| Bose-Einstein condensate is that a large number of bosons would suddenly gathered in a lower energy state as much as possible when the temperature of system reach to the critical temperature, this following the statistical distribution theory of boson. The Fermi gas obey the Fermi statistical distribution in which there is only one Fermi in one quantum energy. As the experimental condition matures, more and more interested in ultracold atoms in recent years. In this paper, we will study the BCS-BEC Crossover of two-component Fermi gas with Rashba Spin-Orbit coupling in Low-dimensions at zero temperature, and pairing imbalance of Fermi gas. Mainly includes the following sections:In chapter one, we mainly introduces some basic theory of bose-Einstein condensation and the latest progress, asymmetric degenerate ultracold Fermi gas in the experimental research results. The basic principle of Feshbash resonance, which plays a big role in the study of degenerate Fermi gas.In chapter two, We discussed in the two-dimensional at zero temperature system, the quality is equal to the chemical potential is not equal to two components of some Fermi gas phase transition. Using functional-path-integral method to get self-consistent equations of the system, and then carries on the numerical analysis.In chapter three, we study the pairing imbalance of a two-component Fermi gas with Rashba spin-orbit coupling at zero temperature in two-dimensional with the same method as chapter two. The gap-order parameter and number densities are found analytically throught the thermodynamic potential at saddle point. We get a series of phase diagram of the system with numerical method. By comparing the thermodynamic potential of superfluid and phase separation to get the phase diagram. As the quality is equal and the chemical potential is not equal in the system, thus we observed in this system, the spin polarization appeared two-component particles, which caused the pairing imbalance. |
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