which appears in J ν (ω) and n(ω) of the FGR expression. For an arbitrary detuning case, there will be an additional factor [1 + cos(2Θ N )] in the FGR expression, see Eq. S21c in the Supporting Information. The scaling (N -1)/N in Eq. 23 is well known, because there are N -1 dark state to transfer to, and the 1/N is originated from the re-scaled phonon coupling c α / √ N . Further, k +→D can already explain the similarity of the decoherence dynamics we observed in Figs. . This is because when N is sufficiently large, (N -1/N ) ∼ 1, and the relaxation rate for the |+⟩ → {|D k ⟩} process is completely dictated by √ N g c as this is the only quantity shown in k +→D (Eq. 23). As such, even though the Hamiltonians used in Fig. and Fig. are different (especially for the number of the dark states), the reduced system dynamics in the {|±⟩, |D k ⟩} are isomorphic to each other as long as √ N g c is identical and N is sufficiently large, and if the dynamics is largely dictated by |+⟩ → {|D k ⟩} transition.