Magnetism Of An Ultracold Fermi Gas Of Atom In An Optical Lattice

Since the realization of highly degenerate Fermi gases of atoms, the study of ultracold Fermi gases of atoms, both theoretically and experimentally has become a very active field of research. In this dissertation, we study the antiferromagnetism of an ultracold Fermi gas of atom in an optical lattice.This dissertation is organized as follows. In Chapter I, The achivement of an untracold Fermi gas of atoms is disccussed. In Chapter II, the creation of an optical lattice as well as its properties and potential applications are discussed.Chapter III, the most important part of this dissertation, contains the new results obtained in the research work performed for this dissertation. The antiferromagnetism of an ultracold Ferim gas of atom in an optical lattice is carefully studied in this chapter by using the quantum field theory method. The transverse spin susceptibility is calculated by using the Green's function and the random-phase approximation. The mean-field Hamiltonian is diagonalizd by using the Bogoliubov transformation method. The free energy is calculated using the diagonalized Hamitonian. The self-consistent equation for the antiferromagnetic gap is numerically solved in conjunction with the self-consistant equation for the chemical potential and the opening temperature T~* of the antiferromagnetic gap is found for various values of the on-site repulsion U and the filling factorδ.We find that T~* depends nearly linearly on U and that T~* is maximum forδ= 1, with its value becoming smaller as 8 becomes less than or greater than 1. We also have obtained the stoner temperature T_S fromthe stoner criterion and found that T_S is always smaller than T~*, which indicates that theremight exist the pseudo gap phenomenon associated with the antiferromagnetic phase transition.