  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
non-zero 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.
