which is only half of the magnitude of ⟨m| Ĥex-R |m⟩ = ν c m,ν R m,ν . This effective reduction of the coupling for the phonon inside the cavity is referred to as the polaron decoupling effect. A detailed discussion of the polaron decoupling effect under the collective coupling regime can be found in Ref. 7. Fig. presents the schematic illustration of the model system considered in this work. Fig. (a) presents a model excitonic system coupled to cavity excitation, where the matter has onsite energy of ε and a transition dipole µ. The matter couples to the cavity mode with coupling strength g c (for monomer m = 1, and for the dimer, the coupling strength g c (m) depends on the transition dipole magnitude µ m , see Eq. 39). The cavity mode has a loss rate of Γ for the decay of Fock states. Fig. (b) presents a molecular dimer coupled to a single cavity mode. Individual monomers in the dimer system have asymmetry in their energies (ϵ 1 ̸ = ϵ 2 ) and their transition dipoles (µ 1 ̸ = µ 2 ). Local excitons (|e 1 , g 2 ⟩ and |g 1 , e 2 ⟩) are coupled with strength J 12 . In addition, the cavity has been tuned to the lower exciton. To complete the double excitation manifold required for the 2DES simulation, we also include the second excited Fock state, |g 1 , g 2 , 2⟩. This state couples to |g 1 , e 2 , 1⟩ and |e 1 , g 2 , 1⟩ through Eq. 37 with strength √ 2g c (m). The cavity loss will cause the decay of |g 1 , g 2 , 2⟩ to |g 1 , g 2 , 1⟩ according to L in Eq. 44, with a decay rate of 2Γ.