This means that under the N → ∞ limit (in real experiments, N ∼ 10 6 -10 12 ), the direct phonon couplings are completely decoupled from the |±⟩ states. As such, the optical lineshape (such as polariton absorption) that corresponds to |G, 0⟩ → |±⟩ optical transition will become much narrower than systems outside the cavities, and this will also present itself in the diagonal peaks of the 2DES spectra. However, polaron decoupling (Eq. 22) is not responsible for a longer ρ +-(t) co-herence time when increasing √ N g c as we have observed in Figs. . This is because although both |+⟩ and |-⟩ have a relative shift R α,0 with respect to |G, 0⟩ (polaron decoupling), there is no absolute shift amongst |+⟩ and |-⟩ states on the diagonal term as can be seen from the first line of Eq. 21a.