Exotic Superfluidity And Pairing Phenomena In Atomic Fermi Gases In Mixed Dimensions

In this dissertation,we mainly investigate the effects of mixed dimensionality on the superfluid and pairing phenomena of a two-component ultracold atomic Fermi gas with a short-range pairing interaction,while one component is confined on a.one-dimensional(1D)optical lattice whereas the other is in a homogeneous 3D continuum.We study the finite temperature phase diagrams throughout the entire BCS-BEC crossover,using a GOG scheme pairing fluctuation theory.We find that mixed dimensionality causes a large Fermi surface mismatch,result in exotic phenomena that not found in conventional Fermi mixtures without dimension mismatch.In Chapter 1,we begin with a brief introduction to the BCS theory,on this basis we raise the BCS-BEC crossover theory.Then we briefly compare the differences betwween the three schemes of T-matrix,and choose the GOG scheme as a theoretical tool of our study.In Chapter 2,we firstly review some important experiments in ultracold Fermi gases.And secondly we introduce the method to realize a mixed dimensional cold atomic system by applying a species-selective optical lattice,and the progresses achieved so far.In Chapter 3,we rewrite the BCS theory in the language of Green's function,and then extend it to a BSC-BEC crossover theory in T-matrix formalism by considering the finite momentum pairs which lead to the pseudogap.We finally get a complete set of self-consistent equations for the excitation gap(or transition temperature),chemical potential,and the pseudogap.In Chapter 4,we obtain the 2D+3D T-matrix formalism and equations by applying the GOG scheme pair fluctuation theory to the mixed dimensional sys-tems.We explore systematically the effects of mixed dimensionality on the pairing and superfluidity at finite temperatures in two-component ultracold atomic Fermi gases.We study the behavior of the superfluid transition temperatures Tc as a function of interaction strength throughout the entire BCS-BEC crossover with a varying optical lattice spacing.We find that the Fermi surface geometry of the lattice component evolves with the lattice parameters such as tunneling amplitude(or hopping integral)and lattice spacing,which can be used to adjust the mis-match of Fermi surfaces.In some cases,Tc solutions bear similarity with simple population imbalance Fermi gases in a 3D continuum,such as intermediate tem-perature superfluidity,but with some distinct features.For small lattice spacing,Tc pinched and split into two parts at intermediate coupling strength,exhibiting a reentrant superfluidity,where the system form a possible Wigner crystallization of the pairs,and hence a pair density wave(PDW)ground state without super-fluidity.For all lattice spacings,Tc curves quickly converge and approach roughly a BEC asymptote as the pure 3D continuum system,and the asymptote increases with the lattice spacing.This result is quite distinct from the pure ID optical lattice case.Finally,we find that one can effectively raise Fermi energy of mixed dimensional systems by increasing the hopping integral and lattice spacing of the optical lattice.This then causes a substantially enhanced Tc,higher than any existing know Fermi systems.The last chapter is a summary of this dissertation and looks forward to some problems that can still be discussed in the future.