Mixed Gas Of Bosons And Fermions

The cooling of a Fermi gas of atoms into its degenerate regime is a cornerstone in theresearch on quantum fluids. An ultra-cold Fermi gas of atoms makes it easy forexperimentalists to access the highly degenerate regime of a pure Fermi gas. With theutilization of the magnetic-field Feshbash resonance, an ultra-cold Fermi gas of atoms enablesphysicists to study condensation of resonance molecules and of atoms and to study thecrossover between Bose-Einstein condensation of resonance molecules andBardeen-Cooper-Schrieffer condensation of atoms. These studies are important to theunderstanding of the nature of Bose-Einstein and BCS condensates and of the interplaybetween Bose and Fermi fluids. Furthermore, these studies will certainly shed significant lighton the construction of a microscopic theory of high temperature superconductivity. In thisdissertation, a model system of mixed gas of bosons and fermions, referred to as a quantumgas of bosons and fermions, is proposed for studying the interplay between Bose and Fermifluids.This dissertation is organized as follows. In Chapterâ… , the bosons and bosonic systemare introduced. In Chapterâ…¡, the fermions and fermionic system are introduced, and thepreparation of an ultracold Fermi gas of atoms is described. In Chapterâ…¢, Feshbachresonance is introduced. Feshbach resonance provides the unique ability to highly control andto tune the fermion-fermion interactions.In Chapterâ…£, a model system of mixed gas of bosons and fermions, referred to as aquantum gas of bosons and fermions (QGBF), has been proposed for studying the interplaybetween Bose and Fermi fluids and the crossover between Bose-Einstein condensation ofbosons and Bardeen-Cooper-Schrieffer condensation of fermions with a boson being a boundstate of two fermions of different spin orientations. We have found that, for a QGBF with anattractive two-body interaction between fermions, bosons and fermions condensesimultaneously. The dependence of the common critical temperature on various interactionshas been studied. The application of the QGBF to an attractive Fermi gas of atoms is brieflydiscussed with resonance molecules taken as bosons and atoms as fermions in the OGBF.