where J c α J = 0 for all dark states α. These states are superpositions of the N matter states {|E J , 0⟩}, and thus are also delocalized across N molecules (one should note their difference compared to the individual localized excited state |E J , 0⟩). Energetically, they are the same as the original single-molecule excitation, E e , and are depicted as the gray states in Fig. . These dark states do not mix with the photon-dressed state |G, 1⟩ and do not contain any photonic excitation component under the TC model consideration. These dark states are also optically dark from the ground state |G, 0⟩ due to the net zero transition dipole ⟨D α , 0| J μJ |G, 0⟩ = µ eg J C α J = 0 if we assume ⟨e|μ J |g⟩ = µ eg for all J ∈ [1, N ] emitters. Optically, one will see no significant absorption in between two polariton absorption peaks (when ignoring disorder). In the recent molecular polariton experiments, the typical number of molecules coupled to the cavity is N ∼ 10 6 -10 11 per cavity mode.