A Study On The Phenomenological Theory Of Batching Fermi Agglomerates In BCS - BEC

With the development of laser cooling and trapping techniques in recent years, the Bose-Einstein Condensation (BEC) in weak interacting bosonic atom gases, the quan-tum degeneracy of fermionic atom gases and condensation of fermionic atom pairs (described by Bardeen-Cooper-Schrieffer theory, BCS theory) have been realized in the experiments. As the invention of the Feshbach resonance technique, people can also tune the strength of interactions among atoms from large negative to large positive values, so that the BCS-BEC crossover (BBC) of fermionic atom gases has also been observed.The atoms in the trapped Fermi condensates in the BBC regime have very stong interaction, and thus have many properties different from the ones in the BCS and BEC regimes. As a consequence, the research in BBC becomes a rapidly developing and very important interdisciplinary of atomic molecular physics, statistical and condense matter physics and so on. Many experiments have been done and a lot of novel charac-teristics have been observed in the BBC regime. As the development of experiments, researchers have also made many theoretical achievements.However, the microscopic mechanism of the trapped Fermi condensates in the B-BC regime is still not clear. Besides, the external trapping potential makes the system inhomogeneous. And it’s even harder to handle the dynamics of the strongly interact-ing quantum many-body problem. Therefore it is a possible and conventional method to construct a series of phenomenological theories. Quantum hydrodynamics in the superfluid phase and kinetic dynamics in the normal phase could be used to describe the physical properties of the trapped Fermi condensates in the BBC regime very well. With the addition of the phenomenological equation of state, we can solve many prob-lems in the BBC regime.Our main research results on the phenomenological theory in the BBC can be sum-marized as follows:1. We propose a phenomenological equation of state for the trapped Fermi con-densates, which is suitable for the whole interacting regime. Its asymptotic behavior exactly matches the series expansion in the BCS and BEC limits, as well as the expres- sion obtained from quantum Monte-Carlo simulations in the unitarity limit. Based on the equation of state, we derive the quantum hydrodynamical equation of the trapped Fermi condensates in the BBC and study the ground state properties of the system. Through the phenomenological equation of state, our quantum hydrodynamical equa-tion is beyond mean-field approximation and valid in the entire crossover regimes.2. We study the dynamics and anisotropic free expansion of the strong interacting trapped Fermi condensates near the unitarity limit. By introducing the time-dependent density functional Lagrangian density and a Fetter-like wavefunction, we obtain the dy-namic equation of the radii of the condensates and successfully simulate the expansion of the Fermi gas observed experimentally by O’Hara et al. in2002. The theoretical results agree well with the experiments.3. We start from the kinetic equation and the quantum hydrodynamical equation of the trapped Fermi gas in the BBC in the normal phase and superfluid phase respective-ly. With the scaling solutions, we study the properties of the collective excitations. We calculate the viscous relaxation rate, damping and transition of the collective excita-tions in the system. It shows that the dependence of the collective modes and damping on the temperature and interaction is consistent with the experiments. It also provides a possible way to interpret the mode transition between collisionless behavior and hy-drodynamics behavior.The phenomenological theoretical results in this dissertation can give us better understanding of the properties of the trapped Fermi gas in the BCS-BEC crossover, and may be useful to the experiments and the construction of a microscopic theory in the future.