Superfluidity Properties Of Fermi Gas In One-dimensional Optical Lattice

The realization of the Bose-Einstein condensate set off people’s enthusiasm to the study of ultracold atomic gases. The research of Bose system is the earliest cold atomic system by researchers,so a series of perfect results were obtained.The realization of degenerate Fermi gas also made a large number of scholars devote themselves to study Fermi gas.The degenerate Fermi gas with Interaction is the most suitable subject to study strongly correlated systems,which provided a new window to people in-depth understanding of strongly correlated many-body quantum theory. Recently,ultracold Fermi gas loaded on an optical lattice has became one of the hot topic of the research.Firstly,in this paper, we describe the basics theory of the Fermi gas. Secondly,we give a brief introduction of the density renormalization group algorithm and the strong correlation software ALPS(Algorithms and Libraries for Physics Simulations).Than,we use the method of density renonnalization group algorithm provided by the strong correlation software to study the characteristics of the superfluid state of ultracold Fermi gas in one-dimensional optical lattice below the half-filling case. We found that in the ordinary optical lattice system, When the lattice size is small than twenty-two and the strength of the repulsive interaction exceeds a critical value, the binding ernergy becomes negative while the Mott insulating core appears in the center of the trap and superfluid is on both sides. The above conclusions will be different with larger lattice size. When the repulsive interaction is increased for larger lattice size, first negative binding energy indicates that the superfluid phase appears but without Mott insulating core. When the repulsive interaction is sufficiently strong, the Mott insulating core will appear. The above discussion generalizes the conclusion of the literature. Keeping the lattice size and the fill factor unchanged.In the superlattice, when the system does not exist isolated minimum point,with increasing of the repulsive interaction,the binding energy of two Fermi atoms becomes positive in the region where it shoud be negative.The positive binding energy description that there does not exist equivalent attractive interaction in the system, so pairing does not occur between two Fermi atoms,without Cooper-pair there would not form a superfluid state. So because of the superlattice potential the superfluid property of the system is also changed.Finally, we summarize the full text which is about characteristics of the superfluid state in ultracold Fermi gases and give an outlook of the future in this field.