Phase diagram for the trapped p-wave fermionic superfluid with population imbalance

We consider the problem of spin-triplet p-wave superfluid pairing with total spin projection m(s) = 0 in atomic Fermi gas across the Feshbach resonance. We allow for imbalanced populations and take into account the effects due to the presence of a harmonic trapping potential. Within the mean-field approximation for the one- and two-channel pairing models we show that the p-wave superfluid state has the lowest energy up to some distance from the trap center, the distance depending on population imbalance and the side of the Feshbach resonance (BCS or BEC) the system is in. Beyond this, the system is in the normal state. Since the system, even in the presence of the harmonic trap, is invariant under O(3) space rotation, the superfluid cores which emerge in the trap are comprised of states that are degenerate with respect to the "orbital ferromagnet" state, p(x) +/- ip(y), as well as the ones in which all angular momentum components of the order parameter are nonzero, provided the modulus of the order parameter maintains a fixed magnitude.