.0 a 0 , and R 3 = 3.875 a 0 . The cuts of the cavity-adiabatic PESs of Fig. are given as functions of R in the left panels for q = 0 and q = 1.5 a 0 and as functions of q in the right panels for R = 2.0 a 0 and R = 4.0 a 0 (which are, respectively, the minimum of one of the two parabolas where the initial wavepacket is centered and the center of the nonadiabatic region). Note that top panels in Fig. show, for reference, the shapes of the PESs in the absence of coupling between the system and the cavity, while the bottom panels provide an idea of how the PESs are modified by the strong coupling between the system and the cavity. In all cases, the PESs as functions of R for given values of q represent a ground-state double-well potential and an excited-state single well. By tuning the parameters of the model, namely the resonance frequency ω and the coupling strength g, we can induce different dynamics, since the potentials that drive the evolution of the system are slightly FIG. . Left: Cuts of the cavity-adiabatic PESs as function of R along q = 0 (light-blue) and q = 1.5 a 0 (purple), for the cavity-free case (upper panels) and for the strong-coupling case (lower panels). Right: Cuts of the cavity-adiabatic PESs as function of q along R = 2 a 0 (fuchsia) and R = 4 a 0 (light-green), for the cavity-free case (upper panels) and for the strong-coupling case (lower panels). Continuous lines are used for the electronic ground state S 0 and dashed lines for the excited state S 1 . s modified, as shown in Fig. . In the cases studied below, and as indicated above, ω is chosen such that the cavity is in resonance with the S 0 -to-S 1 excitation at the Franck-Condon point R = 2 a 0 , q = 0. On the other hand, as function of q, the cavityadiabatic PESs are basically parabolas more or less symetric with respect to q = 0 depending on the coupling g. Exact QD simulations were conducted starting with an initial wavepacket in the excited state, represented as a real twodimensional Gaussian centered at R = 2.0 a 0 and q = 0: this means that the system, which is in the vibrational ground state of the left diabatic well, is photoexcited at the initial time in a cavity with zero photons. In the course the dynamics, depending on the coupling strength and on the resonance frequency, photon emission and nonadiabatic population transfer take place. Specifically, the cavity-free dynamics for g = 0 would be characterized by a nonadiabatic event that takes place when the wavepacket reaches the avoided crossing region, without photon-emission events. Instead, in the strong light-matter coupling regime, achieved with g = 0.01 (ea 0 ) -1 and ω = 0.17 E h in our calculations, the cavity is in resonance with the excitation of the system in the Franck-Condon region, thus, as soon as the nonadiabatic dynamics starts, photon-emission is observed. In order to quantify the photonemission process, we will calculate the expectation value of photon number operator, namely