二维玻色-爱因斯坦凝聚体在简谐和晶格约束下的结构和稳定性
Structure and stability of two-dimensional Bose-Einstein condensates under both harmonic and lattice confinement
摘要：
本文研究了在两个正交方向上具有等周期性的光晶格和柱对称谐振势共同作用下的饼状玻色-爱因斯坦凝聚体。我们首先通过多尺度技术确定潜在的二维线性问题的频谱。然后，我们使用的结果在线性极限作为出发点的非线性存在性和稳定性分析的最低能量状态，从线性的，在非线性问题。为了提高非线性和光晶格强度，对这些态进行了双参数延拓，并研究了它们的不稳定性和时间演化。结果表明，在原子间相互作用中，基态和其中一个激发态都是稳定的或弱不稳定的。
英文摘要：
In this work, we study pancake-shaped Bose-Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal directions. We first identify the spectrum of the underlying two-dimensional linear problem through multiple-scale techniques. Then, we use the results obtained in the linear limit as a starting point for a nonlinear existence and stability analysis of the lowest energy states, emanating from the linear ones, in the nonlinear problem. Two-parameter continuations of these states are performed for increasing nonlinearity and optical lattice strengths, and their instabilities and temporal evolution are investigated. It is found that the ground state as well as one of the excited states are either stable or weakly unstable for both attractive and repulsive interatomic interactions.
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