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We address the phase of a highly polarized Fermi gas across a narrow Feshbachresonance starting from the problem of a single down spin fermion immersed in aFermi sea of up spins. Both polaron and pairing states are considered using thevariational wave function approach, and we find that the polaron to pairingtransition will take place at the BCS side of the resonance, strongly incontrast to a wide resonance where the transition is located at the BEC side.For pairing phase, we find out the critical strength of repulsive interactionbetween pairs above which the mixture of pairs and fermions will not phaseseparate. Therefore, nearby a narrow resonance, it is quite likely thatmagnetism can coexist with s-wave BCS superfluidity at large Zeeman field,which is a remarkable property absent in conventional BCS superconductors (orfermion pair superfluids).

Highly Polarized Fermi Gases across a Narrow Feshbach Resonance