Spin susceptibility and effects of a harmonic trap in the BCS-BEC crossover regime of an ultracold Fermi gas

We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended T-matrix approximation, as well as effects of a harmonic trap in the local density approximation, we calculate the local spin susceptibility χt(r,T) in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover region. We show that pairing fluctuations cause nonmonotonic temperature dependence of χt(r,T). Although this behavior looks similar to the spin-gap phenomenon associated with pairing fluctuations in a uniform Fermi gas, the trapped case is found to also be influenced by the temperature-dependent density profile, in addition to pairing fluctuations. We demonstrate how to remove this extrinsic effect from χt(r,T), to study the interesting spin-gap phenomenon purely originating from pairing fluctuations. Since experiments in cold-atom physics are always done in a trap, our results would be useful for the assessment of preformed pair scenario, from the viewpoint of spin-gap phenomenon.