p-wave superfluid with imbalanced atomic population in harmonic trap

We consider the problem of $p$-wave superfluid pairing in an atomic Fermi gas across Feshbach resonance for imbalanced populations in presence of an optical trap. For our harmonic trapping potential, we employ Local Density Approximation {\bf (LDA)} through chemical potential. In two-channel mean field approximation pairing model, we show that depending on the distance from the trap's center, the p-wave superfluid state will have the lowest energy. The ground state order parameter configuration we find is not invariant under parity and time-reversal symmetry operations. We also present phase diagrams and density profiles in one-channel model for our singlet p-wave pairing and show that the center of trap is occupied by p-wave superfluid. The work of A. K. and M. D. was financially supported by the National Science Foundation Grant No. DMR-1506547.