分裂势阱中Tonks-Girardeau气体的基态性质
Ground State Properties of a Tonks-Girardeau Gas in a Split Trap
摘要：
我们确定了一个玻色子Tonks-Girardeau气体的多体性质，该气体被限制在一个在陷阱中心具有可调$δ$函数势垒的谐振势中。这是通过计算约化的单粒子密度矩阵、对分布函数和气体的动量分布作为势垒强度和粒子数的函数来完成的。随着势垒高度的增加，我们发现，基态占领的对角基础偏离$\sqrt N$行为，预期的情况下，一个简单的谐波陷阱。事实上，占据数的缩放取决于一个粒子的数量是偶数还是奇数。由于这个量是我们的样品的相干性的措施，我们展示了奇偶效应如何体现在玻色气体的动量分布和干涉条纹的可见性在自由时间演化。
英文摘要：
We determine the exact many-body properties of a bosonic Tonks-Girardeau gas confined in a harmonic potential with a tunable $δ$-function barrier at the trap center. This is done by calculating the reduced single particle density matrix, the pair-distribution function, and momentum distribution of the gas as a function of barrier strength and particle number. With increasing barrier height we find that the ground state occupation in a diagonal basis diverges from the $\sqrt N$ behavior that is expected for the case of a simple harmonic trap. In fact, the scaling of the occupation number depends on whether one has an even or odd number of particles. Since this quantity is a measure of the coherence of our sample we show how the odd-even effect manifests itself in both the momentum distribution of the Bose gas and interference fringe visibility during free temporal evolution.
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