Francesco Pirolo

My research project is framed within the low-energy physics of many-body quantum systems. Under the supervision of P. Pieri and collaborators, we will explore the physics of polarized fermionic systems in low dimensionality at zero temperature. Similar systems analyzed in 3D have exhibited an exotic superconducting phase known as FFLO (Fulde–Ferrell–Larkin–Ovchinnikov), characterized by Cooper pairs with a non-zero momentum and a spatially modulated superconducting gap. Ultracold atomic systems represent ideal setups for the observation of this phase; however, in 3D, the FFLO phase is almost entirely covered by a phase separation region, making direct observation impossible. Investigating such systems in lower dimensions, particularly determining a phase diagram that links the polarization of the system to the scattering length, would clarify the parameter space in which the aforementioned phase might be observed. The proposed work is entirely theoretical and concerns the solution (initially non-self-consistent and subsequently self-consistent) of the Dyson series, focusing only on the series of diagrams, commonly referred to as “ladder diagrams.” This approach, known in the literature as the t-matrix approach, allows us to extract crucial quantities (e.g., the pair susceptibility) for the characterization of the system.