Soliton dynamics for trapped Bose-Einstein condensate with higher-order interaction

Ying Wang,Shuyu Zhou

doi:10.1063/1.4999336

Abstract

We model the three-dimensional (3D) trapped Bose-Einstein condensate with the Gross-Pitaevskii equation (GPE) incorporating higher-order nonlinear interaction effects. Based on the F-expansion method and self-similar approach, we analytically derive the exact soliton solutions of the 3D GPE, identifying the oscillatory mode under certain experimental settings. The oscillatory kinetic parameter values we obtained coincide very well with those reported in previous work, which is based on the variational approach, showing the applicability of the theoretical treatment presented in this work.

Highlights

A Bose-Einstein condensate (BEC) is fascinating scenario found in the study of many intriguing physical phenomena
Our theoretical results show that the distribution width of the system oscillates periodically with the key dynamical parameters, and its period and oscillating range coincide pretty well with that reported in previous works aElectronic address: wangying@just.edu.cn bElectronic address: syz@siom.ac.cn 2158-3226/2017/7(8)/085006/7
For the system modeled by Eq (3), we will target on the typical nonlinear properties, the analytical soliton solution

Summary

INTRODUCTION

A Bose-Einstein condensate (BEC) is fascinating scenario found in the study of many intriguing physical phenomena. With the implementation of Feshbach resonance techniques, the strength and sign (+ for repulsive, for attractive interaction) of the interparticle scattering length can be tuned continuously from −∞ to +∞ such that the long pursued Bardeen-Cooper-Schrieffer (BCS)-BEC crossover is realized. This necessitates a delicate formulation of the nonlinear interaction effects in the corresponding theoretical model in the study of BEC-related physics, among which soliton-related phenomena[7,8,9] are a popular topic. THE MODIFIED GPE WITH HIGHER-ORDER INTERACTION AND THE ANALYTICAL SOLUTION FOR ITS ONE-DIMENSIONAL CASE

Formulation of the modified GPE incorporating higher order interaction

SOLITON DYNAMICS FOR THREE-DIMENSIONAL HARMONICALLY TRAPPED BEC

CONCLUSION