where |k⟩ and |k ′ ⟩ are the Fock states (eigenstates of Ĥph in Eq. 36). The light-matter Hamiltonian in Eq. 35 is in the form of Ĥ in Eq. 8, where the quantum subsystem is {|a⟩, |b⟩} = {|G, k⟩, |m, k ′ ⟩}. The exciton-photon-nuclear dynamics will be propagated using the PLDM approach (Eq. 13), and the cavity loss dynamics are accounted for by using the algorithm in Eq. 28. The polariton states of the molecule-cavity hybrid system are defined as