Density Correlation And Ferromagnetic Phase Transition In A Fermi Gas Of Ultracold Atoms

The realization of Bose-Einstein condensed in alkali metal atoms brought about a great advance in ultracold atom physics. With the development of techniques and experimental methods, the emphasis of study shifted to ultracold Fermionic atoms. In1999, the acquirement of degenerate Fermi gases of ultracold atoms provided new directions for research to ultracold Fermi atoms. A set of exotic phenomena have been found in the study, such as quantum degenerate effects, phase transitions and so on. The realization of the Feshbach resonance largely expanded the scope of study on ultracold atoms. In the experiments on ultracold atoms, the strength and sign of interparticle interactions can be easily adjusted by using the Feshbach resonance. Then, many properties under extreme conditions have been discovered, for example, the BCS-BEC crossover, superfluidity and so on.The Fermi gas of ultracold atoms with repulsive interactions undergoes the ferromagnetic phase transition under certain conditions, which is one of important quantum characteristics of ultracold Fermionic atoms. The essence of the ferromagnetic phase transition is a quantum effect, with the phase transition being the correlation effect arising from the interparticle interactions. The behavior of the spatial density correlation function of the system has a close relationship with the ferromagnetic phase transition. The structure and properties of system will change if the correlation effects changed. In the past few years, study on the two-body correlation of ultracold atoms has made some progress, and the density correlation effect of ultracold Bosnic atoms and Fermionic atoms has been given much attention. Density correlation effects become a powerful tool to investigate quantum characteristics of many-body systems, so we study the density correlation effect in the ferromagnetic phase transition.This paper is divided into four chapters. In Chapter â… , we introduce the research progress of ultracold atom physics and experimental methods on ultracold atoms, especially important properties of BCS-BEC crossover. In Chapter â…¡, two important phase transitions in the Fermionic gas of ultracold atoms:The ferromagnetic phase transition and the superfluid transition. In Chapters â…¢ and â…£ which are the most important part of this dissertation, that is, density correlation and ferromagnetic phase transition in a Fermi gas of ultracold atoms, we study the properties of the ferromagnetic phase transition of a Fermi gas of ultracold atoms with interactions using the Stoner model and the mean-field approximation, and study the density correlation function by using the path integral approach. Then, through numerical computations we study the properties of the density correlation function in the ferromagnetic phase transition region, that is, the relationship between the density correlation function and magnetization as well as other thermodynamic properties in the ferromagnetic phase region. Finally, we have come to the conclusion that the density correlation function can be used to characterize the ferromagnetic phase transition.