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The induced interaction among the majority spin species, due to the presence of the minority species, is computed for the case of a population-imbalanced resonantly interacting Fermi gas. It is shown that this interaction leads to an instability, at low temperatures, of the recently observed polaron Fermi liquid phase of strongly imbalanced Fermi gases to a p-wave superfluid state. We find that the associated transition temperature, while quite small in the weakly interacting BCS regime, is experimentally accessible in the strongly interacting unitary regime. © 2011 American Physical Society.

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Physical Review A - Atomic, Molecular, and Optical Physics