Pairing near a sharp boundary in the BEC-BCS crossover

We study attractively-interacting fermions confined to a box-shaped trap. In contrast to the uniform case, where the local pairing order is also spatially uniform and undergoes the 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, exhibiting Friedel-like oscillations in the BEC regime and a sharp onset in the BEC regime.