Presented in this thesis is the construction of an apparatus to produce optically trapped lithium-6 atoms in the two lowest hyperfine states, the observation of cooling the trapped atoms by parametric excitation, and a study on the searching for itinerant ferromagnetism in a two-dimensional Fermi gas.

In the parametric cooling experiment, a technique is developed to cool a cold atomic Fermi gas by parametrically driving atomic motions in a crossed-beam optical dipole trap. This method employs the anharmonicity of the optical dipole trap, in which the hotter atoms at the edge of the trap feel the anharmonic components of the trapping potential, while the colder atoms in the center of the trap feel the harmonic one. By modulating the trap depth with frequencies that are resonant with the anharmonic components, hotter atoms are selectively excited out of the trap while keeping the colder atoms in the trap, generating a cooling effect.

An analytical study of itinerant ferromagnetism in a two-dimensional atomic Fermi gas is presented, based on the past experiments done with three-dimensional Fermi gases. Here, the formation of repulsive polarons in a strongly-interacting Fermi gas is used as an initial condition. Then the observation of itinerant ferromagnetism is realized by detection of ferromagnetic domains in the two-dimensional gas.

Additionally, an experiment and simulation is performed on the effect of velocity-changing collisions on the absolute absorption of lithium-6 vapor in an argon buffer gas. The dependence of probe beam absorption is observed by variation of beam intensity and spatial evolution. The simulation of an effective three-level energy model with velocity-changing collisions determines a collision rate that agrees with transmission data collected.