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We consider a localized impurity atom that interacts with a cloud of fermionsin the paired state. We develop an effective scattering length description ofthe interaction between an impurity and a fermionic atom using their vacuumscattering length. Treating the pairing of fermions at the mean-field level, weshow that the impurity atom acts like a magnetic impurity in the condensedmatter context, and leads to the formation of a pair of Shiba bound statesinside the superconducting gap. In addition, the impurity atom can lead to theformation of deeply bound states below the Fermi sea.

Bound states of a localized magnetic impurity in a superfluid of paired ultracold fermions