• Fano-Feshbach Resonances
• BCS-BEC Crossover
• Quantum Gases

Aim of this thesis work is to explore the evolution of superfluidity in a quantum gas of interacting fermionic particles crossing over from a Bardeen-Cooper-Schrieffer (BCS) superfluidity of Cooper pairs to a Bose-Einstein Condensation (BEC) of composite bosons: in particular, known universal behavior results are extended within a wider class of interaction potentials. Though the BCS-BEC crossover is a crucial concept realized in many different systems including high-temperature superconductors, quantum gases are characterized by extreme conditions of precision and control and therefore represent a very convenient experimental and theoretical laboratory to probe the idea and link it to microscopic models, for example with energy-dependent Fano-Feshbach Resonaces. Using a numerical and theoretical framework in a mean field and zero temperature approximation, a particular model is commented and its results are analyzed. Final results displays and extends universal characteristics of the system where only the fermionic degree of freedom are inserted and energy-dependence is included. This work is a natural precursor of a beyond mean-field calculation (Quantum Monte Carlo techniques).