The Lattice Effect Of Ultracold Fermi Gases In Two-dimensional Optical Lattice

In this article,we mainly investigate the lattice effect on superfluid behavior and pairing phenomena of ultracold atomic Fermi gas in two-dimensional optical lattice,by applying G0G scheme pairing fluctuation theory.There will be an interference between the beams with same frequency propagating toward each other,which is a laser field with alternating light and dark phases and a periodic distribution of field strength.Due to the potential distribution charged by the interaction between the dipole of the atom and the field,the atoms perform periodic central motion.This potential distribution is the optical lattice.Fermi gases are located in an array of one-dimensional tubes in two-dimensional optical lattice,which is a continuum-lattice mixing system.For the physically small lattice hopping integral,the in-plane lattice band will be fully occupied under tight-binding approximation.In this way,the two-dimensional optical lattice is a quasi-one-dimensional system,and be different from the three-dimensional system or optical lattice,having various effect in terms of pairing phenomena and superfluid behavior.In Chapter 1,we begin with a brief introduction to the BCS theory and BCS-BEC crossover theory.In Chapter 2,the superfluid behavior in optical lattice and realization of mixed di-mensional cold atomic system are introduced.In Chapter 3,we rewrite the BCS theory in language of Green's function,and derive the T-matrix expression in G0G scheme,giving the self-consistent equations describing the superfluid behavior.The BCS-BEC crossover is in-vestigated by applying pseudogap.In Chapter 4,based on the self-consistent equations,we numerically analyze the pairing phenomena and superfluid behavior in two-dimensional optical lattice,and the effect of hopping integral and lattice constant.The situations in BCS regime,unitary regime and BEC regime are studied respectively.Superfluid transition temperature is increasing along with the increase of hopping integral and lattice behavior.And we found that,in the BEC regime,because of the shrink of Fermi surface and transition of Fermi energy from positive to negative,there are a special curve for superfluid transition temperature towards hop-ping integral and lattice constant.With the increase of lattice constant and hopping integral,the values of total gap energy,pseudogap energy and order parameter increase.At the same time,with the increase of interaction,the system changes from BCS regime to BEC regime,and the change of total gap energy tends to be more stable.We found that in the deep BCS area,there are pseudogap energy above and below Tc.The total gap energy is a smooth function crossing Tc,and the order parameter becomes 0 at TC.The pseudogap energy decreases with temperature below Tc.At a low temperature,T has a power law relationship with the superfluid density.