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

利用动力学平均场理论研究了光学晶格中的冷费米子原子。我们发现在双带系统中，原子密度波、超流和带绝缘态的出现依赖于轨道分裂和吸引相互作用。我们得到了从吸引力到排斥力的相图。我们接下来证明了带选择性BCS-BEC交叉发生在具有不同带宽的两带系统中。我们进一步研究了光学晶格中的三分量（色）冷费米子原子。我们发现，在低温区的颜色密度波状态的费米液体状态，颜色选择性的莫特状态，和成对的莫特绝缘体取决于排斥相互作用的强度，随着温度的升高。这两个莫特态是三组分体系的特征，可以通过光缔合光谱检测到。

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.