Quasi Two-wei Feimi Gas Bose - Einstein Condensate

The achievement of Bose-Einstein Condensation in dilute alkali gases stimulates people's research interest in the field of ultracold atoms. Recently, studies on the ultracold fermi gas attract vast focus and interest. Although two identical Fermions are not allowed to be in the same quantum state, the paired Fermions can show the characteristics of Bosons, thus the Fermi condensate is still possible, the size of fermion pair has significant impact on the characteristics of Fermi condensate. At the same time, the research on ultracold Fermi gas is helpful to solve the strong correlation problems in other fields of physics, such as the physical mechanism of high temperature superconductivity, and it is also possible to give some new insights to examine and develop the fundamentals of quantum mechanics.Firstly, this thesis presents the introduction to the research background of atomic Bose-Einstein Condensation, corresponding experimental technologies and the Gross-Pitaevskii equation for theoretical study of the system, the dimensionality's impact on the existence of condensate is analysed and the Gross-Pitaevskii equation in quasi-2D condition is discussed. By using Crank-nicolson scheme, the time-dependent Gross-Pitaevskii equation is solved numerically. In chapter 2, the fundamental idea of magnetic Feshbach resonance is introduced with the description of the experiments on Fermi condensate, i.e. the interatomic interaction can be tuned by the external magnetic field, then theoretical models for the BCS-BEC crossover.are discussed..In chapter 3, two Hamiltonians used for the description of quasi-2D BCS-BEC crossover under the mean-field treatment are discussed. Using local density approximation, the cloud size and number density of quasi-2D BCS-BEC crossover are studied in harmonically trapped ultracold fermionic gases.In Chapter 4, the whole thesis is summarized, an outlook of the future study is given.