where Θ N = tan -1 [(2ℏg c √ N )/(ℏω c -∆E)]/2 is the mixing angle under the collective coupling regime, and ∆E = E e -E g is the energy difference between the bright state |B, 0⟩ (as well as the singly excited manifold) and ground state |G, 0⟩. Through the collective coupling to the cavity, the polariton states are delocalized across all N molecules in the cavity and should be viewed as mesoscopic quantum states that involve N molecules and a single cavity mode. When N = 1 (single molecule), the |±⟩ states in Eq. 14 reduces back to the |±, 0⟩ states of the JC model in Eq. 4.