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研究了玻色-爱因斯坦凝聚体在不对称双势阱中, 随着两势阱局域基态能量差和非线性相互作用的变化而表现出的动力学特性. 对双模理论的解析分析可以发现, 在无相互作用情况下, 当双势阱能量差比较大时, 凝聚体会主要聚集在初始分布较多的势阱中, 而和高低势阱的位置无关. 数值计算表明, 当相互作用存在且逐渐增大时, 凝聚体的分布呈现出不同的变化. 当初始分布聚集在一个势阱时, 会呈现出先加强聚集, 然后促进隧穿, 最后又重新导致聚集的现象. 同时, 通过对相图的分析, 利用等效势概念为这些现象的出现给出了合理的解释. 为了验证上述现象, 还对Gross-Pitaevskii方程进行了直接数值模拟, 结果和上述采用双模理论得到的结论一致.Josephson effect of Bose-Einstein condensate in double-well potential is an obvious manifestation of macroscopic quantum coherence. Most of researches focus on the symmetric double-well potential. In this work, we investigate the dynamic of Bose-Einstein condensates in an asymmetric double-well potential by using two-mode theory and computer simulation. In the absence of the interaction between atoms, the dynamic equation of condensate can be solved analytically. The amplitude as a function of energy difference of two wells is obtained. We can find that the change of energy difference will lead to the different dynamic behaviors of condensate. If the energy difference is relatively large, the condensate will primarily occupy the well that is occupied more than the other well at the beginning time. It is interesting that such a trap phenomenon is not dependent on the position of the high energy potential well nor the position of low energy potential well. If the energy difference becomes small, the tunneling and oscillation of condensate will be enhanced. When the interaction between atoms is present, our numerical calculations show that as the nonlinear interaction increases, the dynamic behavior of condensate exhibits different characteristics, such as trapping in a well, enhancing the tunneling and oscillation between two wells, and enhancing the trapping in a well at large nonlinear interaction, which is similar to the dynamic change caused by the energy difference in the case of ideal condensate. That is to say, on the one hand, the nonlinear interaction can lead to the trap of condensate as well as the dynamic trap to happen in symmetric double-well potential. On the other hand, the nonlinearity can promote the tunneling of condensate, counteracting the effect of the asymmetry of potential. And, this counteracting effect is related to the difference in energy between asymmetric potential wells. To understand the underlying mechanism, the full dynamic behavior of two-mode model is illustrated and the dynamic transition can be seen clearly. Combining the results obtained with and without interaction, regarding nonlinear interaction as effective potential provides a clear way to explain dynamic transition of condensate in an asymmetric double-well potential. In addition, we also perform the numerical simulations of the Gross-Pitaevskii equation, and the results are consistent with the conclusions obtained by using the two-mode theory.
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Keywords:
- Bose-Einstein condensate /
- asymmetric double-well potential /
- dynamics
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Google Scholar
[2] Davis K B, Mewes M O, Andrews M R, Vandruten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969
Google Scholar
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Google Scholar
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[9] Josephson B D 1962 Phys. Lett. 1 251
Google Scholar
[10] Milburn G J, Corney J, Wright E M, Walls D F 1997 Phys. Rev. A 55 4318
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Zang X F, Li J P, Tan L 2007 Acta Phys. Sin. 56 4348
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Li J P, Tan L, Zang X F, Yang K 2008 Acta Phys. Sin. 57 7467
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[43] Haldar S K, Alon O E 2019 New J. Phys. 21 103037
Google Scholar
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