Effects Of Dipolar Long-range Interaction And Impurity Scattering On Pairing And Superfluidity In Ultracold Atomic Fermi Gases

This dissertation is devoted to the theoretical investigation of long range dipole-dipole interaction (DDI) and nonmagnetic impurity effects on superfluid pairing and BCS-BEC crossover in ultracold atomic Fermi gases. The first chapter is an introduction to the background. In chapter 2, we first construct a pairing fluctuation theory for equal spin pairing (or single component fermion pairing),based on the already existing G0G scheme pairing fluctuation theory. In contrast to the spin singlet case, here the pairing fluctuation self-energy has one extra exchange diagram. In addition, the present pairing wave function has odd parity.Furthermore, we expand the many-body interaction by using spherical harmonics and obtain the dominant pairing channel caused by DDI, i.e., the pz-wave channel,followed by calculating the corresponding pz-wave symmetry factor. Finally, we solve the gap equation, fermion number equation and pseudogap equation self-consistently, and then study the finite temperature superfluid transition phase diagram and BCS-BEC crossover in one component dipolar Fermi gases. We find that, in contrast to the short range s-wave case, here the long range property of DDI and dominated pz-wave pairing symmetry cause a reentrant behavior of Tc during the crossover from BCS to BEC. The long range interaction puts the system into the effective high density regime, and in the vicinity of ?=0, where? is the chemical potential, the long range interaction and anisotropic pz-wave pairing symmetry, synergetically, make the repulsive interaction energy of pairs dominates over the kinetic energy, along z direction, in which the dipole moments are fully polarized. Then the system forms a Wigner-like crystal structure in z direction, which is called pair density wave (PDW). As a consequence, the uniform superfluid Tc exhibits a reentrant behavior near ?=0.In chapter 3, we study the finite temperature thermodynamics and superfluid density below Tc, in single component dipolar Fermi gases. Here the pairing sym-metry is p-wave polar state with a line node on the Fermi surface. Consequently,the temperature dependences of both superfluid density and the heat capacity are different from the s-wave pairing case, in the fermionic regime. In addition,using local density approximation (LDA), we calculate the density profile of dipo-lar Fermi gases in a three dimensional isotropic harmonic trap, for both normal and superfluid state, with an emphasis on the varying temperature and pairing strength effects.In chapter 4, we study the effects of nonmagnetic impurities on the s-wave fermion pairing and BCS-BEC crossover in ultracold atomic Fermi gases, including the impurity renormalization on frequency and gap function, impurity effects on fermion density of states, superfluid Tc, as well as superfluid order parameter and superfluid density. We find that, while the system is less sensitive to impurities in the Born limit, strong impurity scatters in the unitary scattering regime will highly renormalize both the frequency and the gaps, resulting in a spectral weight transfer from the coherence peak to impurity band and subgaps, and leading to a finite lifetime of Bogoliubov quasiparticles and fermion pairs, and hence a significant suppression of the superfluid Tc and superfluid density. In the deep BCS region, with small gaps, the superfluidity may be readily destroyed by strong impurity scatters,resulting in a quantum superfluid-insulator transition (SIT). In the presence of strong impurity scattering, Anderson's theorem breaks down. In comparison,the unitary and BEC regimes are not as sensitive to impurities as BCS regime, due to relatively larger pairing gaps.Chapter 5 is the summary and outlook.