Spin Density Correlation And Ferromagnetic Phase Transition In An Ultracold Fermi Gas

As a new developing inter-discipline, the ultracold atoms physics has become a hot point. The realization of BEC (Bose-Einstein condensation) in alkali metal atoms bring it into a new level. As the improvement of the techniques both in theory and experiment, the objects of the research had been shifted to the ultracold Fermi atoms from the ultracold Bose atoms. The scope of investigation for the ultracold atoms is largely expanded by Feshbach resonance and the realization of degenerate two-component Fermi gas. Many particular phenomenons of the Fermi gas under the extreme conditions have been realized experimentally, such as the BCS (Bardeen-Cooper-Schreiffer)-BEC crossover, the ferromagnetism or the superfluidity and soThe Fermi gas of ultracold atoms exhibits ferromagnetism when the interatomic interaction is strong enough. The nature of ferromagnetism is the strong correlation effect among the nonlocal atoms. So we can claim that the correlation effect is closely related to the ferromagnetic phase transition. As a intrinsic property, the spin or its spatial distribution is an important issue that we should pay more attention to. Using the Stoner model and the mean-field theory, we study the ferromagnetic phase transition of the two-component Fermi gas of N ultracold Li-6atoms. The spin density-spin density correlation function (spin density correlation function for short) that describes the correlation effect between spin densities is obtained by using the Feynman path integral approach. The relationships between the spin density correlation function and the relative distance between atoms, the interaction strength, the temperature or the pressure in the ferromagnetic phase transition region are investigated through numerical computations. Our results show that the spin density correlation function has a minimum value as a function of the relative atomic distance, and an obvious sudden change (or maximal value) as functions of the interaction strength, the temperature or the pressure in the ferromagnetic phase transition region. These findings imply that the correlation function of spin density can be well characterized the ferromagnetic phase transition of the Fermi gas of ultracold Li-6atoms.This dissertation is divided into four chapters. In Chapter1, we give a brief overview of the ultracold Fermi gas, especially the magnetic Feshbach resonance of the Fermi gas of ultracold atoms. In Chapter2, a brief introduction of the quantum magnetism of the ultracold Fermi gas is given, including the itinerant ferromagnetism and the antiferromagnetism. Chapters3and4are the main parts of this dissertation. Chapter3is composed of the detail derivation of the interaction between two particles and the simplification of Hamiltonian in the Stoner model using the mean-field theory. In Chapter4, the numerical relationships between the spin density correlation function and the relative distance between atoms, the interaction strength, the temperature or the pressure in the ferromagnetic phase transition region are studied by using the Feynman path integral method.