Theory of trapped superfluid fermi gases

自1995年激光冷却碱原子中的玻色-爱因斯坦凝聚（BEC）的惊人发现（经过数十年的努力）以来，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，量子化漩涡等），这是超流体He和超导体中发现的类似物。我目前的研究涉及在费希巴赫共振存在下的被困费米气体，它允许人们“调整”s波散射长度的大小和符号（它完全描述了超冷温度下原子间的相互作用）。由于在这些费米气体中相互作用可以非常大，人们可以在有限温度下探测双流体流体动力学，这是朗道于1941年在超流体He的背景下首次研究的。朗道双流体方程应该描述整个BCS-BEC交叉的动力学过程（从库珀对的BCS凝聚到实际分子的BEC）。我的工作包括对双流体集体振荡（均匀玻色超流体中第一声和第二声的模拟）的详细研究。具有费希巴赫共振的超流体费米气体使我们第一次能够探测被困量子气体的局部平衡区域，在那里碰撞起着至关重要的作用，尽管密度仍然非常小。对被困费米超流体气体中两种流体行为的实验观察将完全类似于1938年对液态氦超流体的历史性观察，尽管量子气体的详细性质将因热力学的不同而大不相同。

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.