Bose - Einstein Condensates And The Nature Of The Ultra-cold Fermi Gas

With the rapid development of theory and experimental technology, studies on the ultracold fermionic gas attract a lot of interest in the field of Bose-Einstein condensation (BEC). The achievement for the molecular BEC and Fermi condensate will shed much light on our understanding of the mechanism of the high-temperature superconductivity.This thesis firstly presents the introduction to the background, corresponding experimental technologies and theoretical study of BEC. Through the description to the process for the experiment on Fermi condensation, the basic idea of magnetic Feshbach resonance is elucidated, i.e. the interaction strength between atoms can be tuned by the external magnetic field. At the same time, the theoretical model for the BCS-BEC crossover is given.Using the local density approximation and the mean field approach, the density distributions of the harmonically trapped ultracold fermionic gases are studied under a nonuniform gradient magnetic field B|-= (B₀ +αz +λz²)e -_x, where B₀ is the magnetic-field Feshbach resonant value,αandλare the external parameters, z is the spatial coordinate and e|-_x is the unit vector of the direction of the magnetic field. Under the conditions of the thermal and chemical equilibrium and appropriate parameter values, the coexistence of the regimes of molecular BEC, BCS superfluid and unitarity limit is obtained. The relations between the particle density distribution in each state of matter and the magnetic field parameters are discussed. In particular, the effect of the magnetic field to the density distribution of the molecular BEC is analyzed. As a result, it is found that the range of the BEC can be controlled by changing the parameter values of the magnetic field.