轴对称谐振势阱中玻色凝聚气体基态和单涡旋态解

A solution to the ground and single vortex states of Bose-condensed gas in an axially symmetric harmonic trap

对囚禁在轴对称谐振势阱中的玻色凝聚气体,提出一种新的试探波函数,运用Gross-Pitaevskii(G-P)平均场能量泛函和变分的方法,得到玻色凝聚气体基态和单涡旋态波函数的解析表达式,并计算出凝聚原子的平均能量、原子云轴向和径向尺度比,以及产生单涡旋态的临界角速度等重要物理量与凝聚原子数N之间的关系.其结果与Dalfovo等人直接数值求解G-P方程所得到的结果相一致.

For a Bose-condensed gas in an axially symmetric harmonic trap at zero temperature, a new trial wave function of the ground and single vortex states is considered based on the mean-field energy functional and variational method. Once the wave function is known, we can explore the particle-number dependence of relevant quantities, such as energy, chemical potential, aspect ratio of the velocity distribution and critical angular velocity for production of vortices. These results agree well with previous numerical solutions of the G-P equation given by Dalfovo et al.