We note from Eq. 18 that since the dark states have no overlap with the collective "bright" states, they do not participate in the interaction with the cavity mode that is mediated by ĤLM . Further, there is no optical transition from |G, 0⟩ to |D α ⟩, hence it is optically dark. The choice of dark state is not unique. For example, one can express them as follows 87,91