Pairing near the boundary of a box-shaped trap in the BEC-BCS crossover

Abstract

We study pairing of attractively interacting fermions confined to a box-shaped trap. In contrast to the infinite translationally-invariant case, where the local pairing order is spatially uniform and undergoes the Bose-Einstein Condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover as interactions are varied, in this case the local pairing is expected to vary rapidly near the edge of the box. We address this problem in the limit of a semi-infinite superfluid, finding that the nature of the edge pairing depends sensitively on the coupling. The local pairing exhibits Friedel-like oscillations in the weak coupling BCS regime that are suppressed with increasing coupling strength towards the BEC regime.