Fig. -f further explores the collective coupling effect under the slow limit. The parameters are kept the same as panels (a)-(c) but with ω f = 2.48 meV, which results in a dimensionless parameter of κ N ≈ 0.126 √ N ≪ 1 under a relatively small N (see Eq. 28). One can see that the polariton lineshape are Gaussian-like. As N increases, a similar linewidth narrowing phenomenon is observed. Moreover, the linewidth scales as 1/ √ N as is exhibited in panel (f), which is expected according to Eq. 29b as well as the Kubo-Anderson theory . Furthermore, the lineshape is almost symmetric for the UP and the LP branches, due to much weaker inter-branch scatterings.