Superfluidity And Pairing Phenomena Of Ultracold Atomic Fermi Gases In A Two-dimensional Optical Lattice

Ultracold atomic Fermi gases have become a powerful platform for investigating condensed matter physics over the past two decades,owing to their multiple experimentally tunable control parameters.They can exhibit a perfect crossover from a BCS type of superfluidity to Bose-Einstein condensation(BEC)of atom pairs,as the pairing strength is tuned from weak to strong via a Feshbach resonance.In this thesis,we study the superfluid behavior and pairing phenomena of population balanced and imbalanced ultracold atomic Fermi gases with a short range attractive interaction in a two-dimensional optical lattice(2DOL),using a pairing fluctuation theory,within the context of BCS-BEC crossover.We find that the mixing of lattice and continuum dimensions,together with population imbalance,has an extraordinary effect on pairing and the superfluidity of atomic Fermi gases.Remarkably,under the combined effects of Pauli exclusion and two lattice dimensions,population imbalance can be used to effectively suppress pairing fluctuations,so as to achieve ultrahigh superfluid transition temperature.We find widespread pseudogap phenomena beyond the BCS regime as the system undergoes BCSBEC crossover.The shape and topology of the Fermi surface play an important role in the behavior of superfluidity and pairing phenomena.And the superfluid transition temperature is strongly suppressed with decreasing hopping integral t and lattice constant d for all population imbalance p≥ 0,in agreement with the evolution of the Fermi surface.In a population balanced case,for relatively large lattice constant d and small hopping integral t,the superfluid transition temperature Tc exhibits a remarkable reentrant behavior as a function of the interaction strength,and leads to a pair density wave(PDW)ground state,where Tc vanishes,for a range of intermediate coupling strength,due to the strong inter-pair repulsive interaction caused by relatively large pair size and moderately strong pairing interaction.In the unitary and weak-coupling regimes,the effective filling factor in the first Brillouin zone(BZ)of the lattice plane may become higher than 1/2,so that the nature of the in-plane and overall pairing changes from particle-like to hole-like as the contributions from lattice dimensions become dominant,with an unexpected nonmonotonic dependence of the chemical potential on the pairing strength and a gapped pair dispersion which serves to reduce the pseudogap.The BEC asymptotic behaviors exhibit distinct power law dependencies on the interaction strength,compared to cases of pure 3D lattice,3D continuum,and IDOL.Meanwhile,in a population imbalanced case,intermediate temperature superfluidity emerges in the BCS and unitary regimes,due to the Fermi surface mismatch between the majority and minority fermions,and the phase of intermediate temperature superfluidity shrinks to zero as imbalance p increases.For relatively small lattice constant d and large hopping integral t,a nonzero p may lead to significant enhancement of Tc on the BEC side of the unitarity,compared with its p=0 counterpart.We find that Tc for p>0 may increase dramatically as the system enters further into the deep BEC regime,where pairing fluctuations are effectively suppressed and thus the pseudogap is reduced,with the nature of the overall pairing evolving from particle-like to hole-like.The Pauli blocking effect between the confined momentum distributions of the excessive majority fermions and paired fermions leads to the distinct hole-like pairing and the suppression of the pseudogap in the BEC region,compared with the population balanced case.A stable polarized superfluid state at both zero and finite temperatures resides only in a small portion of the multi-dimensional phase space,mainly in the low p and bosonic regime of intermediate pairing strength,and for relatively large t and small d.We find that low temperature,strong interaction and large population imbalance,together with small hopping integral and large lattice constant,contribute to increase the distribution of paired fermions in the high kz momentum space and thus add to the occurrence of hole-like pairing and the suppression of the pseudogap in the BEC regime,and a first order phase transition from a homogeneous superfluid to a finite temperature PDW state may eventually emerge.Finally,we show the typical evolution behaviors of various gaps and superfluid density as a function of temperature at different interaction strengths and in both particle-like and hole-like pairing regions,and thereby,present a complete and systematic study on the superfluid and pairing behaviors of imbalanced ultracold atomic Fermi gases in a two-dimensional optical lattice.These theoretical predictions can be tested in future experiments,with all parameters experimentally tunable.