Using the same on-the-fly quantum dynamics approach, Ref. 104 investigated the relaxation of strongly coupled molecule-cavity systems. In this work, the authors study ensembles of rhodamine molecules coupled to a single radiation mode. They find that the nonadiabatic transitions between the dark states, upper, and lower polaritons prolong the relaxation process of the excited molecule-cavity hybrid system. In an empty cavity, when the system is prepared in the |1⟩ (1 photon in the cavity) state, the cavity quickly relaxes to the vacuum states due to cavity loss (see details in Sec. 4.7). When the cavity-molecule hybrid system is prepared in the |±⟩ states, the photoemission rate is controlled by both the cavity loss (as they have significant photonic character) as well as the nonadiabatic transitions to the dark-state manifold. This is because the lower/upper polariton population is transiently transferred to the dark-state manifold, which does not have photonic contributions, thus suppressing cavity loss. This effect is shown in Fig. . After initial excitation to the lower polariton (pink solid line), fast relaxation to the ground state is observed at very short times. Then at ∼ 30 fs, a rise in the dark state population is observed and consequently, the relaxation to the ground state is suppressed marked with the ground state population rising at a slower rate at longer times, for the reasons mentioned before. This is in line with experimental works that show cavity-molecule hybrid systems having a much longer lifetime than the bare cavity. As mentioned in Sec.