Entanglement harvesting and divergences in quadratic Unruh-DeWitt detectors pairs

We analyze correlations between pairs of particle detectors quadratically coupled to a real scalar field. We find that, while a single quadratically coupled detector presents no divergences, when one considers pairs of detectors there emerge unanticipated persistent divergences (not regularizable via smooth switching or smearing) in the entanglement they acquire from the field. We have characterized such divergences, discussed whether a suitable regularization can allow for fair comparison of the entanglement harvesting ability of the quadratic and the linear couplings, and finally we have found a UV-safe quantifier of harvested correlations. Our results are relevant to future studies of the entanglement structure of the fermionic vacuum.