Physical properties of the normal phase, ultracold Fermi gas at unitarity: Thermodynamics, universality, and beyon

This thesis presents theoretical calculations of strongly interacting Fermi gases at unitarity. These strong interactions are obtained via Feshbach resonance which allows for the tuning of interparticle, s-wave scattering lengths using an external magnetic field. The BCS-BEC crossover was studied on both sides of a Feshbach resonance by calculating various Fermi gas thermodynamic properties. The work presented herein derives the self-energy, pressure and entropy for a population balanced Fermi gas on the BCS side of a Feshbach resonance, as well as the pressure for an imbalanced Fermi gas at unitarity in terms of a balanced Fermi gas at unitarity. Also, the BCS single-particle Hamiltonian was transformed into the BCS Bogoliubon Hamiltonian, where the universal function of the Fermi gas was calculated and compared with experimental data to extract the BCS gap energy. Overall, the derived theoretical calculations were in excellent agreement with the corresponding experimental measurements provided by several groups.