BCS to BEC Evolution and Quantum Phase Transitions in Superfluid Fermi Gases
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This thesis focuses on the analysis of Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) evolution in ultracold superfluid Fermi gases when the interaction between atoms is varied. The tuning of attractive interactions permits the ground state of the system to evolve from a weak fermion attraction BCS limit of loosely bound and largely overlapping Cooper pairs to a strong fermion attraction limit of tightly bound small bosonic molecules which undergo BEC. This evolution is accompanied by anomalous behavior of many superfluid properties, and reveals several quantum phase transitions. This thesis has two parts: In the first part, I analyze zero and nonzero orbital angular momentum pairing effects, and show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the $s$-wave case where the BCS to BEC evolution is just a crossover. In the second part, I analyze two-species fermion mixtures with mass and population imbalance in continuum, trap and lattice models. In contrast with the crossover physics found in the mass and population balanced mixtures, I demonstrate the existence of phase transitions between normal and superfluid phases, as well as phase separation between superfluid (paired) and normal (excess) fermions in imbalanced mixtures as a function of scattering parameter and mass and population imbalance.