旋转玻色-爱因斯坦凝聚体中的涡旋
Vortices in rotating Bose-Einstein condensates confined in homogeneous traps
摘要：
本文研究了旋转二维玻色-爱因斯坦凝聚体在渐近均匀的囚禁势中基态涡旋的稳定性。我们的出发点是旋转坐标系中的Gross-Pitaevskii能量泛函。通过估计这个能量的上下界，我们表明，在能量和密度的领先顺序可以描述相应的Ekas-Fermi量，我们推导出下一个订单的贡献，由于涡旋。作为应用，我们考虑了具有斜率s \in [2，无穷大]和各向异性λ \in（0，1]的一般势V（x，y）=（x^2+ λ d^2y^2）^{s/2}，其中分别包含谐波（s=2）和“平坦”（s ->无穷大）陷阱.对于这种势，我们导出了涡旋存在的临界角速度，并证明了所有涡旋都是单量子化的。此外，我们推导出的关系，决定了在凝聚体中的旋涡的分布，即涡图案。
英文摘要：
We investigate analytically the thermodynamical stability of vortices in the ground state of rotating 2-dimensional Bose-Einstein condensates confined in asymptotically homogeneous trapping potentials in the Thomas-Fermi regime. Our starting point is the Gross-Pitaevskii energy functional in the rotating frame. By estimating lower and upper bounds for this energy, we show that the leading order in energy and density can be described by the corresponding Thomas-Fermi quantities and we derive the next order contributions due to vortices. As an application, we consider a general potential of the form V(x,y) = (x^2+lambda^2 y^2)^{s/2} with slope s \in [2,infinity) and anisotropy lambda \in (0,1] which includes the harmonic (s=2) and 'flat' (s -> infinity) trap, respectively. For this potential, we derive the critical angular velocities for the existence of vortices and show that all vortices are singly-quantized. Moreover, we derive relations which determine the distribution of the vortices in the condensate i.e. the vortex pattern.
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