Spin-polarized droplets in the unitary Fermi gas

We demonstrate the existence of a type of spatially localized excitations in the unitary Fermi gas: spin-polarized droplets with a peculiar internal structure involving an abrupt change in the pairing phase at the surface of the droplet. It resembles the structure of the Josephson-pi junction occurring when a slice of a ferromagnet is sandwiched between two superconductors. The stability of the impurity is enhanced by the mutual interplay between the polarization effects and the pairing field, resulting in an exceptionally long-lived state. The prospects for its realization in experiments are discussed.