps, in the framework of the 1D description. We study the influence of the DD interactions on the dynamics of bright solitons, especially as concerns their collapse-induced instability. Both attractive and repulsive contact and DD interactions are considered. The results are summarized in the form of stability/collapse diagrams in a respective parametric space. In particular, it is shown that the attractive DD interactions may prevent the collapse instability in the condensate with attractive contact interactions.