which reflects a simple fact that as ω +-= ω +ω -= 2g c gets larger, the phonon in J ν cannot efficiently mediate the transition |+⟩ → |-⟩ unless there is a high frequency phonon that matches ω +-. Note that the simple scaling at the end of Eq. 28 only works when g c ≫ γ, otherwise 1/T * 2 will exhibit a turnover, dictated by the form of J ν (2g c ) (c.f. Eq. 5). Nevertheless, we have observed this from direct theoretical simulations of 2DES spectra of a single molecule strongly coupled to the cavity, and indeed find that the longer coherence time can be achieved by increasing g c . Further, earlier theoretical work also suggests that one can prolong the ρ +-coherence by increasing g c from the potential energy surface hybridization perspective. Additional numerical results are provided in Sec. VI of the Supporting Information to characterize the ρ +-decoherence for N = 1 with increasing g c . However, we emphasize that the fundamental mechanism for decoherence in the N = 1 case (Eq. 28) is different compared to the collective coupling case (Eq. 27). Fig. presents a numerical check of the scaling predicted by Eq. 27, where we have simulated three cases: (a) fixing the collective coupling √ N g c = 180 meV while increasing N (and thus decrease g c accordingly, (b) fixing g c = 44.7 meV while increasing N , and (c) fixing N = 10 while increasing g c . The results are obtained from HEOM simulations and extracted using Eq. 20 (red dots), the least square fitting using the corresponding scaling (blue curve), as well as from FGR using Eq. 25 (green).