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Journal of University of Jinan

Computation of Husimi Function of Bose-Einstein Condensates

Yang Zhi-an

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The act of evolutionary and tunneling of Bose-Einstein Condensates(BEC) in double-well trap with external periodic modulation can be expressed by husimi function directly.It is a problem to compute husimi function for nonlinear Bose-Einstein condensates.Taking BEC in double-well trap for example,the method of computing husimi function is given.Furthermore,according to numerical calculation,tunneling procedure of BEC with external periodic modulation is discussed by husimi function.

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The act of evolutionary and tunneling of Bose-Einstein Condensates(BEC) in double-well trap with external periodic modulation can be expressed by husimi function directly.It is a problem to compute husimi function for nonlinear Bose-Einstein condensates.Taking BEC in double-well trap for example,the method of computing husimi function is given.Furthermore,according to numerical calculation,tunneling procedure of BEC with external periodic modulation is discussed by husimi function.
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.
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.
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.
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.
The nonlinear Landau—Zener tunneling and nonlinear Rabi oscillations of Bose—Einstein condensate (BEC) with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters (i.e., the modulation amplitude and frequency) and the strength of periodic potential.