Dynamics of a Bright Soliton in Bose-Einstein condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential

TL;DR

This paper derives exact solutions for bright solitons in Bose-Einstein condensates with time-varying interactions, showing how solitons can be compressed and remain dynamically stable under certain conditions.

Contribution

It provides new analytical solutions for soliton dynamics in BECs with time-dependent scattering length in an expulsive potential, aiding experimental and theoretical studies.

Findings

Bright solitons can be compressed into high-density states.

The number of atoms in the soliton remains dynamically stable.

A periodic atomic exchange occurs between the soliton and background.

Abstract

We present a family of exact solutions of one-dimensional nonlinear Schr\"odinger equation, which describe the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under the safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background.