Stability of Bose-Einstein condensates in a Kronig-Penney potential
Stability of Bose-Einstein condensates in a Kronig-Penney potential
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DOI：
10.1103/physreva.75.033612
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发表时间：
2006-10
影响因子：
2.9
通讯作者：
I. Danshita;S. Tsuchiya
中科院分区：
文献类型：
--
作者：
I. Danshita;S. Tsuchiya
研究了一维周期势场中具有超流的玻色-爱因斯坦凝聚的稳定性。利用Kronig-Penney模型，对凝聚态和Bogoliubov带进行了解析计算，讨论了凝聚态在周期势场中的稳定性。当凝聚态的准动量超过某个临界值时，在Kronig-Penney势中会出现朗道不稳定性和动力学不稳定性。发现朗道不稳定性和动力学不稳定性的起始点与低能激发通过每个势垒的完美传输被禁止的点一致。朗道不稳定性是由小q$的激发引起的，而动力学不稳定性是由q=\ensuremath{\pi} scina $的激发引起的，其中q$是激发的准动量，a$是晶格常数。当平均场能量充分大于周期势时，在第一凝聚带的边缘出现燕尾形能量环。我们发现，燕尾的上部总是动态不稳定的，但第二Bogoliubov带的声子谱反映了积极的有效质量。
We study the stability of Bose-Einstein condensates with superfluid currents in a one-dimensional periodic potential. By using the Kronig-Penney model, the condensate and Bogoliubov bands are analytically calculated and the stability of condensates in a periodic potential is discussed. The Landau and dynamical instabilities occur in a Kronig-Penney potential when the quasimomentum of the condensate exceeds certain critical values as in a sinusoidal potential. It is found that the onsets of the Landau and dynamical instabilities coincide with the point where the perfect transmission of low energy excitations through each potential barrier is forbidden. The Landau instability is caused by the excitations with small $q$ and the dynamical instability is caused by the excitations with $q=\ensuremath{\pi}∕a$ at their onsets, where $q$ is the quasimomentum of excitation and $a$ is the lattice constant. A swallow-tail energy loop appears at the edge of the first condensate band when the mean-field energy is sufficiently larger than the strength of the periodic potential. We find that the upper portion of the swallow-tail is always dynamically unstable, but the second Bogoliubov band has a phonon spectrum reflecting the positive effective mass.