硬壁势阱中相互作用双组分玻色气体的基态性质
Ground-state properties of interacting two-component Bose gases in a hard-wall trap
摘要：
利用Bethe近似和精确数值对角化方法研究了硬壁势阱中相互作用的两组分玻色气体的基态性质。对于相等的原子内和原子间相互作用，系统是精确可解的。因此，从Bethe近似解可以得到整个相互作用区的精确基态波函数和密度分布。由于基态是总自旋S=N/2的简并态，因此对于每个简并态，总密度分布是相同的。随着排斥作用的增加，总密度分布从类高斯玻色分布演化为类费米分布。各组分的分布为总密度分布的N_i/N。即使在实验情况下，这也是近似真实的。此外，数值计算结果还表明，随着种间相互作用的增加，两种Tonks-Girardeau气体的分布呈现复合的费米化交叉，在强相互作用区，各组分均出现N个峰。
英文摘要：
We investigate ground-state properties of interacting two-component Bose gases in a hard-wall trap using both the Bethe ansatz and exact numerical diagonalization method. For equal intra- and inter-atomic interaction, the system is exactly solvable. Thus the exact ground state wavefunction and density distributions for the whole interacting regime can be obtained from the Bethe ansatz solutions. Since the ground state is a degenerate state with total spin S=N/2, the total density distribution are same for each degenerate state. The total density distribution evolves from a Gauss-like Bose distribution to a Fermi-like one as the repulsive interaction increases. The distribution of each component is N_i/N of the total density distribution. This is approximately true even in the experimental situation. In addition the numerical results show that with the increase of interspecies interaction the distributions of two Tonks-Girardeau gases exhibit composite fermionization crossover with each component developing N peaks in the strongly interacting regime.
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