Oscillatory pairing of fermions in spin-split traps

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As a means of realizing oscillatory pairing between fermions, we study superfluid pairing between two fermion "spin" species that are confined to adjustable spin-dependent trapping potentials. Focusing on the one-dimensional limit, we find that with increasing separation between the spin-dependent traps the fermions exhibit distinct phases, including a fully paired phase, a spin-imbalanced phase with oscillatory pairing, and an unpaired fully spin-polarized phase. We obtain the phase diagram of fermions in such a spin-split trap and discuss signatures of these phases in cold-atom experiments.