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 Physics B Atomic Molecular and Optical Physics

Chaotic dynamics of a Bose-Einstein condensate in a double-well trap

P. Coullet, Nicolas Vandenberghe

Published Mar 13, 2002• 27 citations
Publisher

Abstract

The dynamics of Bose-Einstein condensates in a double-well magnetic trap is studied using the Gross-Pitaevskii equation (GPE) and a two-mode approximation. The self-trapping instability occurs when a sufficiently high potential barrier is formed in the centre of the trap. Close to the instability threshold, the GPE is reduced to a simple amplitude equation. In the case where weakly dissipative effects are taken into account, the condensate exhibits aperiodic oscillations which can be described by the Lorenz thermal convection model.

DOI
10.1088/0953-4075/35/6/312

Related papers

Chaotic self-trapping of a weakly irreversible double Bose condensate

P. Coullet, Nicolas Vandenberghe

We analyze the dynamics of a weakly open Bose-Einstein condensate trapped in a double-well potential. Close to the self-trapping bifurcation, numerical simulations of the weakly irreversible one-dimensional Gross Pitaevskii equation reveal chaotic behaviors. A two-mode model is used to derive amplitude equations describing the complex dynamic of the condensate.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 19, 2001•49 citations

Dynamic chaos and stability of a weakly open Bose-Einstein condensate in a double-well trap

Xiaobing Luo, Wenhua Hai

We investigate the dynamics of a weakly open Bose-Einstein condensate with attractive interaction in a magneto-optical double-well trap. A set of time-dependent ordinary differential equations describing the complex dynamics are derived by using a two-mode approximation. The stability of the stationary solution is analyzed and some stability regions on the parameter space are displayed. In the symmetric well case, the numerical calculations reveal that by adjusting the feeding from the nonequilibrium thermal cloud or the two-body dissipation rate, the system could transit among the periodic motions, chaotic self-trapping states of the Lorenz model, and the steady states with the zero relative atomic population or with the macroscopic quantum self-trapping (MQST). In the asymmetric well case, we find the periodic orbit being a stable two-sided limited cycle with MQST. The results are in good agreement with that of the direct numerical simulations to the Gross-Pitaevskii equation.

Chaos An Interdisciplinary Journal of Nonlinear Science•Sep 1, 2005•22 citations

Strong-coupling dynamics of Bose–Einstein condensate in a double-well trap

Valentin O. Nesterenko, A N Novikov, E. Suraud

Dynamics of the repulsive Bose–Einstein condensate (BEC) in a double-well trap is explored within the 3D time-dependent Gross–Pitaevskii equation. The model avoids numerous common approximations (two-mode treatment, time-space factorization, fixed values of the chemical potential and barrier penetrability, etc) and thus may provide a realistic description of BEC dynamics, including both weak-coupling (sub-barrier) and strong-coupling (above-barrier) regimes and their crossover. The strong coupling regime is achieved by increasing the number N of BEC atoms and thus the chemical potential. The evolution with N of Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) is examined and the crucial impact of the BEC interaction is demonstrated. At weak coupling, the calculations well reproduce the JO/MQST experimental data. At strong coupling with a significant overlap of the left and right BECs, we observe a remarkable persistence of the Josephson-like dynamics: the JO and MQST converge to a high-frequency JO-like mode where both population imbalance and phase difference oscillate around the zero averages.

arXiv:1205.3687•Journal of Physics B Atomic Molecular and Optical Physics•Oct 24, 2012•5 citations

Josephson Dynamics of a Bose–Einstein Condensate Trapped in a Double-Well Potential

Hongwei Yang, Zuo Wei

The Josephson equations for a Bose–Einstein Condensate gas trapped in a double-well potential are derived with the two-mode approximation by the Gross–Pitaevskii equation. The dynamical characteristics of the equations are obtained by the numerical phase diagrams. The nonlinear self-trapping effect appeared in the phase diagrams are emphatically discussed, and the condition E c N >4 E J is presented.

Chinese Physics Letters•Feb 19, 2007•4 citations

Mean-Field Dynamics of a Two-Mode Bose-Einstein Condensate Subject to Decoherence

B. Cui, Wu Song-Lin, YI Xue-Xi

We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherence (or particle loss). Starting from the full many-body dynamics described by the master equation, an effective Gross-Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.

Chinese Physics Letters•Jul 1, 2010•2 citations

Dynamics of Bose-Einstein Condensates in a Driven Double-well

HE Xiao-yan

The dynamic of Bose-Einstein condensates in a double-well under a monochromatic external driving force is studied.With the different driving intensity and frequency,the motion of the classical particle can be either regular or chaotic or even both of them.The equation that describes the Bose-Einstein condensates is Gross-Pitaevskii equation.Firstly,the study gets the Gross-Pitaevskii equation′s classical form by a superposition of the single well wave function,then,studies the dynamics of their phase space and the self-trapping behavior of Bose-Einstein condensate under periodic driving force.

Journal of Hebei Normal University•Jan 1, 2008•0 citations
The dynamics of Bose-Einstein condensates in a double-well magnetic trap is studied using the Gross-Pitaevskii equation (GPE) and a two-mode approximation. The self-trapping instability occurs when a sufficiently high potential barrier is formed in the centre of the trap. Close to the instability threshold, the GPE is reduced to a simple amplitude equation. In the case where weakly dissipative effects are taken into account, the condensate exhibits aperiodic oscillations which can be described by the Lorenz thermal convection model.
We investigate the dynamics of a weakly open Bose-Einstein condensate with attractive interaction in a magneto-optical double-well trap. A set of time-dependent ordinary differential equations describing the complex dynamics are derived by using a two-mode approximation. The stability of the stationary solution is analyzed and some stability regions on the parameter space are displayed. In the symmetric well case, the numerical calculations reveal that by adjusting the feeding from the nonequilibrium thermal cloud or the two-body dissipation rate, the system could transit among the periodic motions, chaotic self-trapping states of the Lorenz model, and the steady states with the zero relative atomic population or with the macroscopic quantum self-trapping (MQST). In the asymmetric well case, we find the periodic orbit being a stable two-sided limited cycle with MQST. The results are in good agreement with that of the direct numerical simulations to the Gross-Pitaevskii equation.
Dynamics of the repulsive Bose–Einstein condensate (BEC) in a double-well trap is explored within the 3D time-dependent Gross–Pitaevskii equation. The model avoids numerous common approximations (two-mode treatment, time-space factorization, fixed values of the chemical potential and barrier penetrability, etc) and thus may provide a realistic description of BEC dynamics, including both weak-coupling (sub-barrier) and strong-coupling (above-barrier) regimes and their crossover. The strong coupling regime is achieved by increasing the number N of BEC atoms and thus the chemical potential. The evolution with N of Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) is examined and the crucial impact of the BEC interaction is demonstrated. At weak coupling, the calculations well reproduce the JO/MQST experimental data. At strong coupling with a significant overlap of the left and right BECs, we observe a remarkable persistence of the Josephson-like dynamics: the JO and MQST converge to a high-frequency JO-like mode where both population imbalance and phase difference oscillate around the zero averages.
We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherence (or particle loss). Starting from the full many-body dynamics described by the master equation, an effective Gross-Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.
The dynamic of Bose-Einstein condensates in a double-well under a monochromatic external driving force is studied.With the different driving intensity and frequency,the motion of the classical particle can be either regular or chaotic or even both of them.The equation that describes the Bose-Einstein condensates is Gross-Pitaevskii equation.Firstly,the study gets the Gross-Pitaevskii equation′s classical form by a superposition of the single well wave function,then,studies the dynamics of their phase space and the self-trapping behavior of Bose-Einstein condensate under periodic driving force.