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As a means of realizing oscillatory pairing between fermions, we studysuperfluid pairing between two fermion "spin" species that are confined toadjustable spin-dependent trapping potentials. Focusing on the one-dimensionallimit, we find that with increasing separation between the spin-dependent trapsthe fermions exhibit distinct phases, including a fully paired phase, aspin-imbalanced phase with oscillatory pairing, and an unpaired fullyspin-polarized phase. We obtain the phase diagram of fermions in such aspin-split trap and discuss signatures of these phases in cold-atomexperiments.

Oscillatory pairing of fermions in spin-split traps