In Fig. , we fix the light-matter coupling g c = 57 meV (≈ 456 cm -1 ), while varying the cavity loss Γ. For Γ = 0 meV (top panel), we observe a Rabi splitting of the monomer peak into upper and lower polaritons. The two polariton peaks (red curves) have a reduced line width compared to that of the bare monomer, hinting at the effective decoupling of polariton states from the phonon bath, due to the fact that the photonic DOF is not directly coupled to the phonon (nuclear bath), see Eq. 46.