Applving BCWS-BEC Crossover Theory To Investigate The Superfluidity Of Fermi-Fermi Mixtures

In this thesis, we mainly investigate the superfluidity and pseudogap phe-nomena in ultracold Fermi-Fermi mixtures as they undergo the Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover, using a pairing fluctuation theory. We focus on their finite temperature phase diagrams in a3D isotropic harmonic trap and the distribution of exotic pairing states Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in phase diagrams.In Chapter1, we begin with a brief review of the BCS theory, then we introduce the history of BCS-BEC crossover theory and its application in high temperature superconductors. Lastly, we give several important experimental progresses in ultracold Fermi gases, which are the best systems to realize the BCS-BEC crossover.In Chapter2, we begin with an introduction to the ground state wavefunc-tion of the BCS-BEC crossover theory, i.e., the BCS-Leggett ground state. Then we deduce the BCS theory and the BCS-BEC crossover theory in a manner of T-matrix approach in detail. Lastly, we compare three choices for the T-matrix and give the differences among them.In Chapter3, we present some representative phase diagrams of Fermi-Fermi mixtures as they undergo BCS-BEC crossover with population and mass imbal-ances (as well as the imbalance of trapping frequencies), using a pairing fluc-tuation theory. We focus on the finite temperature and trap effects, with an emphasis on the mixture of6Li and40K atoms, while keeping other mass ratios in mind. We show that in the BEC regime there exist exotic types of phase sep-arations with a normal Fermi gas core in the trap center surrounded by paired (superfluid or pseudogap) state in the outer shell. This type of phase separation is different from conventional types. We also show that in the BCS and unitary regimes there exist sandwich-like shell structures at low temperature with super-fluid or pseudogapped normal state in the central shell, especially when the light species is the majority. Such a sandwich-like shell structure appears when the mass imbalance is beyond a certain threshold. Lastly, we change the trapping frequencies between different species and find that it is similar to that of changing the mass ratios.In Chapter4, we give some typical phase diagrams of the FFLO states in a homogeneous Fermi-Fermi mixtures as they undergo BCS-BEC crossover with population and mass imbalances, using a pairing fluctuation theory. We also focus on the finite temperature effect and with an emphasis on the6Li and40K mixture. From these phase diagrams we know that we can get the highest superfluid transition temperature Tc at unitarity. We also find that when the heavier species is the majority, the stable region of FFLO superfluid becomes larger as the mass ratio increases, and the superfluid transition temperature also becomes higher. This makes it easier to be detected in experiments. In contrast, when the lighter species is the majority, the stable region of FFLO superfluid may become smaller and smaller as the mass ratio increases and then disappears at a certain threshold. So in order to find stable FFLO states in3D Fermi gases, we may take large mass ratio of Fermi-Fermi mixtures, make the heavier species is majority and tune the interaction near unitarity to do experiments.In Chapter5, we give a concluding remarks on this thesis and present some topics that we can work on in the future.