In Figs. and, we compare the exact photon-nuclear density (lower panels) at times t = 500 a.t.u. and t = 1250 a.t.u. for model A and at times t = 540 a.t.u. and t = 810 a.t.u. for model B, respectively, with their corresponding mean-field approximations (upper panels). Note that this analysis is different from the work by Maitra and coworkers , where the performance of the mean-field approximation in terms of MTE was investigated between the photons and the electrons. Here, we aim to retain the full correlation between the electronic and the photon-nuclear dynamics, while investigating the effect of the mean-field treatment of the photonic and nuclear coupling for the particular dynamics studied in this work. Indeed, we note that, as expected, the details of the dynamics are slightly washed out, but the mean-field approximation seems to perform quite well. The mean-field approximation analyzed in Figs. 11 and 12 via Eq. ( ) is to be considered the "best" possible mean-field description of the photon-nuclear density since it is derived using the exact QD density as starting point to define the marginal densities.