Nonautonomous Bright and Dark Solitons of Bose-Einstein Condensates with Feshbach-Managed Time-Dependent Scattering Length

TL;DR

This paper derives and analyzes nonautonomous bright and dark soliton solutions in Bose-Einstein condensates with time-dependent scattering length, demonstrating control over soliton properties via Feshbach resonance.

Contribution

It introduces new analytical solutions for nonautonomous solitons in BECs with variable scattering length and explores their properties and stability.

Findings

Soliton amplitude, width, and velocity can be manipulated by Feshbach resonance.

Total particle number is conserved despite soliton parameter changes.

Pattern formation results from superposition of dark and bright solitary waves.

Abstract

We present a family of nonautonomous bright and dark soliton solutions of Bose-Einstein condensates with the time-dependent scattering length in an expulsive parabolic potential. These solutions show that the amplitude, width, and velocity of soliton can be manipulated by adjusting the atomic scattering length via Feshbach resonance. For the cases of both attractive and repulsive interaction, the total particles number is a conservation quantity, but the peak (dip) density can be controlled by the Feshbach resonance parameter. Especially, we investigate the modulation instability process in uniform Bose-Einstein condensates with attractive interaction and nonvanishing background, and clarify that the procedure of pattern formation is in fact the superposition of the perturbed dark and bright solitary wave. At last, we give the analytical expressions of nonautonomous dark one- and two-soliton solutions for repulsive interaction, and investigate their properties analytically.