Leading order kFa corrections to the free energy and phase separation in two-component Fermion systems

We study phase separation in a dilute two-component Fermi system with attractive interactions as a function of the coupling strength and the polarization or number density asymmetry between the two components. In weak and strong couplings with a finite number density asymmetry, phase separation is energetically more favorable. A heterogeneous phase containing a symmetric superfluid component and an asymmetric normal phase has lower energy than a homogeneous normal phase. We show that for a small number density asymmetry, taking into consideration the leading order corrections at order k(F)a of the interaction parameter, phase separation is stable against the normal phase in the whole BCS range. We investigate the consequences of the consideration of the leading order kFa corrections to the thermodynamic potentials of the normal and BCS phase on the Chandrasekhar-Clogston limit. We have also investigated the stability of a Bose-Fermi mixture in the far-BEC limit. We find that the molecular BEC is locally stable against an external magnetic field h, provided vertical bar h vertical bar is smaller than the pairing gap Delta(gap).