Here, σ † n = |e n ⟩⟨g n | and σn = |g n ⟩⟨e n | creates annilates an excitation on the n th molecule, respectively, with |g n ⟩ and -e n ⟩ as the ground and excited states for molecule n, and 1ph is the identity operator for the photonic subspace. The photonic Hamiltonian is described by a single cavity mode