to probe their coherence. The meaning of the g c → 0 + limit is actually the decoherence among |E n , 0⟩ in the |B⟩ = 1 √ N |E n , 0⟩ state, due to the coupling of |E n , 0⟩ with its own individual bath. We return to detailed discussions of the above in Sec. VII of the Supporting Information.