where the coherence oscillates with a frequency of the Rabi splitting Ω R = 2 √ N g c (for an isolated two-level system), the coherence decay follows an exponential behavior with the characteristic time T 2 (due to coupling to phonons), and the coherence beatings last until ∼ 150 fs. Eq. 20 fits the HEOM data exceptionally well, which are plotted as colored cross markers in each panel, and give the decoherence time T 2 as 61.2 fs (panel a), 100.9 fs (panel b), and 146.5 fs (panel c). For comparison, the coherence lifetime for lim gc→0 + Re[ρ +-(t)] is T 2 = 15.7 fs when fitted to a Gaussian decay profile, which is the typical electronic coherence time under room temperature. Coupling to a cavity can significantly prolong T 2 to ∼ 60 fs with a realistic collective coupling parameter √ N g c = 100 meV. In the 2DES experiments of molecular polariton, the largest Rabi splitting achieved was Ω R = 380 meV (or √ N g c ≈ 190 meV). The recordhigh Rabi splitting that we are aware of is the squaraine dye molecules coupled to the cavity, generating Ω R = 420 meV (or √ N g c ≈ 210 meV). Results in Fig. suggest that under the collective coupling of a few molecules with the cavity when N is fixed and increasing g c , the coherence ρ +-(t) will be increased. This is also the case when N = 1, and with an increasing g c one can significantly prolong the coherence ρ +-(t), as shown in Fig. in the Supporting Information. We note that the decoherence mechanism when N = 1 is fundamentally different than when N > 1 because the former case does not contain any dark state. ] decay at a slower rate and the coherence lifetimes for the coupled states are about 4 to 9.3 times greater than the coherence lifetime for the uncoupled system. Further, comparing to Fig. , one observes that the decoherence dynamics are nearly identical with each other, as long as the collective coupling strength √ N g c is the same. To be clear, the Hamiltonian in Fig. is different compared to Fig. . The former is fixing N and varying g c , and the latter one is fixing g c and varying N . Nevertheless, it seems that the decoherence dynamics is only sensitive to √ N g c , agreeing with the empirical rule in the early numerical simulations with Lindblad dynamics. To understand the decoherence mechanism under the collective coupling regime and make sense of the exact numerical results presented in Figs. , we focus on the population dynamics presented in Fig. . One can see that there is a significant population transfer from the |+⟩ state to the dark state manifold {|D k }, such that the decoherence mechanism is not pure-dephasing (which does not have any population transfer). This also makes the decoherence mechanism for the collective coupling case (N ̸ = 1) fundamentally different from the single molecule case (N = 1), because the latter does not have any dark state. For the collective coupling regime, the main contribution for the ρ +-(t) decoherence, as shown in Fig. , is the population transfer from |+⟩ state to the dark states manifold {|D k ⟩}. In Fig. (where N = 20), we can see that ρ ++ (t) population gradually decay from 1/2 and the dark state population ρ DD (t) gradually increase, whereas the ρ --(t) population oscillates To obtain an insight into the decoherence mechanism, we derive an analytic expression of the coherence time. We begin by transforming the total Hamiltonian in Eq. 1 into the polariton state and Dark state basis {|±⟩, D k }. Because these states are the eigenstates of Ĥs (Eq. 10), they will make Ĥs purely diagonal. Transitions among these states are induced by the phonon couplings, specifically from Ĥsb (Eq. 4b). The full Hamiltonian expression in this polariton basis is provided in Sec. I of the Supporting Information. Here, we focus on Ĥsb (Eq. 4b) in the polaritonic basis Ĥsb = Ĥ± + Ĥ{±,D} + ĤD , where Ĥ± provides the phonon-mediated transitions between |+⟩ and |-⟩ states, Ĥ{±,D} provides the phonon-mediated transitions between the |±⟩ states to the dark state manifolds {|D k ⟩}, and ĤD provides the phononmediated transitions among dark states. In particular, under the resonance condition ∆ = 0 (Eq. 13), the mixing angle is Θ N = π/4, Ĥ± and Ĥ{±,D} are expressed as follows