Effects of a Fluctuating Interface between a Superfluid and a Polarized Fermi Gas

Motivated by recent experiments in trapped Fermi gas with spin population imbalance, we discuss the effects of the quantum and thermal fluctuations of the interface between a fully paired superfluid core and a fully polarized Fermi gas. We demonstrate that even if there is no true partially polarized thermodynamic phase in bulk, the interface fluctuation can give rise to a partially polarized transition regime in trap. Our theory yields a definite prediction for the functional forms of the spatial profile of spin polarization and pairing gap, and we show that the spin-resolved density profiles measured by both the MIT and Rice groups obey this function form. We also show that sufficient large fluctuation will lead to a visibly unequal density even at the center of the cloud. We hope this picture can shed lights on the controversial discrepancies in recent experiments.