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

Journal of the Physical Society of Japan

Phase Engineering and Solitons of Bose–Einstein Condensates with Two- and Three-Body Interactions

Vaduganathan Ramesh Kumar, Ramaswamy Radha, Miki Wadati

Published Jul 15, 2010• 49 citations
Publisher

Abstract

We introduce a phase imprint into the macroscopic order parameter governing the dynamics of Bose–Einstein condensates with attractive two-body interactions described by a cubic Gross–Pitaevskii (GP) equation and then engineer the imprinted phase suitably to generate the modified GP equation. The modified GP equation describes the dynamics of condensates with both two- (attractive) and three-body (attractive and repulsive) interactions in an expulsive harmonic trap. Employing gauge transformation approach, we then construct bright solitons of the modified GP equation. We observe that the attractive three-body interactions introduce an additional nontrivial phase in the matter wave solitons arising due to attractive two-body interactions without changing their density while the repulsive three-body interactions enormously increase the density of the condensates without causing any change in the phase of the solitons originating from attractive two-body interactions.

DOI
10.1143/jpsj.79.074005

Related papers

Impact of Three-Body Interactions and Nonlinear Dispersion on the Dynamics of Bose-Einstein Condensates with Time-Dependent Scattering Length in a Harmonic Potential

Emmanuel Kengne, Ahmed Lakhssassi

A one-dimensional (1D) Gross-Pitaevskii (GP) equation which governs the dynamics of Bose-Einstein condensates (BECs) with time-dependent scattering length in a harmonic potential is considered. Through a modified phase imprint transformation into the macroscopic order parameter, we suitably generate a derivative cubic-quintic Gross-Pitaevskii (DCQ-GP) equation that describes the dynamics of condensates in the harmonic potential for both twoand three-body interatomic interactions in the presence of nonlinear dispersion. Employing a modified lens-type transformation, we reduce the DCQ-GP equation into a derivative cubic-quintic Ginzburg-Landau (DCQ-GL) equation that allows us to investigate the modulational instability (MI) of the system and study, through the analytical exact solutions of the considered 1D GP equation, the effects of the three-body interactions and nonlinear dispersion on the dynamics of the BECs. We observe that for BECs with repulsive two-body interatomic interactions, the attractive three-body interactions and the nonlinear dispersion have opposite effects on the condensate: (i) The attractive three-body interactions enhance the instability, while the nonlinear dispersion softens the instability of the system; (ii) the attractive three-body interactions contributes to the ejections of atoms from the condensates while the nonlinear dispersion contributes to the accumulation of atoms in the condensates; (iii) the attractive three-body interactions contributes to the broadening of the matter wave solitons, while the nonlinear dispersion contributes to the compression of the matter wave solitons.

Chinese Journal of Physics•Feb 1, 2015•4 citations

THREE-BODY INTERACTIONS BEYOND THE GROSS–PITAEVSKII EQUATION AND MODULATIONAL INSTABILITY OF BOSE–EINSTEIN CONDENSATES

D. Belobo Belobo, G. H. Ben-Bolie, Timoléon Crépin Kofané

Beyond the mean-field theory, a new model of the Gross–Pitaevskii equation (GPE) that describes the dynamics of Bose–Einstein condensates (BECs) is derived using an appropriate phase-imprint on the old wavefunction. This modified version of the GPE in addition to the two-body interactions term, also takes into account effects of the three-body interactions. The three-body interactions consist of a quintic term and the delayed nonlinear response of the condensate system term. Then, the modulational instability (MI) of the new GPE confined in an attractive harmonic potential is investigated. The analytical study shows that the three-body interactions destabilize more the condensate system while the external potential alleviates the instability. Numerical results confirm the theoretical predictions. Further numerical investigations of the behavior of solitons reveal that the three-body interactions enhance the appearance of solitons, increase the number of solitons generated and deeply change the lifetime of solitons. Moreover, the external potential delays the appearance of solitons. Besides, a new initial condition is introduced which enables to increase the number of solitons created and deeply affects the trail of chains of solitons generated. Moreover, the MI of a condensate without the external potential, and in a repulsive potential is also investigated.

International Journal of Modern Physics B•Nov 8, 2012•4 citations

Phase engineering, modulational instability, and solitons of Gross–Pitaevskii-type equations in 1+1 dimensions

Emmanuel Kengne, Ahmed Lakhssassi, Wu‐Ming Liu +1 more

Motivated by recent proposals of "collisionally inhomogeneous" Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we introduce a phase imprint into the macroscopic order parameter governing the dynamics of BECs with spatiotemporal varying scattering length described by a cubic Gross-Pitaevskii (GP) equation and then suitably engineer the imprinted phase to generate the modified GP equation, also called the cubic derivative nonlinear Schrödinger (NLS) equation. This equation describes the dynamics of condensates with two-body (attractive and repulsive) interactions in a time-varying quadratic external potential. We then carry out a theoretical analysis which invokes a lens-type transformation that converts the cubic derivative NLS equation into a modified NLS equation with only explicit temporal dependence. Our analysis suggests a particular interest in a specific time-varying potential with the strength of the magnetic trap ~1/(t+t(*))(2). For a time-varying quadratic external potential of this kind, an explicit expression for the growth rate of a purely growing modulational instability is presented and analyzed. We point out the effect of the imprint parameter and the parameter t(*) on the instability growth rate, as well as on the solitary waves of the BECs.

Physical Review E•Feb 22, 2013•29 citations

Matter-wave solitons of Bose–Einstein condensates with time-dependent complex potentials

Emmanuel Kengne, Ahmed Lakhssassi

To analytically investigate the matter-wave solitons of Bose–Einstein condensates (BECs) in time-dependent complex potential, we consider a cubic-quintic Gross–Pitaevskii (GP) equation with distributed coefficients and a dissipative term. By introducing a suitable ansatz, we establish the criterion of the modulational instability (MI) of the system and present an explicit expression for the growth rate of a purely growing MI. Effects of the parabolic background potential, as well as of the linear potential, the gain/loss parameter, and the two- and three-body interatomic interactions on the MI are investigated. We show how the feeding/loss parameter can be well used to control the instability of the system. The analytical resolution of the considered GP equation leads to exact bright, dark and kink solitary wave solutions which are used to investigate analytically the dynamics of matter-wave solitons in BECs under consideration. These analytical investigations show that the amplitude and the motion of bright, dark and kink solitary waves depend on the strengths of the two- and three-body interatomic interactions, as well as on the strengths of the external trapping potential and the parameter of the gain/loss of atoms in the condensate.

International Journal of Modern Physics B•Apr 27, 2018•3 citations

Dynamics and Matter-Wave Solitons in Bose-Einstein Condensates with Two- and Three-Body Interactions

Jing Chen, Jie Yang, Lu Zhang

By means of similarity transformation, this paper proposes the matter-wave soliton solutions and dynamics of the variable coefficient cubic-quintic nonlinear Schrödinger equation arising from Bose-Einstein condensates with time-dependent two- and three-body interactions. It is found that, under the effect of time-dependent two- and three-body interaction and harmonic potential with time-dependent frequency, the density of atom condensates will gradually diminish and finally collapse.

Advances in Condensed Matter Physics•Jan 1, 2014•4 citations

Spatial solitons of trapped atomic Bose-Einstein condensate

Xu SiLIiu, Chen ShunFang

We present two families analytical solutions to the extended Gross-Pitaevskii equation (GPE), which describe the dynamics of bright and dark solitons in Bose-Einstein condensations(BECs) with varying coefficients of two and three-body interactions in a parabolic and complex potential. The properties of the dynamical evolutions of the bright and dark matter-wave solitons are investigated. It is interesting that the matter-wave can be controlled by applying the external magnetic field and a background.

International Conference on Consumer Electronics, Communications and Networks (CECNet)•Apr 1, 2011•0 citations
We introduce a phase imprint into the macroscopic order parameter governing the dynamics of Bose–Einstein condensates with attractive two-body interactions described by a cubic Gross–Pitaevskii (GP) equation and then engineer the imprinted phase suitably to generate the modified GP equation. The modified GP equation describes the dynamics of condensates with both two- (attractive) and three-body (attractive and repulsive) interactions in an expulsive harmonic trap. Employing gauge transformation approach, we then construct bright solitons of the modified GP equation. We observe that the attractive three-body interactions introduce an additional nontrivial phase in the matter wave solitons arising due to attractive two-body interactions without changing their density while the repulsive three-body interactions enormously increase the density of the condensates without causing any change in the phase of the solitons originating from attractive two-body interactions.
A one-dimensional (1D) Gross-Pitaevskii (GP) equation which governs the dynamics of Bose-Einstein condensates (BECs) with time-dependent scattering length in a harmonic potential is considered. Through a modified phase imprint transformation into the macroscopic order parameter, we suitably generate a derivative cubic-quintic Gross-Pitaevskii (DCQ-GP) equation that describes the dynamics of condensates in the harmonic potential for both twoand three-body interatomic interactions in the presence of nonlinear dispersion. Employing a modified lens-type transformation, we reduce the DCQ-GP equation into a derivative cubic-quintic Ginzburg-Landau (DCQ-GL) equation that allows us to investigate the modulational instability (MI) of the system and study, through the analytical exact solutions of the considered 1D GP equation, the effects of the three-body interactions and nonlinear dispersion on the dynamics of the BECs. We observe that for BECs with repulsive two-body interatomic interactions, the attractive three-body interactions and the nonlinear dispersion have opposite effects on the condensate: (i) The attractive three-body interactions enhance the instability, while the nonlinear dispersion softens the instability of the system; (ii) the attractive three-body interactions contributes to the ejections of atoms from the condensates while the nonlinear dispersion contributes to the accumulation of atoms in the condensates; (iii) the attractive three-body interactions contributes to the broadening of the matter wave solitons, while the nonlinear dispersion contributes to the compression of the matter wave solitons.
Beyond the mean-field theory, a new model of the Gross–Pitaevskii equation (GPE) that describes the dynamics of Bose–Einstein condensates (BECs) is derived using an appropriate phase-imprint on the old wavefunction. This modified version of the GPE in addition to the two-body interactions term, also takes into account effects of the three-body interactions. The three-body interactions consist of a quintic term and the delayed nonlinear response of the condensate system term. Then, the modulational instability (MI) of the new GPE confined in an attractive harmonic potential is investigated. The analytical study shows that the three-body interactions destabilize more the condensate system while the external potential alleviates the instability. Numerical results confirm the theoretical predictions. Further numerical investigations of the behavior of solitons reveal that the three-body interactions enhance the appearance of solitons, increase the number of solitons generated and deeply change the lifetime of solitons. Moreover, the external potential delays the appearance of solitons. Besides, a new initial condition is introduced which enables to increase the number of solitons created and deeply affects the trail of chains of solitons generated. Moreover, the MI of a condensate without the external potential, and in a repulsive potential is also investigated.
Motivated by recent proposals of "collisionally inhomogeneous" Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we introduce a phase imprint into the macroscopic order parameter governing the dynamics of BECs with spatiotemporal varying scattering length described by a cubic Gross-Pitaevskii (GP) equation and then suitably engineer the imprinted phase to generate the modified GP equation, also called the cubic derivative nonlinear Schrödinger (NLS) equation. This equation describes the dynamics of condensates with two-body (attractive and repulsive) interactions in a time-varying quadratic external potential. We then carry out a theoretical analysis which invokes a lens-type transformation that converts the cubic derivative NLS equation into a modified NLS equation with only explicit temporal dependence. Our analysis suggests a particular interest in a specific time-varying potential with the strength of the magnetic trap ~1/(t+t(*))(2). For a time-varying quadratic external potential of this kind, an explicit expression for the growth rate of a purely growing modulational instability is presented and analyzed. We point out the effect of the imprint parameter and the parameter t(*) on the instability growth rate, as well as on the solitary waves of the BECs.
To analytically investigate the matter-wave solitons of Bose–Einstein condensates (BECs) in time-dependent complex potential, we consider a cubic-quintic Gross–Pitaevskii (GP) equation with distributed coefficients and a dissipative term. By introducing a suitable ansatz, we establish the criterion of the modulational instability (MI) of the system and present an explicit expression for the growth rate of a purely growing MI. Effects of the parabolic background potential, as well as of the linear potential, the gain/loss parameter, and the two- and three-body interatomic interactions on the MI are investigated. We show how the feeding/loss parameter can be well used to control the instability of the system. The analytical resolution of the considered GP equation leads to exact bright, dark and kink solitary wave solutions which are used to investigate analytically the dynamics of matter-wave solitons in BECs under consideration. These analytical investigations show that the amplitude and the motion of bright, dark and kink solitary waves depend on the strengths of the two- and three-body interatomic interactions, as well as on the strengths of the external trapping potential and the parameter of the gain/loss of atoms in the condensate.
We present two families analytical solutions to the extended Gross-Pitaevskii equation (GPE), which describe the dynamics of bright and dark solitons in Bose-Einstein condensations(BECs) with varying coefficients of two and three-body interactions in a parabolic and complex potential. The properties of the dynamical evolutions of the bright and dark matter-wave solitons are investigated. It is interesting that the matter-wave can be controlled by applying the external magnetic field and a background.