Dynamical Response of an Interacting 1-Dimensional Fermi Gas

Ultracold atoms with optical lattices provide a highly tunable system to measure the dynamic structure factor, $S(q,\omega)$, of an interacting one-dimensional (1D) Fermi gas. We use the two lowest hyperfine levels of the $^6$Li atom to form a pseudo-spin-1/2 system whose interactions are tunable via a Feshbach resonance. Bragg spectroscopy is used to measure the dynamic response of the 1D system to density (``charge'') mode excitations at a momentum $q$ and frequency $\omega$. In this thesis, we provide a quantitative comparison between the experimental result and the theoretical calculations based on Tomonaga-Luttinger theory.