We show, under a very general set of assumptions, that pairs of identical particle detectors in spacelike separation, such as atomic probes, can only harvest entanglement from the vacuum state of a quantum field when they have a nonzero energy gap. Furthermore, we show that degenerate probes are strongly challenged to become entangled through their interaction through scalar and electromagnetic fields even in full light contact. We relate these results to previous literature on remote entanglement generation and entanglement harvesting, giving insight into the energy gap’s protective role against local noise, which prevents the detectors from getting entangled through the interaction with the field.