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

This paper investigates the ultraviolet (UV) behavior of entanglement harvesting when particle detectors are coupled to the renormalized energy density of a massless scalar field. Previous research indicated that quadratic couplings to field operators often lead to persistent UV divergences that cannot be removed by spatial smearing. The authors seek to determine if this divergence is a universal feature of quadratic couplings or if the energy density coupling—a physically significant observable—exhibits different behavior.

Using Unruh-DeWitt detector models, the authors analyze the interaction between two inertial detectors and the renormalized stress-energy tensor of a massless scalar field. They employ distributional methods in position space to evaluate the reduced density matrix of the detectors. By examining the switching correlation functions, they identify the specific mathematical mechanism—coincident interaction times—that drives the UV divergences. They further demonstrate that these divergences are controlled by the switching functions and can be eliminated by ensuring the detectors' interaction intervals do not overlap.

Contrary to expectations based on earlier studies of quadratic couplings, the authors find that entanglement harvesting via energy density coupling is UV finite. For pointlike detectors, the persistent divergences are entirely removed when the switching functions have non-overlapping support. In higher dimensions, while divergences may appear for overlapping switchings, they are absent when the interaction intervals are disjoint. The authors provide a general formalism for arbitrary zero-mean Gaussian states and illustrate the protocol's viability with a thermal field state, showing that entanglement can be successfully harvested under these conditions.

The energy density is a fundamental quantity in semiclassical gravity, and understanding how it can be probed by quantum systems is essential for studying the interface between quantum field theory and gravity. By proving that these protocols can be UV finite, this work validates the use of energy density coupling as a robust tool for extracting entanglement from quantum fields, potentially opening new avenues for experimental proposals in quantum information and relativistic quantum optics.