Superfluid Fermi gases in an optical lattice with random defects

Gentaro Watanabe A

Jibiao Wang, Qijin Chen

Qijin Chen, Jibiao Wang

Yoshihiro Yunomae, Ippei Danshita, Daisuke Yamamoto +2 more

Gentaro Watanabe A, 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 enable us to study the Bose and the Fermi superfluids in a unified point of view. We discuss basic static and long-wavelength properties (such as the 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 causes 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 and in the Bose case, but the mechanism of emergence in the Fermi case is very different from that in bosonic case. Other quantum phases that the cold atomic gases in optical lattices can show are also briefly discussed based on their roles as quantum simulators of Hubbard models.

Tomi Paananen

This is a study of ultra-cold Fermi gases in different systems. This thesis is focused on exotic superfluid states, for an example on the three component Fermi gas and the FFLO phase in optical lattices. In the two-components case, superfluidity is studied mainly in the case of the spin population imbalanced Fermi gases and the phase diagrams are calculated from the mean-field theory. Different methods to detect different phases in optical lattices are suggested. In the three-component case, we studied also the uniform gas and harmonically trapped system. In this case, the BCS theory is generalized to three-component gases. It is also discussed how to achieve the conditions to get an SU(3)-symmetric Hamiltonian in optical lattices. The thesis is divided in chapters as follows: Chapter 1 is an introduction to the field of cold quantum gases. In chapter 2 optical lattices and their experimental characteristics are discussed. Chapter 3 deals with two-components Fermi gases in optical lattices and the paired states in lattices. In chapter 4 three-component Fermi gases with and without a harmonic trap are explored, and the pairing mechanisms are studied. In this chapter, we also discuss three-component Fermi gases in optical lattices. Chapter 5 devoted to the higher order correlations, and what they can tell about the paired states. Chapter 6 concludes the thesis.