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:0912.2483 · Physical Review A

Solitary waves in mixtures of Bose gases confined in annular traps

J. Smyrnakis, Manolis Magiropoulos, G. M. Kavoulakis, Andrew David Jackson

Published Jun 1, 2010• 12 citations
arXivHTMLPDF

Abstract

A two-component Bose-Einstein condensate that is confined in a one-dimensional ring potential supports solitary-wave solutions, which we evaluate analytically in the limit of a large ring. The derived solutions are shown to be unique. The corresponding dispersion relation that generalizes the case of a single-component system shows interesting features.

DOI
10.1103/physreva.81.063601

Related papers

Excitation spectrum of a two-component Bose–Einstein condensate in a ring potential

J Smyrnakis, M Magiropoulos, A D Jackson +1 more

A mixture of two distinguishable Bose–Einstein condensates confined in a ring potential has numerous interesting properties under rotational and solitary-wave excitation. The lowest energy states for a fixed angular momentum coincide with a family of solitary-wave solutions. In the limit of weak interactions, exact diagonalization of the many-body Hamiltonian is possible and permits evaluation of the complete excitation spectrum of the system.

arXiv:1203.2020•Journal of Physics B Atomic Molecular and Optical Physics•Nov 16, 2012•5 citations

Solitary Wave Complexes in Two-Component Condensates

Natalia G. Berloff

Axisymmetric three-dimensional solitary waves in uniform two-component mixture Bose-Einstein condensates are obtained as solutions of the coupled Gross-Pitaevskii equations with equal intracomponent but varying intercomponent interaction strengths. Several families of solitary wave complexes are found: (1) vortex rings of various radii in each of the components; (2) a vortex ring in one component coupled to a rarefaction solitary wave of the other component; (3) two coupled rarefaction waves; (4) either a vortex ring or a rarefaction pulse coupled to a localized disturbance of a very low momentum. The continuous families of such waves are shown in the momentum-energy plane for various values of the interaction strengths and the relative differences between the chemical potentials of two components. Solitary wave formation, their stability, and solitary wave complexes in two dimensions are discussed.

arXiv:cond-mat/0412099•Physical Review Letters•Mar 28, 2005•45 citations

Systematic solitary waves from their linear limits in two-component Bose–Einstein condensates with unequal dispersion coefficients

Wenlong Wang

Abstract We systematically construct vector solitary waves in harmonically trapped one-dimensional two-component Bose–Einstein condensates with unequal dispersion coefficients by a numerical continuation in chemical potentials from the respective analytic low-density linear limits to the high-density nonlinear Thomas-Fermi regime. The main feature of the linear states herein is that the component with the larger quantum number has instead a smaller linear eigenenergy, enabled by suitable unequal dispersion coefficients, leading to new series of solutions compared with the states similarly obtained in the equal dispersion setting. Particularly, the lowest-lying series gives the well-known dark-anti-dark waves, and the second series yields the dark-multi-dark states, and the following series become progressively more complex in their wave structures. The Bogoliubov-de Gennes spectra analysis shows that most of these states bear unstable modes, but they can be long-lived and remarkably all of them can be fully stabilized in suitable parameter regimes.

arXiv:2206.14500•Journal of Physics B Atomic Molecular and Optical Physics•Jun 2, 2023•6 citations

Mixtures of Bose gases confined in concentrically coupled annular traps

Francesc Malet, G. M. Kavoulakis, S. M. Reimann

A two-component Bose-Einstein condensate confined in an axially symmetric potential with two local minima, resembling two concentric annular traps, is investigated. The system shows a number of phase transitions that result from the competition between phase coexistence and radial-azimuthal phase separation. The ground-state phase diagram, as well as the rotational properties, including the (meta)stability of currents in this system, is analyzed.

arXiv:0911.2355•Physical Review A•Jan 28, 2010•24 citations

Lieb Mode in a Quasi-One-Dimensional Bose-Einstein Condensate of Atoms

Andrew David Jackson, G. M. Kavoulakis

We calculate the dispersion relation associated with a solitary wave in a quasi-one-dimensional Bose-Einstein condensate of atoms confined in a harmonic, cylindrical trap in the limit of weak and strong interactions. In both cases, the dispersion relation is linear for long-wavelength excitations and terminates at the point where the group velocity vanishes. We also calculate the dispersion relation of sound waves in both limits of weak and strong coupling.

arXiv:cond-mat/0202178•Physical Review Letters•Jul 30, 2002•40 citations

Solitary waves of Bose-Einstein-condensed atoms confined in finite rings

J. Smyrnakis, Manolis Magiropoulos, G. M. Kavoulakis +1 more

Motivated by recent progress in trapping Bose-Einstein-condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schr\"odinger equation subject to periodic boundary conditions. When the circumference of the ring is much larger than the size of the wave, the density profile is well approximated by that of an infinite ring; however, the density and the velocity of propagation cannot vanish simultaneously. When the size of the ring becomes comparable to the size of the wave, the density variation becomes sinusoidal and the velocity of propagation saturates to a constant value.

arXiv:1006.3705•Physical Review A•Aug 11, 2010•17 citations
A two-component Bose-Einstein condensate that is confined in a one-dimensional ring potential supports solitary-wave solutions, which we evaluate analytically in the limit of a large ring. The derived solutions are shown to be unique. The corresponding dispersion relation that generalizes the case of a single-component system shows interesting features.
Axisymmetric three-dimensional solitary waves in uniform two-component mixture Bose-Einstein condensates are obtained as solutions of the coupled Gross-Pitaevskii equations with equal intracomponent but varying intercomponent interaction strengths. Several families of solitary wave complexes are found: (1) vortex rings of various radii in each of the components; (2) a vortex ring in one component coupled to a rarefaction solitary wave of the other component; (3) two coupled rarefaction waves; (4) either a vortex ring or a rarefaction pulse coupled to a localized disturbance of a very low momentum. The continuous families of such waves are shown in the momentum-energy plane for various values of the interaction strengths and the relative differences between the chemical potentials of two components. Solitary wave formation, their stability, and solitary wave complexes in two dimensions are discussed.
Abstract We systematically construct vector solitary waves in harmonically trapped one-dimensional two-component Bose–Einstein condensates with unequal dispersion coefficients by a numerical continuation in chemical potentials from the respective analytic low-density linear limits to the high-density nonlinear Thomas-Fermi regime. The main feature of the linear states herein is that the component with the larger quantum number has instead a smaller linear eigenenergy, enabled by suitable unequal dispersion coefficients, leading to new series of solutions compared with the states similarly obtained in the equal dispersion setting. Particularly, the lowest-lying series gives the well-known dark-anti-dark waves, and the second series yields the dark-multi-dark states, and the following series become progressively more complex in their wave structures. The Bogoliubov-de Gennes spectra analysis shows that most of these states bear unstable modes, but they can be long-lived and remarkably all of them can be fully stabilized in suitable parameter regimes.
Motivated by recent progress in trapping Bose-Einstein-condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schr\"odinger equation subject to periodic boundary conditions. When the circumference of the ring is much larger than the size of the wave, the density profile is well approximated by that of an infinite ring; however, the density and the velocity of propagation cannot vanish simultaneously. When the size of the ring becomes comparable to the size of the wave, the density variation becomes sinusoidal and the velocity of propagation saturates to a constant value.