Theory of trapped superfluid fermi gases

自从1995年在激光冷却的碱金属原子中发现玻色-爱因斯坦凝聚（BEC）以来（经过几十年的努力），世界范围内对超冷原子和超冷物质性质的研究出现了爆炸式增长。 BEC涉及宏观数量的原子占据相同的单粒子量子态，这导致超流体性质（持续电流，量子化涡旋等）。这是在超流氦和超导体中发现的类似物。 我目前的研究涉及在存在Feshbach共振的情况下被捕获的费米气体，这允许人们“调整”s波散射长度的大小和符号（这完全描述了超冷温度下的原子间相互作用）。 由于在这些费米气体中相互作用可以变得非常大，人们可以探索有限温度下的双流体流体动力学，这是朗道在1941年首次在超流液体He的背景下研究的。 朗道双流体方程应该描述整个BCS-BEC交叉的动力学（从库珀对的BCS凝聚物到真实的分子的BEC）。 我的工作涉及到对双流体集体振荡（均匀玻色超流体中第一和第二声音的模拟）的详细研究。 具有Feshbach共振的超流费米气体使我们能够首次探测被困量子气体的局部平衡区域，即使密度仍然非常小，碰撞也起着至关重要的作用。 实验观察到的费米超流气体中的双流体行为将与1938年历史上观察到的液氦中的超流性完全相似，尽管由于热力学的不同，量子气体的详细性质会有很大不同。

Since the dramatic discovery in 1995 of Bose-Einstein condensation (BEC) in laser-cooled alkali atoms (after decades of effort), there has been a worldwide explosion of research on the properties of ultracold atoms and ultracold matter.  BEC involves a macroscopic number of atoms occupying the same single-particle quantum state, which results in superfluid properties (persistent currents, quantized vortices, etc.) which are the analogue of those found in superfluid He and superconductors.        My current research deals with trapped Fermi gases in the presence of a Feshbach resonance, which allows one to "tune" the size and sign of the s-wave scattering length (which completely describes the interatomic interaction at ultracold temperature).  Because the interaction can be made very large in these Fermi gases, one can probe the two-fluid hydrodynamics at finite temperatures, first studied by Landau in 1941 in the context of superfluid liquid He.  The Landau two-fluid equations should describe the dynamics across the entire BCS-BEC crossover (going from a BCS condensate of Cooper pairs to a BEC of real molecules).  My work involves a detailed study of the two-fluid collective oscillations (the analogue of first and second sound in a uniform Bose superfluid).  Superfluid Fermi gases with a Feshbach resonance allow us for the first time to probe the local equilibrium region of trapped quantum gases where collisions play a crucial role, even though the density is still extremely small.  Experimental observation of two-fluid behaviour in trapped Fermi superfluid gases would be the complete analogue of the historic observations in 1938 of superfluidity in liquid Helium, although the detailed properties will be quite different in quantum gases because of the different thermodynamics.