Exotic fermionic superfluidity in low-dimensional atomic Fermi gases

Superfluidity and superconductivity are quantum mechanical features of gases of atoms cooled down close to -273.15 Celsius, where they display neither viscosity nor electrical resistence. Forcing a gas to live in a two-dimensional space almost all the superfluidity-related properties are enhanced and easier to test experimentally. In this thesis we conduct a study of a typical 2D phase, called FFLO, and we built a general setting to address the investigation of Fermi gases when brought to low-dimensionality by a new type of confinement. Results presented include signatures and protocols experimentalists might use to probe the systems we described.