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/0607361 · Physical Review A

Collective excitations of a Bose-Einstein condensate in an anharmonic trap

Guan-Qiang Li, Libin Fu, Ju-Kui Xue, Xuzong Chen, Jie Liu

Published Nov 1, 2006• 44 citations
arXivHTMLPDF

Abstract

We investigate the collective excitations of a one-dimensional Bose-Einstein condensate with repulsive interaction between atoms in a quadratic plus quartic trap. Using variational approaches, the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived. Then, two low-energy excitation modes are obtained analytically. The frequency shift induced by the anharmonic distortion, and the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes, are discussed.

DOI
10.1103/physreva.74.055601

Related papers

Collective Excitations of a Dipolar Bose—Einstein Condensate in an Anharmonic Trap

Wei Qi, Zhaoxin Liang, Zhang Zhi-dong

The collective excitations of a one-dimensional dipolar Bose—Einstein condensate trapped in an anharmonic potential are investigated theoretically. Using the variational approach, we obtain the coupled equations of motion for the center-of-mass coordinate of the condensate and its width. In particular, analytical expressions for the low-lying excitation modes are given. The results show that dipole-dipole interactions reduce the frequency shift induced by quartic distortion. The interplay between dipole-dipole interactions and anharmonic distortion for the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes are also discussed.

Chinese Physics Letters•Jun 1, 2013•6 citations

Effect of the anharmonicity of the trap on the collective excitations in Bose-Einstein condensates

Xue Ju-Kui

It is investigated that the collective excitations of a one-dimensional Bose-Einstein condensate(BEC) with repulsive interaction between atoms in a quadratic plus quartic trap V(x)=12(x~2+λx~4).By using the variational approach,the analytical expressions are derived for two low-energy collective modes,and the effect of the anharmonicity of the potential trap on BEC collective excitations is studied.When(λ0) the frequencies will be blue shifted and when λ0 the frequencies will be red shifted.Meanwhile,the variations of the center-of-mass of the condensate and its width under different values of the driving amplitude are discussed.It is found that the two modes couple each other due to the anharmonicity,and the beating structure for the variation of the width occur.Finally,the response result corresponding to the frequency driving is given.

Journal of Northwest Normal University•Jan 1, 2007•0 citations

Collective Excitations and Nonlinear Dynamics of 1D BEC with Two- and Three-body Interactions in Anharmonic Traps

Guan-Qiang Li, Peng Ping, Liu Jian-Ke +1 more

The collective excitations of low-dimensional Bose–Einstein condensates with two- and three-body interactions in anharmonic potentials are investigated. Using the standard variational approach, the governing equations of motions for the low-energy excitations are obtained by solving time-dependent Gross–Pitaevskii–Ginzburg equation, and the excitation spectrums are calculated in small amplitude limit. The frequency shift and nonlinear mode coupling induced by the anharmonic distortion (adding cubic, quartic, or quintic term to a harmonic trap) are studied.

Communications in Theoretical Physics•Nov 1, 2008•6 citations

Collective excitations of a BEC under anharmonic trap position jittering

F. Kh. Abdullaev, R. M. Galimzyanov, Kh. N. Ismatullaev

Collective excitations of a Bose-Einstein condensate under periodic oscillations of a quadratic plus quartic trap position has been studied. A coupled set of variational equations is derived for the width and the condensate wave function center. Analytical expressions for the growth of oscillation amplitudes in the resonance case are derived. It is shown that jittering of an anharmonic trap position can cause double resonance of the BEC width and the center of mass oscillation in the wide range of the BEC parameters values. The predictions of variational approach are confirmed by full numerical simulations of the 1D GP equation.

arXiv:0709.4357•Journal of Physics B Atomic Molecular and Optical Physics•Dec 20, 2007•15 citations

Collective excitations of two-component degenerate Fermi gases in an anharmonic trap

Kezhi Zhang

The collective excitations of two-component degenerate Fermi gases in a harminic trap with a quartic distortion are investigated.Using variational approaches,the coupled equations of motions for the center-of-mass coordinate and width of two-component degenerate Fermi gases are derived.Then two low-energy excitation modes are obtained analytically.The freqency shift,collapse and revival of the collective excitations of two-component degenerate Fermi gases induced by the anharmonic distortion under different values of the effective s-and p-wave interactions are discussed,respectively.

Journal of Northwest Normal University•Jan 1, 2010•0 citations

Dynamics of Bose-Einstein condensates under anharmonic trap

Hamid Al-Jibbouri

The dynamics of weakly interacting three-dimensional Bose-Einstein condensates (BECs), trapped in external axially symmetric plus anharmonic distortion potential are studied. Within a variational approach and time-dependent Gross-Pitaevskii equation, the coupled condensate width equations are derived. By modulating anharmonic distortion of the trapping potential, nonlinear features are studied numerically and illustrated analytically, such as mode coupling of oscillation modes, and resonances. Furthermore, the stability of attractive interaction BEC in both repulsive and attractive anharmonic distortion is examined. We demonstrate that a small repulsive and attractive anharmonic distortion is effective in reducing (extending) the condensate stability region since it decreases (increases) the critical number of atoms in the trapping potential.

arXiv:2206.15295•Condensed Matter Physics•Jan 1, 2022•1 citation
We investigate the collective excitations of a one-dimensional Bose-Einstein condensate with repulsive interaction between atoms in a quadratic plus quartic trap. Using variational approaches, the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived. Then, two low-energy excitation modes are obtained analytically. The frequency shift induced by the anharmonic distortion, and the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes, are discussed.
The collective excitations of a one-dimensional dipolar Bose—Einstein condensate trapped in an anharmonic potential are investigated theoretically. Using the variational approach, we obtain the coupled equations of motion for the center-of-mass coordinate of the condensate and its width. In particular, analytical expressions for the low-lying excitation modes are given. The results show that dipole-dipole interactions reduce the frequency shift induced by quartic distortion. The interplay between dipole-dipole interactions and anharmonic distortion for the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes are also discussed.
It is investigated that the collective excitations of a one-dimensional Bose-Einstein condensate(BEC) with repulsive interaction between atoms in a quadratic plus quartic trap V(x)=12(x~2+λx~4).By using the variational approach,the analytical expressions are derived for two low-energy collective modes,and the effect of the anharmonicity of the potential trap on BEC collective excitations is studied.When(λ0) the frequencies will be blue shifted and when λ0 the frequencies will be red shifted.Meanwhile,the variations of the center-of-mass of the condensate and its width under different values of the driving amplitude are discussed.It is found that the two modes couple each other due to the anharmonicity,and the beating structure for the variation of the width occur.Finally,the response result corresponding to the frequency driving is given.
The collective excitations of low-dimensional Bose–Einstein condensates with two- and three-body interactions in anharmonic potentials are investigated. Using the standard variational approach, the governing equations of motions for the low-energy excitations are obtained by solving time-dependent Gross–Pitaevskii–Ginzburg equation, and the excitation spectrums are calculated in small amplitude limit. The frequency shift and nonlinear mode coupling induced by the anharmonic distortion (adding cubic, quartic, or quintic term to a harmonic trap) are studied.
Collective excitations of a Bose-Einstein condensate under periodic oscillations of a quadratic plus quartic trap position has been studied. A coupled set of variational equations is derived for the width and the condensate wave function center. Analytical expressions for the growth of oscillation amplitudes in the resonance case are derived. It is shown that jittering of an anharmonic trap position can cause double resonance of the BEC width and the center of mass oscillation in the wide range of the BEC parameters values. The predictions of variational approach are confirmed by full numerical simulations of the 1D GP equation.
The collective excitations of two-component degenerate Fermi gases in a harminic trap with a quartic distortion are investigated.Using variational approaches,the coupled equations of motions for the center-of-mass coordinate and width of two-component degenerate Fermi gases are derived.Then two low-energy excitation modes are obtained analytically.The freqency shift,collapse and revival of the collective excitations of two-component degenerate Fermi gases induced by the anharmonic distortion under different values of the effective s-and p-wave interactions are discussed,respectively.
The dynamics of weakly interacting three-dimensional Bose-Einstein condensates (BECs), trapped in external axially symmetric plus anharmonic distortion potential are studied. Within a variational approach and time-dependent Gross-Pitaevskii equation, the coupled condensate width equations are derived. By modulating anharmonic distortion of the trapping potential, nonlinear features are studied numerically and illustrated analytically, such as mode coupling of oscillation modes, and resonances. Furthermore, the stability of attractive interaction BEC in both repulsive and attractive anharmonic distortion is examined. We demonstrate that a small repulsive and attractive anharmonic distortion is effective in reducing (extending) the condensate stability region since it decreases (increases) the critical number of atoms in the trapping potential.