双势阱中的物质波暗孤子
Matter-wave dark solitons in a double-well potential
摘要：
研究了双势阱中准一维玻色-爱因斯坦凝聚体的第一激发态的稳定性，称之为“$π$ -态”。$π$态的密度陷波可以看作是一个静止的暗孤子。从激发光谱，我们确定的临界势垒高度，超过该高度的$π$状态是动态不稳定的。我们发现临界势垒高度随着凝聚原子数的增加而单调减小。我们还通过求解含时Gross-Pitaevskii方程模拟了$π$态的动力学。我们发现，由于动力学不稳定性的暗孤子开始远离陷阱中心，并表现出大幅振荡。
英文摘要：
We study stability of the first excited state of quasi-one-dimensional Bose-Einstein condensates in a double-well potential, which is called "$π$-state". The density notch in the $π$-state can be regarded as a standing dark soliton. From the excitation spectrum, we determine the critical barrier height, above which the $π$-state is dynamically unstable. We find that the critical barrier height decreases monotonically as the number of condensate atoms increases. We also simulate the dynamics of the $π$-state by solving the time-dependent Gross-Pitaevskii equation. We show that due to the dynamical instability the dark soliton starts to move away from the trap center and exhibits a large-amplitude oscillation.
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