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

Stability of static solitonic excitations of two-component Bose-Einstein condensates in finite range of interspecies scattering length a12

Dániel Schumayer, Barnabás Apagyi

Published Apr 27, 2004• 27 citations
Publisher

Abstract

A simple method is presented to analyze the stability of static solitonic excitations of two-component Bose-Einstein condensates described within the Gross-Pitaevskii approximation. First, a quick assessment can be made for the values of interspecies scattering length ${a}_{12}$ allowing existence of static solitons independent of the particle numbers ${N}_{1}$ and ${N}_{2}$. If the true value of ${a}_{12}$ falls into that acceptable interval, then a fine tuning is performed to get the ratio ${N}_{2}∕{N}_{1}$ at which the static solitons may be created. The technique is illustrated for the lithium-rubidium and sodium-rubidium condensates.

DOI
10.1103/physreva.69.043620

Related papers

Effect of scattering lengths on the dynamics of a two-component Bose-Einstein condensate

Gábor Csire, Dániel Schumayer, Barnabás Apagyi

We examine the effect of the intra- and interspecies scattering lengths on the dynamics of a two-component Bose-Einstein condensate, particularly focusing on the existence and stability of solitonic excitations. For each type of possible soliton pairs, stability ranges are presented in tabulated form. We also compare the numerically established stability of bright-bright, bright-dark, and dark-dark solitons with our analytical prediction and with that of Painlev\'e analysis of the dynamical equation. We demonstrate that tuning the interspecies scattering length away from the predicted value (keeping the intraspecies coupling fixed) breaks the stability of the soliton pairs.

arXiv:1009.2122•Physical Review A•Dec 7, 2010•20 citations

Stability of a Two-Component Bose-Einstein Condensate

Hirofumi Morise, Takeya Tsurumi, Miki Wadati

The stability of a two-component Bose-Einstein condensate is studied. Using the variational method, we investigate the stable and unstable conditions as functions of the particle numbers and the s-wave scattering lengths. We find that interaction between the different species of atoms (simply, interspecies interaction) has significant effects on the stability of each condensate.

Journal of the Physical Society of Japan•Jun 15, 1999•7 citations

“Stability Signature” in Two-Species Dilute Bose-Einstein Condensates

C. K. Law, Han Pu, N. P. Bigelow +1 more

We identify an eigenvalue associated with a dilute two-species Bose-Einstein condensate as the determiner of condensate stability. It plays the same role as the sign of scattering length in a one-species condensate. We predict that there is a range of interspecies interaction strength in which a sodium-rubidium mixture can be stable in a harmonic trap.

Physical Review Letters•Oct 27, 1997•115 citations

Controlling the Collision Between Two Solitons in a Two-Component Condensate by Interspecies Interactions

Zhiqiang Zhang, Denglong Wang, Xiao‐Qing Luo +1 more

We present a family of the solutions of two-component Bose—Einstein condensates with time-dependent scattering length by means of multiple-scale method. Our numerical calculations show that the collision properties (the position, the time, and the frequency of the collision) between two solitons can be controlled by the time-dependent interspecies scattering length. Meanwhile, we also find that the amplitude of the solitons is close related to the time-dependent interspecies scattering length.

Communications in Theoretical Physics•Sep 1, 2011•1 citation

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 and collective excitations of a two-component Bose-Einstein condensed gas: A moment approach

Thomas Busch, J. I. Cirac, Víctor M. Pérez‐García +1 more

The dynamics of a two-component dilute Bose-Einstein gas of atoms at zero temperature is described in the mean-field approximation by a two-component Gross-Pitaevskii equation. We solve this equation assuming a Gaussian shape for the wave function, where the free parameters of the trial wave function are determined using a moment method. We derive equilibrium states and the phase diagrams for the stability for positive and negative $s$-wave scattering lengths, and obtain the low-energy excitation frequencies corresponding to the collective motion of the two Bose-Einstein condensates.

arXiv:cond-mat/9705008•Physical Review A•Oct 1, 1997•120 citations
A simple method is presented to analyze the stability of static solitonic excitations of two-component Bose-Einstein condensates described within the Gross-Pitaevskii approximation. First, a quick assessment can be made for the values of interspecies scattering length a12{a}_{12}a12​ allowing existence of static solitons independent of the particle numbers N1{N}_{1}N1​ and N2{N}_{2}N2​. If the true value of a12{a}_{12}a12​ falls into that acceptable interval, then a fine tuning is performed to get the ratio N2∕N1{N}_{2}∕{N}_{1}N2​∕N1​ at which the static solitons may be created. The technique is illustrated for the lithium-rubidium and sodium-rubidium condensates.
We examine the effect of the intra- and interspecies scattering lengths on the dynamics of a two-component Bose-Einstein condensate, particularly focusing on the existence and stability of solitonic excitations. For each type of possible soliton pairs, stability ranges are presented in tabulated form. We also compare the numerically established stability of bright-bright, bright-dark, and dark-dark solitons with our analytical prediction and with that of Painlev\'e analysis of the dynamical equation. We demonstrate that tuning the interspecies scattering length away from the predicted value (keeping the intraspecies coupling fixed) breaks the stability of the soliton pairs.
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.
The dynamics of a two-component dilute Bose-Einstein gas of atoms at zero temperature is described in the mean-field approximation by a two-component Gross-Pitaevskii equation. We solve this equation assuming a Gaussian shape for the wave function, where the free parameters of the trial wave function are determined using a moment method. We derive equilibrium states and the phase diagrams for the stability for positive and negative sss-wave scattering lengths, and obtain the low-energy excitation frequencies corresponding to the collective motion of the two Bose-Einstein condensates.