where |D J , 0⟩ is the state where the J th molecule is in its donor excited state while the rest of the molecules are in their ground states with 0 photons in the cavity and |G, 1⟩ represents the molecules in their ground state with 1 photon in the cavity. First, note the cavity-mediated electronic coupling between |±⟩ and |A J , 0⟩ state is ⟨±| Ĥpl |A J , 0⟩. Here only the |D J , 0⟩ component in the |±⟩ is coupled to the |A J , 0⟩ state through Ĥen . This leads to the effective electronic coupling