谐波势阱中的相互作用费米气体
Interacting Fermi gas in a Harmonic Trap
摘要：
鉴于目前正在进行的实验，以捕获超冷自旋极化$^6$锂，我们研究了各种性质的相互作用费米气体在谐波陷阱考虑离散性质的未扰动谐波陷阱能级准确。由于$^6$ Li具有较大的负散射长度，我们着重研究了原子-原子吸引相互作用对Li的热力学性质以及动量和密度分布的影响。得到了化学势、比热、密度和动量分布与阱中粒子数的关系。我们还计算了气体的能量。与半经典计算的结果和非相互作用气体的性质进行了比较。我们发现，相互作用的影响是相当大的现实陷阱频率。因此，在任何与实验相关的定量预测中包括这些相互作用是很重要的。
英文摘要：
In view of ongoing experiments to trap ultracold spin-polarized $^6$Li, we study various properties of an interacting Fermi gas in a harmonic trap taking the discrete nature of the unperturbed harmonic trap levels into account exactly. As $^6$Li has a rather large and negative scattering length, we focus on the effects of the attractive atom-atom interaction on several thermodynamic properties and on the momentum and density distributions. The dependence of the chemical potential, the specific heat and the density and momentum distributions on the number of particles in the trap is obtained. We also calculate the energy of the gas. Comparison is made with results of a semiclassical calculation and with the properties of a non-interacting gas. We find that the effect of the interactions is rather large for realistic trap frequencies. Hence, it is important to include these interactions in any quantitative predictions relevant for experiments.
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