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Journal of Shanxi University

Dynamics of Dark Solitons in One-dimensional Bose-Einstein Condensates in An Expulsive Parabolic Potential

Lu Li

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The motion of a dark soliton in one-dimensional Bose-Einstein condensates with an expulsive parabolic potential is investigated.Furthermore,the dynamics of dark soliton and the interaction between two dark solitons are discussed in detail by numerical simulation.The results show that the motion of dark soliton is periodical,and the interaction between two dark solitons exhibits to collide each other periodically.As the separation between two dark solitons becomes shorter,the periodical colliding is shrinking and the period of the colliding action is shorter.It is meaning for us to understand the dynamics of microphysical field.

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The motion of a dark soliton in one-dimensional Bose-Einstein condensates with an expulsive parabolic potential is investigated.Furthermore,the dynamics of dark soliton and the interaction between two dark solitons are discussed in detail by numerical simulation.The results show that the motion of dark soliton is periodical,and the interaction between two dark solitons exhibits to collide each other periodically.As the separation between two dark solitons becomes shorter,the periodical colliding is shrinking and the period of the colliding action is shorter.It is meaning for us to understand the dynamics of microphysical field.
We present two families of analytical solutions of the one-dimensional nonlinear Schr\"odinger equation, which describe the dynamics of bright and dark solitons in Bose-Einstein condensates (BECs) with the time-dependent interatomic interaction in an expulsive parabolic and complex potential. We also demonstrate that the lifetime of both a bright soliton and a dark soliton in BECs can be extended by reducing both the ratio of the axial oscillation frequency to radial oscillation frequency and the loss of atoms. It is interesting that a train of bright solitons may be excited with a strong enough background. An experimental protocol is further designed for observing this phenomenon.
We present an analytical study on the dynamics of bright and dark solitons in Bose–Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross–Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton's parameters (amplitude, width, and period) can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.