Entanglement Harvesting and Divergences in Unruh-DeWitt Detector Pairs

We analyze correlations between pairs of detectors quadratically coupled to real and complex scalar bosonic fields in 3+1 dimensions. This is a first step toward studying the entanglement structure of the fermionic vacuum through the entanglement harvesting protocol. We find that, while a single quadratically coupled Unruh-DeWitt presents no divergences, when one considers pairs of detectors there emerge persistent divergences (not regularizable via smooth switching or smearing) in the entanglement they acquire from the field. These divergences were not anticipated in previous studies. We characterize the divergences, discuss whether a suitable regularization can allow for fair comparison of the entanglement harvesting ability of the quadratic and the linear couplings, and finally find a UV-safe quantifier of harvested correlations