Applying BCS-BEC Crossoyer Theory To High Density Fermi Matter: Studying Superfluidity In High Density Fermi Matter

According to the point of view in statistical theory, in a boson system, macroscopic numbers of particles are condensed to the lowest-energy state when the temperature falls below a critical temperature, which is defined as Bose-Einstein condensation (BEC). However, in a Fermi system, as the temperature of the system is below the Fermi temperature, no quantum state can be occupied by more than one particle in light of the Pauli principle. All states having energy below a certain value are inhabited, while the states with higher energy surpassing this critical energy remain unoccupied. The threshold energy is named as Fermi energy.Since the superconductor was discovered, immense physical qualities on it had been studied. Bardeen, Cooper, and Schrieffer (BCS) gave the theory on conventional superconductor in 1957. According the BCS theory, there are two processes to make ordinary metals evolve from normal state to superconducting state:Firstly, two electrons are attracted into each other forming cooper pairs by an attracting interaction by means of phonons; Second, energy of cooper pairs is collectively condensed into a certain lowest energy. In 1986, cooper-based high-temperature superconductor was discovered. Numerous theories relevant to HTC superconducting mechanism was put forward in the process of research, namely: with the increase of attractive interaction strength, the ground-state wave function of cooper pairs evolves continuously from BCS situation to BEC situation. From the view of experiment, the BCS-BEC crossover can be achieved by using a Feshbach resonance in a magnetic field to tune the interaction. Subsequently, most of work in this field mainly focuses on the research of ultracold fermionic gases and the BCS-BEC crossover.This thesis is arranged as follows:In chapter 1, firstly, we discuss the properties and the phase transition at zero temperature in both the Boson and Fermi system, then, we turn to background introduction and fundamental theories of Fechbach resonance. Finally, Fermi superfluidity, molecules BEC and the means to write this paper were discussed.In chapter 2, we introduce the BEC theory which is the most successful theories in condensed matter physics, the background and development of the BCS-BEC crossover theory and the research results on the BCS-BEC crossover problems.In chapter 3, we apply the standard mean-field description of BCS-BES crossover theory to high density Fermi matter and study the properties of superfluidity in high density Fermi matter. We assume the interacting form of high density Fermi matter is NSR, and research the influence of density on superfluid critical temperature and superfluid gap of Fermi matter. Based on the above research, we study the thermodynamic properties of high density Fermi matter. Our researches are mainly focusing on the situation with the scattering lengthα→±∞, because it is similar with the nuclear matter and Fermi atom gases. The result shows that the superfluid transition temperature increases with density, but the relevant increase will be suppressed by the extremely high density.