The remaining N -1 eigenstates are the dark states |D k ⟩ (not to be confused with the donor exciton states |D j , 0⟩) which are superpositions of only {|D j , 0⟩} states that can be expressed as follows 1,70,75 where k ∈ {1, • • • , N -1} labels the dark states. The energy of the dark states remains the same as the exciton site energy but with a large density of states N -1. Note that the dark states have no overlap with the collective "bright" states, and they do not participate in the interaction with the cavity mode mediated by Ĥmp since ∑ N j=1 c k, j = 0 which renders them optically dark (i.e. having no transition dipole from the ground state |G⟩).