  We study (non-perturbatively) the interactions of delta-coupled detectors
with coherent states of a scalar field. We show that the time-evolved density
matrix spectra of i) a single detector, ii) two detectors, and iii) the partial
transpose of the latter, are all independent of which coherent state the field
was in. Furthermore, we find that the eigenvalues in iii) are non-negative,
implying that a delta-coupled detector pair cannot harvest entanglement from
the vacuum, or any other coherent field state.
