Strongly Correlated Fermi Gases

The thrust of this research is the study of strongly interacting Fermi gases at the interface between condensed matter physics and the physics of ultracold atomic gases. A particular emphasis is placed on how strong few-body correlations in these systems impact the many-body behavior. The first half of this thesis comprises three theoretical studies on cold atoms: Fermi gases with SU(N) symmetry, how to engineer long-lived trimers, and frustrated Feshbach resonances. The second half contains three theoretical studies in the solid state: electron-exciton interactions in doped two-dimensional semiconductors, exciton-polaritons in quantum wells of finite width, and Rydberg exciton-polaritons in magnetic fields.