Ultraviolet structure of entanglement harvesting from energy density and other quadratic couplings

We study entanglement harvesting with particle detectors coupled to the renormalized energy density of a massless scalar field. Our analysis identifies the distributional mechanism underlying the persistent ultraviolet divergences previously observed for quadratic detector couplings and discusses that the energy density coupling exhibits the same underlying structure. We show that these divergences are entirely controlled by the switching correlation at coincident interaction times. Consequently, pointlike detectors are UV finite whenever the switchings do not overlap. For Gaussian-smeared detectors, the harvesting correlations are automatically finite in 1+1 and 2+1 dimensions, while in higher dimensions the remaining divergences are removed by non-overlapping switchings. Finally, we derive general expressions for arbitrary zero-mean Gaussian states and illustrate the formalism with a thermal field state.