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Acta Physica Sinica

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

Guanfang Wang, Fu Li-Bin, Zhao Hong, Liu Jie, (1)北京应用物理与计算数学研究所,北京 100088; (2)兰州大学物理科学与技术学院理论物理研究所,兰州 730000; (3)兰州大学物理科学与技术学院理论物理研究所,兰州 730000;中国工程物理研究院北京研究生部，北京 100088

Published Jan 1, 2005• 29 citations
Publisher

Abstract

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.

DOI
10.7498/aps.54.5003

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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.
With phase space analysis approach, we investigate the self-trapping phenomenon for two weakly coupled Bose-Einstein condensates (BECs) in a symmetric double well potential. We identify two kinds of self-trapping by their different relative phase behavior. By applying a periodic modulation on the energy bias of the system we find that the self-trapping can be controlled, in other words, the transition parameters can be adjusted effectively by the periodic modulation. Analytic expressions for the dependence of the transition parameters on the modulation parameters are derived for high- and low-frequency modulations. For an intermediate-frequency modulation, we find the resonance between the periodic modulation and nonlinear Rabi oscillation dramatically affect the tunneling dynamics and demonstrate many phenomena. Finally, we study the effects of many-body quantum fluctuation on the self-trapping and discuss the possible experimental realization.
Based on the mean-field approximation and a phase-space analysis, we discuss the dynamics of Bose-Einstein condensates (BECs) in a double-well potential. The condensates are found to be trapped in the time-dependent eigenstates of the effective Hamiltonian; we refer to this effect as time-dependent self-trapping of BECs. By comparison of this self-trapping with the adiabatic evolution, we find that adiabatic evolution beyond the traditional adiabatic condition can be achieved in BECs. Furthermore, the population imbalance of the BECs in the wells can be controlled by manipulating the atom-atom couplings and the driving field. The fixed points for the system are also calculated and discussed.
In the mean-field theory and two-mode approximation, we study the self-trapping of superfluid Fermi gases in the BEC regime and in unitarity by observing the evolution of the population imbalance with time and the variation of the average of population imbalance with several non-linear interaction parameters. The high-frequency modulations of both the symmetric double-well potential and the potential well are studied. The boundary conditions of the self-trapping and non-self-trapping are given. We find that high-frequency modulation in a certain range of modulation can make the self-trapping phenomenon easier to achieve. Finally, we study the influence of the initial value on self-trapping, and find that the increase of the absolute of the initial value can make the self-trapping more conducive to the realization.
We investigate the nonlinear self-trapping phenomenon of a Bose-Einstein condensate (BEC) in a symmetric double well, emphasizing its underlying dynamical phase transition. As the nonlinear parameter characterizing the interaction between the degenerate atoms increases, the BEC becomes self-trapped, manifesting an asymmetric distribution of the atomic density profile. The essence of this phenomenon is revealed to be a continuous phase transition and the underlying critical behavior is studied analytically and found to follow a logarithmic scaling law. We then go beyond the mean-field treatment and extend our treatment to discuss the effect of many-body quantum fluctuations on the transition. It is found that the transition point is shifted and the scaling law is broken. In particular, the quantum phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point. The underlying physics is revealed.
We investigate the effect of an external periodic driving to the self-trapping transitions of two weakly coupled Bose-Einstein condensates in a double-well potential. It is shown that the self-trapping can be effectively controlled by modulating the double-well with a high frequency driving and thus renormalizing the transition parameters. In particular, an exact solution is constructed under the balance condition between the external field and the nonlinear interaction among particles, which allows one to precisely control theself-trapping states.
In the framework of semi-classical theory,the author plots and analyzes the dynamical behaviors of Bose-Einstein condensate when initial phase difference is 0 and π,respectively,in a symmetric trap in weak interaction,without damping effects and periodical modulation.For the system is conservative,atoms never stop random oscillations in critical states instead of stopping automatically oscillations with damping effects.Atomic oscillations display properties of both Josephson oscillation and self-trapping oscillation in critical states between these two kinds of oscillation,and two kinds of properties of self-trapping oscillation in critical states between π phase mode self-trapping oscillation and running phase mode self-trapping oscillation.