Strong Coupling Theory For Ultracold Fermi Gases In The BCS-BEC Crossover Regime

The experimental observations of Bose-Einstein condensation of resonance molecules and of BCS transition of atoms in an ultracold Fermi gas of atoms have stimulated a great interest in the BCS—BEC crossover phenomenon. The crossover regime in an ultracold Fermi gas of atoms can be easily accessed and controlled experimentally through the Feshbach resonance. The knowledge gained from the study of the crossover regime will certainly enhance our understanding of the properties of quantum fluids and of the interaction between Bose and Fermi fluids. Particularly, it will be of great value for the construction of a microscopic mechanism for high T_c superconductivity in many aspects.In the past few years, the properties of BCS—BEC crossover region have been studied in the mean field theory framework. Although this theory may successfully describe some of the properties of many systems, shortcomings do exist in many aspects such as in the description of fluctuations in the critical region and in the calculation of phase transition temperatures. In this paper, we make use of the method of quantum field theory to study properties of ultracold Fermi gases in the BCS—BEC crossover regime.This dissertation is organized as follows. In chapter I, we discuss the background and experimental technologies of BEC. In chapter II, we discuss the condensation properties of ultracold Fermi gases in the BCS—BEC crossover regime. Chapter III is the most important part of this dissertation. In this chapter, we study the properties of ultracold Fermi gases in the BCS—BEC crossover regime by using the Green's function method in the quantum field theory. We first introduce the Green's functions for fermions and bosons. Then, we derive the Dyson's equations for fermions and bosons by expanding the S matrix. And then, we simplify the self-energy functions and derive the self-consistent equations for self-energy functions. Finally, we set up a strong coupling theory for an ultracold Fermi gas of atoms in the BCS—BEC crossover regime. This work establishes a new framework for further studies in this area.