Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Vector solitons in two-component Bose-Einstein condensates with tunable interactions and harmonic potential

Xiao-Fei Zhang, Xinghua Hu, Xunxu Liu, Weixi Liu

Published Mar 31, 2009• 118 citations
Publisher

Abstract

We present a family of exact vector-soliton solutions for the coupled nonlinear Schr\"odinger equations with tunable interactions and harmonic potential, and then apply the model to investigate the dynamics of solitons and collisions between two orthogonal solitons in the case with equal interaction parameters. Our results show that the exact vector-soliton solutions can be obtained with arbitrary tunable interactions as long as a proper harmonic potential is applied. The dynamics of solitons can be controlled by the Feshbach resonance and the collisions are essentially elastic and do not depend on the initial conditions.

DOI
10.1103/physreva.79.033630

Related papers

Feshbach resonance management of vector solitons in two-component Bose—Einstein condensates

Qiang Wang, Lin Wen, Zai-Dong Li

We consider two coupled Gross—Pitaevskii equations describing a two-component Bose—Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential, and investigate the dynamics of vector solitons. By using a direct method, we construct a novel family of vector soliton solutions, which are the linear combination between dark and bright solitons in each component. Our results show that due to the superposition between dark and bright solitons, such vector solitons possess many novel and interesting properties. The dynamics of vector solitons can be controlled by the Feshbach resonance technique, and the vector solitons can keep the dynamic stability against the variation of the scattering length.

Chinese Physics B•Aug 1, 2012•8 citations

Stability properties of vector solitons in two-component Bose—Einstein condensates with tunable interactions

Xiao-Fei Zhang, Pei Zhang, Wan-Quan He +1 more

By using a unified theory of the formation of various types of vector-solitons in two-component Bose—Einstein condensates with tunable interactions, we obtain a family of exact vector-soliton solutions for the coupled nonlinear Schrödinger equations. Moreover, the Bogoliubov equation shows that there exists stable dark soliton in specific situations. Our results open up new ways in considerable experimental interest for the quantum control of multi-component Bose—Einstein condensates.

Chinese Physics B•Feb 1, 2011•15 citations

Dynamics of vector solitons in two-component Bose–Einstein condensates with time-dependent interactions and harmonic potential

Zheng Zhou, Yu Hui-You, Yan Jia-Ren

We present two kinds of exact vector-soliton solutions for coupled nonlinear Schrödinger equations with time-varying interactions and time-varying harmonic potential. Using the variational approach, we investigate the dynamics of the vector solitons. It is found that the two bright solitons oscillate about slightly and pass through each other around the equilibration state which means that they are stable under our model. At the same time, we obtain the opposite situation for dark-dark solitons.

Chinese Physics B•Jan 1, 2010•11 citations

Dynamics of Bose-Einstein condensates near Feshbach resonance in external potential

Xiao-Fei Zhang, Xinghua Hu, Deng‐Shan Wang +2 more

We review our recent theoretical advances in the dynamics of Bose-Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross-Pitaevskii equations are developed to study the nonlinear dynamics of Bose-Einstein condensates. Analytically, we present the integrable conditions for the Gross-Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose-Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose-Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose-Einstein condensates.

Frontiers of Physics•Nov 13, 2010•11 citations

Controlling soliton interactions in Bose-Einstein condensates by synchronizing the Feshbach resonance and harmonic trap

Xiao-Fei Zhang, Qin Yang, Jie-Fang Zhang +2 more

We present how to control interactions between solitons, either bright or dark, in Bose-Einstein condensates by synchronizing Feshbach resonance and harmonic trap. Our results show that as long as the scattering length is to be modulated in time via a changing magnetic field near the Feshbach resonance, and the harmonic trapping frequencies are also modulated in time, exact solutions of the one-dimensional nonlinear Schr\"odinger equation can be found in a general closed form, and interactions between two solitons are modulated in detail in currently experimental conditions. We also propose experimental protocols to observe the phenomena such as fusion, fission, warp, oscillation, elastic collision in future experiments.

arXiv:0808.3831•Physical Review A•Feb 11, 2008•100 citations

Matter-Wave Solitons in Two-Component Bose—Einstein Condensates with Tunable Interactions and Time Varying Potential

Hengnong Xuan, Miao Zuo

We present three families of exact matter-wave soliton solutions for an effective one-dimension two-component Bose—Einstein condensates (BECs) with tunable interactions, harmonic potential and gain or loss term. We investigate the dynamics of bright-bright solitons, bright-dark solitons and dark-dark solitons for the time-dependent expulsive harmonic trap potential, periodically modulated harmonic trap potential, and kinklike modulated harmonic trap potential. Through the Feshbach resonance, these dynamics can be realized in experiments by suitable control of time-dependent trap parameters, atomic interactions, and interaction with thermal cloud.

Communications in Theoretical Physics•Dec 1, 2011•10 citations
We present a family of exact vector-soliton solutions for the coupled nonlinear Schr"odinger equations with tunable interactions and harmonic potential, and then apply the model to investigate the dynamics of solitons and collisions between two orthogonal solitons in the case with equal interaction parameters. Our results show that the exact vector-soliton solutions can be obtained with arbitrary tunable interactions as long as a proper harmonic potential is applied. The dynamics of solitons can be controlled by the Feshbach resonance and the collisions are essentially elastic and do not depend on the initial conditions.
We consider two coupled Gross—Pitaevskii equations describing a two-component Bose—Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential, and investigate the dynamics of vector solitons. By using a direct method, we construct a novel family of vector soliton solutions, which are the linear combination between dark and bright solitons in each component. Our results show that due to the superposition between dark and bright solitons, such vector solitons possess many novel and interesting properties. The dynamics of vector solitons can be controlled by the Feshbach resonance technique, and the vector solitons can keep the dynamic stability against the variation of the scattering length.
We present two kinds of exact vector-soliton solutions for coupled nonlinear Schrödinger equations with time-varying interactions and time-varying harmonic potential. Using the variational approach, we investigate the dynamics of the vector solitons. It is found that the two bright solitons oscillate about slightly and pass through each other around the equilibration state which means that they are stable under our model. At the same time, we obtain the opposite situation for dark-dark solitons.
We review our recent theoretical advances in the dynamics of Bose-Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross-Pitaevskii equations are developed to study the nonlinear dynamics of Bose-Einstein condensates. Analytically, we present the integrable conditions for the Gross-Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose-Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose-Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose-Einstein condensates.
We present how to control interactions between solitons, either bright or dark, in Bose-Einstein condensates by synchronizing Feshbach resonance and harmonic trap. Our results show that as long as the scattering length is to be modulated in time via a changing magnetic field near the Feshbach resonance, and the harmonic trapping frequencies are also modulated in time, exact solutions of the one-dimensional nonlinear Schr\"odinger equation can be found in a general closed form, and interactions between two solitons are modulated in detail in currently experimental conditions. We also propose experimental protocols to observe the phenomena such as fusion, fission, warp, oscillation, elastic collision in future experiments.
We present three families of exact matter-wave soliton solutions for an effective one-dimension two-component Bose—Einstein condensates (BECs) with tunable interactions, harmonic potential and gain or loss term. We investigate the dynamics of bright-bright solitons, bright-dark solitons and dark-dark solitons for the time-dependent expulsive harmonic trap potential, periodically modulated harmonic trap potential, and kinklike modulated harmonic trap potential. Through the Feshbach resonance, these dynamics can be realized in experiments by suitable control of time-dependent trap parameters, atomic interactions, and interaction with thermal cloud.