p-wave Pairing in Two-Component Fermi System with Unequal Population: Weak Coupling BCS to Strong Coupling BEC Regimes

We study p-wave pairing in a two-component Fermi system with unequal population across weak-coupling BCS to strong-coupling BEC regimes. We find a rich $m_s=0$ spin triplet p-wave superfluid ground state structure as a function of population imbalance. Under a phase stability condition, the "global" energy minimum is given by a multitude of "mixed" SF states formed of linear combinations of $m=\pm1,0$ sub-states of the $\ell=1$ orbital angular momentum state. Except for the "pure" SF states, ($\ell=1, m=\pm1$), other states exhibit oscillation in energy with the relative phase between the constituent gap amplitudes. We also find states with "local" energy minimum that can be stable at higher polarizations, suggesting a quantum phase transition between the "global" and "local" minima phases driven by polarization. The local and global minimum states may be associated with Morse and non-Morse critical points. We discuss possible consequences for experiments.