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:0904.3376 · Journal of Physics B Atomic Molecular and Optical Physics

Dynamic behaviour of Bose–Einstein condensates in optical lattices with two- and three-body interactions

Yan Chen, Kezhi Zhang, Yong Chen

Published Sep 8, 2009• 6 citations
arXivHTMLPDF

Abstract

We study the dynamic behaviour of Bose–Einstein condensates with two- and three-atom interactions in optical lattices with analytical and numerical methods. It is found that the steady-state relative population displays tuning-fork bifurcation when the system parameters are changed to certain critical values. In particular, the existence of the three-body interaction not only transforms the bifurcation point of the system but also greatly affects the macroscopic quantum self-trapping behaviours associated with the critically stable steady-state solution. In addition, we investigated the influence of the initial conditions, three-body interaction, and the energy bias on the macroscopic quantum self-trapping. Finally, by applying the periodic modulation on the energy bias, we observed that the relative population oscillation exhibits a process from order to chaos, via a series of period-doubling bifurcations.

DOI
10.1088/0953-4075/42/18/185302

Related papers

Atomic population oscillations between two coupled Bose–Einstein condensates with time-dependent nonlinear interaction

Li Fei, Shu Wei-Xing, Luo Hai-Lu +1 more

The atomic population oscillations between two Bose–Einstein condensates with time-dependent nonlinear interaction in a double-well potential are studied. We first analyse the stabilities of the system's steady-state solutions. And then in the perturbative regime, the Melnikov chaotic oscillation of atomic population imbalance is investigated and the Melnikov chaotic criterion is obtained. When the system is out of the perturbative regime, numerical calculations reveal that regulating the nonlinear parameter can lead the system to step into chaos via period doubling bifurcations. It is also numerically found that adjusting the nonlinear parameter and asymmetric trap potential can result in the running-phase macroscopic quantum self-trapping (MQST). In the presence of a weak asymmetric trap potential, there exists the parametric resonance in the system.

Chinese Physics•Feb 26, 2007•12 citations

Quantum Switching at a Mean-Field Instability of a Bose-Einstein Condensate in an Optical Lattice

V. S. Shchesnovich, V. V. Konotop

It is shown that bifurcation of the mean-field dynamics of a Bose-Einstein condensate can be related to the quantum phase transition of the original many-body system. As an example we explore the intraband tunneling in the two-dimensional optical lattice. Such a system allows for easy control by the lattice depth as well as for macroscopic visualization of the phase transition. The system manifests switching between two self-trapping states or from a self-trapping state to a superposition of the macroscopically populated self-trapping states with a steplike variation of the control parameter about the bifurcation point. We have also observed the magnification of the microscopic difference between the even and odd number of atoms to a macroscopically distinguishable dynamics of the system.

arXiv:0810.0307•Physical Review Letters•Feb 4, 2009•19 citations

Dynamics of a period-3 pattern-loaded Bose-Einstein condensate in an optical lattice

Ana María Rey, P. B. Blakie, Charles W. Clark

We discuss the dynamics of a Bose-Einstein condensate initially loaded into every third site of an optical lattice using a description based upon the discrete nonlinear Schr\"odinger equation. An analytic solution is developed for the case of a periodic initial condition and is compared with numerical simulations for more general initial configurations. We show that mean field effects in this system can cause macroscopic quantum self-trapping, a phenomenon already predicted for double-well systems. In the presence of a uniform external potential, the atoms exhibit generalized Bloch oscillations which can be interpreted in terms of the interference of three different Bloch states. We also discuss how the momentum distribution of the system can be used as an experimental signature of the macroscopic self-trapping effect.

arXiv:cond-mat/0212376•Physical Review A•May 27, 2003•11 citations

Stability and Chaos of Two Coupled Bose–Einstein Condensates with Three-Body Interaction

Ya Li, Wenhua Hai

We study the dynamics of two Bose–Einstein condensates (BECs) tunnel-coupled by a double-well potential. A real three-body interaction term is considered and a two-mode approximation is used to derive two coupled equations, which describe the relative population and relative phase. By solving the equations and analyzing the stability of the system, we find the stable stationary solutions for a constant atomic scattering length. When a periodically time-varying scattering length is applied, Melnikov analysis and numerical calculation demonstrate the existence of chaotic behavior and the dependence of chaos on the three-body interaction parameters.

Communications in Theoretical Physics•Nov 1, 2005•4 citations

Self-trapping and its periodic modulation of Bose-Einstein condensates in double-well trap

Guanfang Wang, Fu Li-Bin, Zhao Hong +2 more

Self-trapping of Bose-Einstein condensates (BEC) in double-well trap is investigated. Two kinds of self-trapping are discussed through phase space analysis in the mean-field approximation: 1) The number of atoms oscillates near an equilibrium point in the phase space, while relative phase increases monotonously with time (running-phase); 2) Both the number of particles and the relative phase oscillate near an equilibrium point in the phase space. In particular, we investigate how an external periodic filed influence the self-trapping. It is found that the external periodic field may dramatically modulate the critical points at which the transition to self-trapping occurs. With this, we can observe self-trapping phenomenon in a dilute Bose-Einstein condensate with a very weak interaction as well. Finally, the effect of many-body quantum fluctuation on self-trapping is also studied. We also discuss how to observe the self-trapping phenomenon with present experimental techniques.

Acta Physica Sinica•Jan 1, 2005•29 citations

Stationary Classical Chaos of Trapped Two-Component Bose–Einstein Condensates in 1-D Optical Lattice Potentials

Jianshu Fang, Wing‐Ki Liu, Zhu Shan-Hua

We study the nonlinear dynamics of two-component Bose–Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross–Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.

Communications in Theoretical Physics•Jul 1, 2007•2 citations
We study the dynamic behaviour of Bose–Einstein condensates with two- and three-atom interactions in optical lattices with analytical and numerical methods. It is found that the steady-state relative population displays tuning-fork bifurcation when the system parameters are changed to certain critical values. In particular, the existence of the three-body interaction not only transforms the bifurcation point of the system but also greatly affects the macroscopic quantum self-trapping behaviours associated with the critically stable steady-state solution. In addition, we investigated the influence of the initial conditions, three-body interaction, and the energy bias on the macroscopic quantum self-trapping. Finally, by applying the periodic modulation on the energy bias, we observed that the relative population oscillation exhibits a process from order to chaos, via a series of period-doubling bifurcations.
The atomic population oscillations between two Bose–Einstein condensates with time-dependent nonlinear interaction in a double-well potential are studied. We first analyse the stabilities of the system's steady-state solutions. And then in the perturbative regime, the Melnikov chaotic oscillation of atomic population imbalance is investigated and the Melnikov chaotic criterion is obtained. When the system is out of the perturbative regime, numerical calculations reveal that regulating the nonlinear parameter can lead the system to step into chaos via period doubling bifurcations. It is also numerically found that adjusting the nonlinear parameter and asymmetric trap potential can result in the running-phase macroscopic quantum self-trapping (MQST). In the presence of a weak asymmetric trap potential, there exists the parametric resonance in the system.
It is shown that bifurcation of the mean-field dynamics of a Bose-Einstein condensate can be related to the quantum phase transition of the original many-body system. As an example we explore the intraband tunneling in the two-dimensional optical lattice. Such a system allows for easy control by the lattice depth as well as for macroscopic visualization of the phase transition. The system manifests switching between two self-trapping states or from a self-trapping state to a superposition of the macroscopically populated self-trapping states with a steplike variation of the control parameter about the bifurcation point. We have also observed the magnification of the microscopic difference between the even and odd number of atoms to a macroscopically distinguishable dynamics of the system.
We discuss the dynamics of a Bose-Einstein condensate initially loaded into every third site of an optical lattice using a description based upon the discrete nonlinear Schr\"odinger equation. An analytic solution is developed for the case of a periodic initial condition and is compared with numerical simulations for more general initial configurations. We show that mean field effects in this system can cause macroscopic quantum self-trapping, a phenomenon already predicted for double-well systems. In the presence of a uniform external potential, the atoms exhibit generalized Bloch oscillations which can be interpreted in terms of the interference of three different Bloch states. We also discuss how the momentum distribution of the system can be used as an experimental signature of the macroscopic self-trapping effect.
We study the dynamics of two Bose–Einstein condensates (BECs) tunnel-coupled by a double-well potential. A real three-body interaction term is considered and a two-mode approximation is used to derive two coupled equations, which describe the relative population and relative phase. By solving the equations and analyzing the stability of the system, we find the stable stationary solutions for a constant atomic scattering length. When a periodically time-varying scattering length is applied, Melnikov analysis and numerical calculation demonstrate the existence of chaotic behavior and the dependence of chaos on the three-body interaction parameters.
Self-trapping of Bose-Einstein condensates (BEC) in double-well trap is investigated. Two kinds of self-trapping are discussed through phase space analysis in the mean-field approximation: 1) The number of atoms oscillates near an equilibrium point in the phase space, while relative phase increases monotonously with time (running-phase); 2) Both the number of particles and the relative phase oscillate near an equilibrium point in the phase space. In particular, we investigate how an external periodic filed influence the self-trapping. It is found that the external periodic field may dramatically modulate the critical points at which the transition to self-trapping occurs. With this, we can observe self-trapping phenomenon in a dilute Bose-Einstein condensate with a very weak interaction as well. Finally, the effect of many-body quantum fluctuation on self-trapping is also studied. We also discuss how to observe the self-trapping phenomenon with present experimental techniques.
We study the nonlinear dynamics of two-component Bose–Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross–Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.