Induced $p$-wave superfluidity at unitarity in strongly imbalanced Fermi gases

We compute the induced interaction among the majority spin-up fermions, due to the presence of the minority spin-down fermions, in a population imbalanced Fermi gas. This interaction leads to an instability of the spin-polaron Fermi liquid, favoring a $p$-wave superfluid. For the majority component, near unitarity, the transition temperature is found to be within experimental reach, of order a few percent of the Fermi energy. As a probe of this phase, the radio-frequency spectroscopic line-shape is calculated for the $p_{x}+ip_{y}$ ground state.