| Recent experimental advances on ultracold atomic Fermi gases pose new challenges to condensed matter theory. It has been established that there is a continuous crossover from BCS to molecular Bose-Einstein condensation (BEC) as the attractive interaction is increased. The lowest order ground state wave function which describes this crossover was first introduced by D. M. Eagles and A. J. Leggett (EL).; The present Thesis aims at formulating an improved many-body ground state wave function, which represents a modification of the Eagles-Leggett ground state to include 4-fermion, and all higher correlations. We show that this theory, importantly, contains the exactly determined 4-fermion scattering behavior at short distances and, meanwhile, reduces to composite-boson Bogoliubov physics at long distances, with the correct intermolecular interaction built in. Our approach can be viewed as a new diagrammatic methodology, based on a perturbation series in the many-body wave function as distinct from a perturbation series in the interparticle interactions. Some basic properties of this wave function are studied, and its parameters, as well as the system's equation of state, are computed beyond mean-field. Using the constraints imposed by collective mode and cloud size experiments near the unitary interaction regime, we determine the range of kFa where the new perturbation method is applicable, and the range where the positive frequency shifts in the breathing modes of a trapped atomic cloud, albeit small, may be observable. Here kF is the Fermi wave vector and a is the 2-fermion scattering length. Other observable implications of this theory are briefly discussed. We also discuss the possible implications of this theory in other physical systems, in particular high temperature superconductors. |
