BEC-BCS crossover in ultra-cold Fermi gases

Abstract

Ultra-cold atomic gas has attracted intensive interests due to its extreme flexibility. Particularly, the fact that the interaction between atoms can be tuned with Feshbach resonance has stimulated the study of BEC-BCS crossover in two-component Fermi gas. The crossover demonstrates that a two-component Fermi gas will smoothly evolve from a condensate of weakly correlated Cooper pairs to a Bose-Einstein condensation of strongly bound bosonic molecules when increasing the attractive interaction between different components. In this thesis, we study theoretically the superfluid properties of two-component Fermi gases with certain kinds of impurity. With random-phase approximation, the sound velocity, the critical velocity and the dynamic structure factor were calculated for the experimentally achieved mixture of Bose and Fermi superfluid, where the impurity is a Bose-Einstein condensation. Further comments with respect to the results are provided. Moreover, motivated by the realization of spin-orbit coupling with artificial non-Abelian gauge fields, we study aspects of the two-fluid model in the two-dimensional Fermi gas with the effects from both spin-orbit coupling and static impurities. By incorporating the effects of disorder at the level of Gaussian fluctuation, we calculated the paring gap and normal density of the system. Our results can be compared with experiments in the future.