Ground-state description of a single vortex in an atomic Fermi gas: From BCS to Bose Einstein condensation
Ground-state description of a single vortex in an atomic Fermi gas: From BCS to Bose Einstein condensation
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费米原子气体中单个涡旋的基态描述：从 BCS 到玻色爱因斯坦凝聚
DOI：
10.1103/physreva.73.041603
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发表时间：
2005
影响因子：
2.9
通讯作者：
K. Levin
中科院分区：
文献类型：
--
作者：
C. Chien;Yan He;Qijin Chen;K. Levin
在原子和凝聚态物理学中最令人兴奋的发展之一是在被囚禁的费米子系统中观察到超流性[1，2，3，4]。在这些系统中，Feshbach共振的存在提供了一种利用外加磁场调节吸引配对相互作用的手段。这样，系统经历了从BCS到玻色-爱因斯坦凝聚（BEC）超流性的连续演化。对超流相最有说服力的证明是对涡旋的实验观察[5]。从理论的角度来看，特别有趣的是涡从BCS到BEC的演变方式。这种演化不仅与涡旋大小的减小有关，而且与构成核心的费米子态的完全重排有关。结果，涡旋内的粒子密度不断变化，从而影响实验室中涡旋的可见度。本文讨论了系统从BCS过渡到BEC时单涡的行为。我们的工作是基于最简单的BCS类基态，首先由Leggett [6]和Eagles [7]引入来处理BCS-BEC交叉。与这种选择的基态不均匀性的影响很容易纳入广义Bogoliubov-de Gennes（BdG）理论。在这里，我们证明了解析的BdG强耦合描述的T = 0涡旋状态相吻合的通常的Gross-Pitaevskii（GP）处理的玻色子超流体中的涡旋。因此，基于BdG的费米子理论是非常包容的，并且在这种方法中，人们期望从BCS到BEC极限的涡旋的平滑演化，因为统计有效地从费米子到玻色子c变化。先前对这些费米子超流体中涡旋的研究解决了T = 0 [8]和T = Tc [9]的BCS极限。还有关于T = 0严格酉情形的工作[10]，其中使用BdG方法，包括Hartree-Fock贡献。在目前的工作中，相比之下，我们讨论了整个交叉制度，重要的是，提出了一个详细的分析的能源和空间结构内的核心，以及它是如何演变的BCS BEC。在参考文献[11]中引入了一种非常不同的路径积分方法来处理BCS-BEC交叉的涡流，但作者在这里指出，在BCS区域中密度耗尽效应似乎不符合物理学。我们的分析方法在很大程度上建立在以前的工作[12]，其中显示了GP理论和BdG之间的一般联系。由此可以得出结论，广义BCS理论[6]将玻色子自由度视为与GP理论相同的水平。可以考虑不同的基态（比如不完全凝聚），但它们与BdG理论不相容。以类似的方式，一旦T 6 0，就必须包含非凝聚对和相关的赝能隙物理[13]，这在有限温度BdG理论中不存在。在大多数情况下，BdG方法需要详细的数值解[8，14，15，16]，因此在BEC极限中使用分析工具特别有用。我们首先提出这种非数值描述。我们的一般自洽方程[17]是：h − μ μ（r）μ（r）−h μ + μ n vn = En μ n vn
One of the most exciting developments in atomic and condensed matter physics has been the observation of superfluid ity in trapped fermionic systems [1, 2, 3, 4]. In these system s, the presence of a Feshbach resonance provides a means of tuning the attractive pairing interaction with applied mag netic field. In this way the system undergoes a continuous evolutio n from BCS to Bose-Einstein condensed (BEC) superfluidity. The most conclusive demonstration of the superfluid phase has been the experimental observation of vortices [5]. Particularly interesting from a theoretical viewpoint is the way vortices evolve from BCS to BEC. This evolution is associated, not just with a decrease in vortex size but with a complete rearrangement of the fermionic states which make up the core. As a result, there is a continuous evolution of the particle den sity within a vortex, thereby affecting the visibility of vortic es in the laboratory. In this paper we discuss the behavior of a (si ngle) vortex as the system crosses from BCS to BEC. Our work is based on simplest BCS-like ground state first introduced by Leggett [6] and Eagles [7] to treat BCS-BEC crossover. With this choice of ground state inhomogeneity effects are readily incorporated as in generalized Bogoliubov-de Gennes (BdG) theory. Here we demonstrate analytically that the BdG strong coupling description of the T = 0 vortex state coincides with the usual Gross-Pitaevskii (GP) treatment of vortices in bosonic superfluids. A fermionic theory based on BdG is, thus, very inclusive, and within this approach one expects a smooth evolution of vortices from the BCS to BEC limit as the statistics effectively change from fermionic to bosoni c. Previous studies of vortices in these fermionic superfluids addressed the BCS limit at T = 0 [8] and T ≈ Tc [9]. There is also work [10] on the T = 0 strict unitary case where a BdG approach was used with Hartree-Fock contributions included. In the present work, by contrast, we discuss the entire crossover regime and, importantly, present a detailed analysis of the energy and spatial structure within the core and how it evolves from BCS to BEC. A very different path integral approach was introduced in Ref. [11] to address vortices with BCS-BEC crossover, but here the authors note that density depletion effects appear to be unphysically large in the BCS regime. Our analytical approach builds heavily on previous work [12] which showed a general connection between GP theory and BdG. From this one can conclude that a generalized BCS theory [6] treats the bosonic degrees of freedom at the same level as GP theory. Different ground states can be contemplated, (with incomplete condensation, say) but they will not be compatible with BdG theory. In a similar way, once T 6 0 one has to incorporate noncondensed pairs, and associated pseudogap physics [13] which are not present in a finite temperature BdG theory. For the most part, BdG approaches require detailed numerical solution [8, 14, 15, 16], so it is particularly useful to have analytical tools in the BEC limit. We present this nonnumerical description first. Our general self consistent eq uations [17] are � h − µ �(r) � ∗ (r) −h ∗ + µ �� u n vn � = En � u n vn