Simultaneous Onset Of Condensation Of Molecules And Atoms In An Attractive Fermi Gas Of Atoms

The crossover regime of Bose-Einstein condensation (BEC) of molecules and Bardeen-Cooper-Schrieer (BCS) condensation of atoms in a Fermi gas of atoms has recently been an active research field since it contains abundant information on the interplay of two kinds of quantum fluids (the Bose and Fermi quantum liquids) that exist in the nature. Progress in understanding of this crossover regime will certainly furnish significant implications and shed much light on our understanding of a plethora of macroscopic quantum phenomena including high temperature superconductivity.This thesis firstly presents the introduction to physics in the crossover between BEC and BCS condensation using an ultracold gas of atomic fermions. From the theoretical prediction to the experimental realization of BEC, many procedures were followed to the system that creates degenerate Fermi gas (DFG) of atoms which has its unique properties.Scattering resonances in these ultracold gases (known as Feshbach resonances), discussed in chapter 2, provide the unique ability to highly control and to tune the fermion-fermion interactions. A specific example is given after the general description.Chapter 3 presents the theory of BCS-BEC crossover regime and the respective critical temperatures. The experimental parameters and diagrams of BCS-BEC crossover were also shown in this chapter.Our study of BCS-BEC crossover regime is given in the last chapter concerning the theoretical calculations according to the crossover regime in a Fermi gas of atoms with an attractive two-body interaction between atoms. The self-consistent equations for the order parameters of BEC of molecules and BCS condensation of atoms have been derived within the Hartree-Fock-Bogoliubov approximation from the path integral representation of the grand partition function. We found that the order parameters for BEC and BCS are proportional to each other, which implies that BEC and BCS onsets simultaneously. We also concluded that the common critical temperature of BEC and BCS increases as the average number of molecules increases and that the atom-molecule coupling enhances the common critical temperature.