Study on cold fermionic atoms in optical lattices based on a dynamical mean field theory

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We investigated cold fermionic atoms in optical lattices by using a dynamical mean field theory. We showed that in the two-band systems the atomic density-wave, the superfluid, and the band insulating states appear depending on the orbital splitting and the attractive interaction. We obtained the phase diagram from the attractive to the repulsive interactions. We next showed that the band-selective BCS-BEC crossover occurs in the two-band system with the different ban-widths. We further investigated three-component (color) cold fermionic atoms in optical lattices. We showed that color density-wave state in the low-temperature region changes into the Fermi liquid state, the color-selective Mott state, and the paired Mott insulator depending on the strength of the repulsive interaction, as temperature is increased. These two Mott states are characteristic of the three-component system and can be detected by a photo-association spectroscopy.