Multiband superfluidity and superfluid-to-band-insulator transition of strongly interacting fermionic atoms in an optical lattice

We study the multiband superfluid (SF) and the SF to band-insulator transition of strongly interacting fermionic atoms in an optical lattice at a filling of two fermions per well. We present physical arguments to show that a consistent mean-field description of this problem is obtained by retaining only intraband pairing between the fermions. Using this approach we obtain a reasonable account of the experimentally observed critical lattice depth for the SF-BI transition and the modulated components of the condensate density and make predictions for the lattice depth dependence of the quasiparticle gap which can be tested in future experiments. We also highlight some interesting features unique to cold atom superfluids within this intraband pairing approximation; for instance, the pair field is forced to be uniform in space and the Hartree field vanishes identically. These arise as a result of the fact that while the pairing interaction is cut off at the scale of the Debye frequency in conventional superconductors or at the lattice scale in tight-binding model Hamiltonians, such a cutoff is absent for cold Fermi gases.

我们研究了在每个格点填充两个费米子的光学晶格中强相互作用的费米原子的多能带超流（SF）以及从超流到能带绝缘体的转变。我们提出物理论据表明，通过仅保留费米子之间的带内配对，可以得到对该问题的一致的平均场描述。利用这种方法，我们对实验观测到的超流 - 能带绝缘体转变的临界晶格深度以及凝聚态密度的调制分量给出了合理的解释，并对准粒子能隙随晶格深度的依赖关系做出了预测，这些预测可在未来的实验中得到检验。我们还强调了在这种带内配对近似下冷原子超流所特有的一些有趣特征；例如，对场在空间中被迫是均匀的，并且哈特里场完全消失。这些情况的出现是由于以下事实：在常规超导体中配对相互作用在德拜频率的尺度上被截断，在紧束缚模型哈密顿量中在晶格尺度上被截断，而对于冷费米气体不存在这样的截断。