Note that in the above scaling law, we explicitly assumed that β √ N g c ≫ 1, such that 1 + n ≈ 1. This is indeed the case for exciton-polaritons under room temperature conditions k B T ≈ 26 meV and √ N g c > 50 meV. For lower temperature or vibrational strong coupling cases (where usually √ N g c < 10 meV) one also needs to explicitly consider the scaling coming from n( √ N g c ) and n(2 √ N g c ). Further, the scaling in Eq. 26 will depend upon the detailed form of the spectral density J ν (ω), but one is guaranteed to figure out this scaling once the detailed form of J ν (ω) is known. Thus, for large N , T * 2 ≫ 2T 1 , and we see that the contribution of the coherence decay rate between |+⟩ and |-⟩ state to T 2 is negligible; the decoherence time for the collective coupling case is