  We study the persistent currents of an attractive Fermi gas confined in a
tightly-confining ring trap and subjected to an artificial gauge field all
through the BCS-BEC crossover. At weak attractions, on the BCS side, fermions
display a parity effect in the persistent currents, ie their response to the
gauge field is paramagnetic or diamagnetic depending on the number of pairs on
the ring. At resonance and on the BEC side of the crossover we find a doubling
of the periodicity of the ground-state energy as a function of the artificial
gauge field and disappearance of the parity effect, indicating that persistent
currents can be used to infer the formation of tightly-bound bosonic pairs. Our
predictions can be accessed in ultracold atoms experiments through noise
interferograms.
