Competition between magnetic and superconducting pairing exchange interactions in confined systems

We analyze the competition between magnetic and pairing interactions in confined systems relevant to either small superconducting grains or trapped ultracold atomic gases. The response to the imbalance of the chemical potential for the two spin states leads to various inhomogeneous profiles of the pair energy distribution. We show that the position in the energy spectrum for the unpaired particles can be tuned by varying the filling or the pairing strength. When small grains are considered, the antiferromagnetic exchange stabilizes the pair correlations, whereas for Fermi gases, a transition from a mixed configuration to a phase-separated one beyond a critical polarization threshold appears, as does an unconventional phase with a paired shell around a normal core.