| Summary: | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2015. === Cataloged from PDF version of thesis. === Includes bibliographical references (pages 241-259). === In this thesis, I present experiments that study the thermodynamics and solitonic excitations of a strongly-interacting Fermi gas, realized with 6Li atoms at a Feshbach resonance where the scattering length is large. The strongly-interacting Fermi gas, also called the unitary Fermi gas, exhibits a novel superfluidity that is a crossover of the Bose-Einstein condensation of molecules and Bardeen-Cooper-Schrieffer superfluid of long-ranged Cooper pairs, with a high critical temperature and a small healing length. The unitary Fermi gas serves as a model for other strongly correlated fermions, such dilute neutron matter in the crust of neutron stars. The homogeneous equation of state of a unitary Fermi gas was measured with high precision via a method that requires no theoretical input nor external thermometer. The measurement provides an accurate value of the critical temperature and the Bertsch parameter that characterizes the ground state energy. The equation of state is then used to provide a prediction for the higher collective modes. I also describe a method to obtain the equation of state of global thermodynamic quantitites of harmonically trapped gases from their column density. In another set of experiments, long-lived solitonic excitation was generated via a one-sided phase imprinting. The excitation's slow oscillation within the trapped superfluid indicates a large ratio of the inertial mass to the gravitational mass. Tomographic imaging identifies the excitation to be a solitonic vortex. The precession period in the BEC-BCS crossover was measured, and good agreement is found with predictions from a hydrodynamic model. Prior to the formation of the vortex, the evolution of the superfluid after the phase imprint was investigated. A dark planar soliton was observed to emerge after the phase imprint, undergo snake instability, subsequently decay into a ring defect, and eventually convert into a single vortex. The growth rate of the transverse modes during the snake instability was measured. === by Mark Jen-Hao Ku. === Ph. D.
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