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Acta Physica Sinica

Phase transition and entanglement entropy of Bose-Einstein condensates in double-well trap under periodic modulation

Fang Yong-Cui, Yang Zhi-An, Yang Li-Yun, (1)北京应用物理与计算数学研究所，北京 100088; (2)济南大学理学院，济南 250022

Published Jan 1, 2008• 13 citations
Publisher

Abstract

Dynamical phase transition of Bose-Einstein condensates (BEC) in double-well trap with external periodic modulation applied to the interaction term is investigated in this paper. Particularly, phase transition to chaos is studied. It is found that, when resonance between the modulation frequency and the natural frequency of the system happens, the system turns to instability (chaos) at certain values of the parameters. In the chaotic region, distribution of particles is random, and the average of population difference fluctuates around zero. Especially, chaos can be manifested by the entanglement entropy. In the chaotic zone, both of the average entanglement entropies approach to their maxima.

DOI
10.7498/aps.57.661

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Dynamical phase transition of Bose-Einstein condensates (BEC) in double-well trap with external periodic modulation applied to the interaction term is investigated in this paper. Particularly, phase transition to chaos is studied. It is found that, when resonance between the modulation frequency and the natural frequency of the system happens, the system turns to instability (chaos) at certain values of the parameters. In the chaotic region, distribution of particles is random, and the average of population difference fluctuates around zero. Especially, chaos can be manifested by the entanglement entropy. In the chaotic zone, both of the average entanglement entropies approach to their maxima.
Phase transition to chaos of Bose-Einstein condensates in double-well trap with external periodic modulation is investigated in this paper. Particularly, chaos tunneling is studied. It is found that, when resonance between external periodic frequency and natural frequency is established, this system can turn to instability (chaos). The evolutions of Husimi function in quantum condition are discussed. It is found that, when chaos emerges, chaos region and chaos tunneling varies with the interaction between the particles.
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.
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.
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 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.
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.