Gentaro Watanabe, Sukjin Yoon
We review our studies on Bose and Fermi superfluids of cold atomic gases in optical lattices at zero temperature. Especially, we focus on superfluid Fermi gases along the crossover between the Bardeen-Cooper-Schrieffer (BCS) and the Bose-Einstein condensate (BEC) states, which enables us to study the Bose and Fermi superfluids in a unified point of view. We discuss basic static and long-wavelength properties (such as equation of state, incompressibility, and effective mass), energetic stability, and energy band structures of the superfluid Fermi gases in an optical lattice periodic along one spatial direction. The periodic potential makes pairs of atoms to be strongly bound, and this can affect the static and long-wavelength properties and the stability of the superflow. Regarding the band structure, a peculiar loop structure called "swallowtail" can appear in superfluid Fermi gases as well as in the Bose case while its mechanism of the emergence is very different from the bosonic counterpart. Other quantum phases that the cold atomic gases in optical lattices can show are also briefly discussed from their role as quantum simulators of the Hubbard models.
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http://arxiv.org/abs/1301.3363
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