Pairing fluctuations and the superfluid density through the BCS-BEC crossover
Pairing fluctuations and the superfluid density through the BCS-BEC crossover
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DOI：
10.1103/physreva.74.063626
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发表时间：
2006-09
影响因子：
2.9
通讯作者：
E. Taylor;A. Griffin;N. Fukushima;Y. Ohashi
中科院分区：
文献类型：
--
作者：
E. Taylor;A. Griffin;N. Fukushima;Y. Ohashi
我们通过 BCS-BEC 交叉，根据存在强加超流体流动的热力学势，推导出均匀二组分费米气体的超流体密度表达式。按照 Nozieres 和 Schmitt-Rink 的方法处理高斯近似中的配对波动，我们使用 {rho}{sub s} 的定义来获得在有限温度和整个 BCS-BEC 交叉上有效的显式结果。至关重要的是，BCS 间隙 {delta}、化学势 {mu} 和 {rho}{sub s} 都以自洽的方式包含同一水平波动的影响。我们证明，正常流体密度 {rho}{sub n}{identical_to}n-{rho}{sub s} 自然地分解为费米 BCS 准粒子 ({rho}{sub n}{sup F}) 和玻色集体模式 ({rho}{sub n}{sup B}) 贡献的总和。 {rho}{sub n}{sup F} 的表达式只是 BCS 费米超流体的朗道公式，但现在是通过 BCS-BEC 交叉计算的。玻色贡献的表达式 {rho}{sub n}{sup B} 更为复杂，并且仅在极端 BEC 极限下简化为玻色超流体的朗道公式，其中所有费米子都形成稳定的玻色对，并且相关分子玻色凝聚体的 Bogoliubov 激发更多 » 无阻尼。在一篇配套论文中，我们使用与本文中导出的表达式等效的表达式，在 BCS-BEC 交叉（包括幺正性）和有限温度下对 {rho}{sub s} 进行了数值计算。« less
We derive an expression for the superfluid density of a uniform two-component Fermi gas through the BCS-BEC crossover in terms of the thermodynamic potential in the presence of an imposed superfluid flow. Treating the pairing fluctuations in a Gaussian approximation following the approach of Nozieres and Schmitt-Rink, we use this definition of {rho}{sub s} to obtain an explicit result which is valid at finite temperatures and over the full BCS-BEC crossover. It is crucial that the BCS gap {delta}, the chemical potential {mu}, and {rho}{sub s} all include the effect of fluctuations at the same level in a self-consistent manner. We show that the normal fluid density {rho}{sub n}{identical_to}n-{rho}{sub s} naturally separates into a sum of contributions from Fermi BCS quasiparticles ({rho}{sub n}{sup F}) and Bose collective modes ({rho}{sub n}{sup B}). The expression for {rho}{sub n}{sup F} is just Landau's formula for a BCS Fermi superfluid but now calculated over the BCS-BEC crossover. The expression for the Bose contribution {rho}{sub n}{sup B} is more complicated and only reduces to Landau's formula for a Bose superfluid in the extreme BEC limit, where all the fermions have formed stable Bose pairs and the Bogoliubov excitations of the associated molecular Bose condensate aremore » undamped. In a companion paper, we present numerical calculations of {rho}{sub s} using an expression equivalent to the one derived in this paper, over the BCS-BEC crossover, including unitarity, and at finite temperatures.« less