Bose-condensed Bright Solitons under Transverse Confinement

TL;DR

This paper studies the behavior and stability of Bose-condensed bright solitons under transverse confinement, revealing critical interaction thresholds, analyzing their dynamics, and examining their tunneling and collapse phenomena.

Contribution

It introduces an effective 1D NPSE model for accurate transverse dynamics and provides new insights into soliton stability, tunneling suppression, and collapse conditions under confinement.

Findings

Existence of a critical attractive interaction depending on confinement

Suppressed interference during tunneling compared to non-solitonic waves

Collapse occurs when density reaches a critical value, influenced by barrier scattering and collisions

Abstract

We investigate the dynamics of Bose-condensed bright solitons made of alkali-metal atoms with negative scattering length and under harmonic confinement in the transverse direction. Contrary to the 1D case, the 3D bright soliton exists only below a critical attractive interaction which depends on the extent of confinement. Such a behavior is also found in multi-soliton condensates with box boundary conditions. We obtain numerical and analytical estimates of the critical strength beyond which the solitons do not exist. By using an effective 1D nonpolynomial nonlinear Schr\"odinger equation (NPSE), which accurately takes into account the transverse dynamics of cigar-like condensates, we numerically simulate the dynamics of the "soliton train" reported in a recent experiment (Nature {\bf 417} 150 (2002)). Then, analyzing the macroscopic quantum tunneling of the bright soliton on a Gaussian barrier we find that its interference in the tunneling region is strongly suppressed with respect to non-solitonic case; moreover, the tunneling through a barrier breaks the solitonic nature of the matter wave. Finally, we show that the collapse of the soliton is induced by the scattering on the barrier or by the collision with another matter wave when the density reaches a critical value, for which we derive an accurate analytical formula.