两维有限深势阱中BEC的稳定性分析

研究两维轴对称有限深势阱中BEC的稳定性，利用变分法分别讨论了系统的基态和激发态特性。研究表明系统存在塌缩态、束缚态和扩散态三种状态，并计算出系统状态发生变化的耦合常数的两个临界值，发现势阱的形状与系统的稳定性紧密相关。同时在激发态下进一步讨论了原子间相互作用发生周期性调制的BEC的动力学特性，分析发现有限深势阱中BEC的塌缩可以通过周期性调制散射长度来控制。本文最后讨论了涡旋态下BEC的稳定性，发现系统的塌缩点由于涡旋态的存在而降低。

The Stability of BEC in a Two-dimensional Finite Potential Well

The stability of BEC in a two-dimensional axisymmetric finite deep well is studied. The ground state and excited state of the system are discussed by using variational method. The results show that there are three states of collapse state, bound state and diffusion state, and the two critical values of coupling constant of the system state change are calculated. The state of the system is closely related to the shape of the potential well. At the same time, the dynamic characteristics of BEC which is periodically modulated by the interaction between atoms are further discussed in the excited state. It is found that the collapse of BEC in a finite deep well can be controlled by modulating the scattering length periodically. Finally, the stability of BEC in the vortex state is discussed. Because of the existence of the vortex state, the collapse point of the system decreases.