Persistent currents in a Fermi gas confined on a ring shaped potential

This thesis aims to study an ultracold atoms Fermi gas confined on a ring-shaped potential and subjected to attractive contact interactions. In particular, we focus on the analysis of the continuous crossover between the weakly interacting regime, in which the ground state of the system is composed of weakly bound paired fermions and the strongly interacting regime, in which the tight bounds among the atoms allow to neglect the fermionic nature of the pairs. In this limit, the particles can be effectively considered as point-like bosons. In order to determine some observables that keep track of the different regimes of this crossover, we consider an artificial gauge field acting on the gas: the latter induces a persistent current in the ring that presents a periodic behaviour with respect to the artificial gauge flux. The exact solution to this model is provided using Bethe Ansatz and the periodicity can be determined at any interaction strength. Afterwards, we study in detail the number parity effect, that is measurable at low interactions and vanishes in the high interacting bosonic limit of the model, as we expect from the general theory. Such parity effect, that can be detected studying the behaviour of the persistent current, results to be a useful tool to probe the different regimes of the crossover, providing a well-defined distinction between the fermionic and the bosonic limit of the gas.