Investigations On Coherent Effect Of Superfluid Atomic Fermi Gases In The BCS-BEC Crossover

Bose-Einstein condensation(BEC) is a phenomenon of macroscopic occupa-tion in one or several quantum states by a large number of identical bosons when the system temperature is below to a critical temperature. BEC is formed by Bosons quantum statistical effect, is one of the most important conclusions in quantum statistical physics. Due to the Pauli's exclusion principle, fermions can only form BEC through the formation of Cooper pairs based on the Barden-Cooper-Schrieffer (BCS) theory. It is revealed that as the interaction between par-ticles changes from attractive to repulsive in Fermi systems, a continuous tran-sition from a Bardeen-Cooper-Schrieffer(BCS) type superfluid of loosely bound pairs to BEC of molecules occurs, while BCS and BEC are the two-limiting cases of the BCS-BEC crossover.Physicist use the laser cooling and trapping techniques, make the dilute gases of certain atoms to nanoKelvin temperatures, which allows the realiza-tions of BEC in weakly interacting bosonic atomic gases and quantum degen-erate fermionic atomic gases, and using a Feshbach resonance they explore the superfluidity as well as BCS-BCS crossover in quantum degenerate Fermi gases. Ultracold atomic physics has being one of the hotspot of physics. The theory of the Fermi gases not only largely helped developing the basic Physics, but also has been used in precision measurement of high and new technology.The coherent effect of the superfluid Fermi gases in BCS-BEC cossover could be studied in microscopic description in principle. However, a complete descrip-tion of ultracold fermionic atom gases in the BCS-BEC crossover based on quan-tum many-body theory is still not clear. Moreover, the external trapping potential makes the problem more complicated. Therefore, in this dissertation we use an order-parameter equation, which is based on extended Thomas-Fermi functional theory and generalized superfluid hydrodynamics equations, to investigate co-herent properties of superfluid Fermi gases in the BCS-BEC crossover in details.An important topic in the study of ultracold Fermi gases is a direct obser-vation of superfluid properties in the BCS-BEC crossover. One expects that in-terference patterns appear after superfliud Fermi gases released from combined harmonic oscillator and optical lattice potentials due to the long-range phase co-herence. We first start from superfluid hydrodynamics equations and include a proper quantum pressure term, then obtain an order-parameter equation. We solve the order-parameter equation valid for the crossover from BCS superfluid to BEC to obtain an initial distribution of subcondensates formed in an 2D opti-cal lattice. Then useing Feynman Propagator method we investigate the coherent evolution of the subcondensates in two case: One is when both harmonic oscilla-tor and 2D optical lattice potentials are switched off; The other is when only 2D optical lattice potentials is switched off. Then compare the two cases. It has been discovered that the coherent effect of Fermi gases in 2D optical lattice is more obvious, which is more easily observed in experiments.The results in this dissertation will not only help better understanding of superfluidity properties of Ferimi gases in BCS-BEC crossover, but also is the reference for future experiments.