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

arXiv:cond-mat/0605412 · Journal of Physics B Atomic Molecular and Optical Physics

Solitons in coupled atomic–molecular Bose–Einstein condensates

Bartłomiej Oleś, Krzysztof Sacha

Published Mar 5, 2007• 12 citations
arXivHTMLPDF

Abstract

We consider a coupled atomic–molecular Bose–Einstein condensate system in a quasi-one-dimensional trap. In the vicinity of a Feshbach resonance the system can reveal parametric soliton-like behaviour. We analyse bright soliton, soliton train and dark soliton solutions for the system in the trap and in the presence of the interactions between particles and find the range of the system parameters where the soliton states can be experimentally prepared and detected.

DOI
10.1088/0953-4075/40/6/002

Related papers

Dark-bright solitons and their lattices in atomic Bose-Einstein condensates

D. Yan, F. Tsitoura, P. G. Kevrekidis +1 more

In the present contribution, we explore a host of different stationary states, namely dark-bright solitons and their lattices, that arise in the context of multicomponent atomic Bose-Einstein condensates. The latter are modeled by systems of coupled Gross-Pitaevskii equations with general interaction (nonlinearity) coefficients ${g}_{ij}$. It is found that in some particular parameter ranges such solutions can be obtained in analytical form, however, numerically they are computed as existing in a far wider parametric range. Many features of the solutions under study, such as their analytical form without the trap or the stability and dynamical properties of one dark-bright soliton even in the presence of the trap are obtained analytically and corroborated numerically. Additional features, such as the stability of soliton lattice homogeneous states or their existence and stability in the presence of the trap, are examined numerically.

arXiv:1402.1895•Physical Review A•Feb 20, 2015•63 citations

Complex solitons with power law behaviour in Bose-Einstein condensates near Feshbach resonance

Utpal Roy, Rajneesh Atre, C. Sudheesh +2 more

Complex, localized stable solitons, characterized by a power law behaviour, are found for a quasi-one-dimensional Bose-Einstein condensate near Feshbach resonance. Both dark and bright solitons can be excited in the experimentally allowed parameter domain, when two and three-body interactions are respectively repulsive and attractive. These solutions are obtained for non-zero chemical potential, unlike their unstable real counterparts which exist in the limit of vanishing $μ$. The dark solitons travel with constant speed, which is quite different from the Lieb mode, where profiles with different speeds, bounded above by sound velocity can exist for specified interaction strengths.

arXiv:0708.3646•Aug 27, 2007•0 citations

Multiple dark-bright solitons in atomic Bose-Einstein condensates

D. Yan, JiaJia Chang, Chris Hamner +6 more

Motivated by recent experimental results, we present a systematic theoretical analysis of dark-bright-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component Bose-Einstein condensates. We study analytically the interactions between two dark-bright solitons in a homogeneous condensate and then extend our considerations to the presence of the trap. We illustrate the existence of robust stationary dark-bright-soliton ``molecules,'' composed of two or more solitons, which are formed due to the competition of the interaction forces between the dark- and bright-soliton components and the trap force. Our analysis is based on an effective equation of motion, derived for the distance between two dark-bright solitons. This equation provides equilibrium positions and characteristic oscillation frequencies of the solitons, which are found to be in good agreement with the eigenfrequencies of the anomalous modes of the system.

arXiv:1104.4359•Physical Review A•Nov 28, 2011•102 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

Dynamics of atomic and molecular solitary waves inatom-molecular hybrid Bose-Einstein condensates coupled by Magnetic Feshbach Resonance: Role of induced decays of Feshbach Molecules

Krishna Rai Dastidar, Deb Shankar Ray

Dynamics of atomic and molecular bright solitons in a hybrid atom-molecular BEC (Bose Einstein Condensate) system of 85Rb coupled through Magnetic Feshbach Resonance (MFR) has been investigated. By solving the time independent atom-molecular coupled equations, the initial atomic and molecular wavefunctions were obtained and the dynamics of the initial atomic and molecular waves in a spherical one-dimensional trap were studied by solving the time-dependent atom-molecular coupled equations. During evolution two types of induced or stimulated decays of the feshbach molecules were switched on. These two types of stimulated decays of the feshbach molecules to the two-atom continuum and to the bound level of the lowest hyperfinee state of the molecule were induced by laser or Radio Frequency fields. Hence the strength of these two induced decays can be controlled by varying the laser or RF field parameters e.g. intensity, detuning etc. It is found that depending on the relative strength of these two types of stimulated or induced decays initial atomic and molecular waves assume solitonic nature as bright solitons during evolution and the stability of these solitonic waves can be achieved by controlling the relative strength of induced decays in two different channels. It is shown that these two induced decays lead to the formation of stable atomic and molecular solitons by suppressing the initial oscillations and instability in the atom-molecular coupled system of 85Rb atoms.

arXiv:1602.08992•Feb 29, 2016•0 citations

Bright Soliton Trains of Trapped Bose-Einstein Condensates

Usama Al Khawaja, Henk T. C. Stoof, Randall G. Hulet +2 more

We variationally determine the dynamics of bright soliton trains composed of harmonically trapped Bose-Einstein condensates with attractive interatomic interactions. In particular, we obtain the interaction potential between two solitons. We also discuss the formation of soliton trains due to the quantum mechanical phase fluctuations of a one-dimensional condensate.

arXiv:cond-mat/0206184•Physical Review Letters•Oct 29, 2002•219 citations
We consider a coupled atomic–molecular Bose–Einstein condensate system in a quasi-one-dimensional trap. In the vicinity of a Feshbach resonance the system can reveal parametric soliton-like behaviour. We analyse bright soliton, soliton train and dark soliton solutions for the system in the trap and in the presence of the interactions between particles and find the range of the system parameters where the soliton states can be experimentally prepared and detected.
In the present contribution, we explore a host of different stationary states, namely dark-bright solitons and their lattices, that arise in the context of multicomponent atomic Bose-Einstein condensates. The latter are modeled by systems of coupled Gross-Pitaevskii equations with general interaction (nonlinearity) coefficients gij{g}_{ij}gij​. It is found that in some particular parameter ranges such solutions can be obtained in analytical form, however, numerically they are computed as existing in a far wider parametric range. Many features of the solutions under study, such as their analytical form without the trap or the stability and dynamical properties of one dark-bright soliton even in the presence of the trap are obtained analytically and corroborated numerically. Additional features, such as the stability of soliton lattice homogeneous states or their existence and stability in the presence of the trap, are examined numerically.
Complex, localized stable solitons, characterized by a power law behaviour, are found for a quasi-one-dimensional Bose-Einstein condensate near Feshbach resonance. Both dark and bright solitons can be excited in the experimentally allowed parameter domain, when two and three-body interactions are respectively repulsive and attractive. These solutions are obtained for non-zero chemical potential, unlike their unstable real counterparts which exist in the limit of vanishing μμμ. The dark solitons travel with constant speed, which is quite different from the Lieb mode, where profiles with different speeds, bounded above by sound velocity can exist for specified interaction strengths.
Motivated by recent experimental results, we present a systematic theoretical analysis of dark-bright-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component Bose-Einstein condensates. We study analytically the interactions between two dark-bright solitons in a homogeneous condensate and then extend our considerations to the presence of the trap. We illustrate the existence of robust stationary dark-bright-soliton ``molecules,'' composed of two or more solitons, which are formed due to the competition of the interaction forces between the dark- and bright-soliton components and the trap force. Our analysis is based on an effective equation of motion, derived for the distance between two dark-bright solitons. This equation provides equilibrium positions and characteristic oscillation frequencies of the solitons, which are found to be in good agreement with the eigenfrequencies of the anomalous modes of the system.
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.
Dynamics of atomic and molecular bright solitons in a hybrid atom-molecular BEC (Bose Einstein Condensate) system of 85Rb coupled through Magnetic Feshbach Resonance (MFR) has been investigated. By solving the time independent atom-molecular coupled equations, the initial atomic and molecular wavefunctions were obtained and the dynamics of the initial atomic and molecular waves in a spherical one-dimensional trap were studied by solving the time-dependent atom-molecular coupled equations. During evolution two types of induced or stimulated decays of the feshbach molecules were switched on. These two types of stimulated decays of the feshbach molecules to the two-atom continuum and to the bound level of the lowest hyperfinee state of the molecule were induced by laser or Radio Frequency fields. Hence the strength of these two induced decays can be controlled by varying the laser or RF field parameters e.g. intensity, detuning etc. It is found that depending on the relative strength of these two types of stimulated or induced decays initial atomic and molecular waves assume solitonic nature as bright solitons during evolution and the stability of these solitonic waves can be achieved by controlling the relative strength of induced decays in two different channels. It is shown that these two induced decays lead to the formation of stable atomic and molecular solitons by suppressing the initial oscillations and instability in the atom-molecular coupled system of 85Rb atoms.