the intention of looking for the overlap so that the likelihood of the prediction and realizeability becomes more reliable [@jpb42215506]. With this conviction, the time evolution of the entanglement is studied applying the criteria usually dubbed as logarithmic negativity [@pra65032314], Duan-Giedke-Cirac-Zoller (DGCZ) [@prl842722] and Hillery-Zubairy (HZ) [@prl96050503]. The obtained results are compared whenever possible.

In the study of the time evolution of a similar system when many parameters are involved, the usual approach is numerically calculating the required correlations making use of either the characteristic function [@pra79013831; @pra72022305] or the rate equation [@pra77062308; @oc283781]. However, in this article, the dynamics of the cavity radiation is analyzed following a straightforward analytic procedure recently outlined elsewhere [@pra74043816; @pra79033810; @sinta; @sint]. The resulting analytical solutions were successfully employed earlier in the study of the time evolution of the two-mode squeezing and intensity [@sint]. Particularly, the time evolution of the two-mode squeezing shows that the phase fluctuation inherent with the imperfect preparation can enhance nonclassical features when the atoms are driven with a strong external radiation by creating spontaneous emission transition root via weakening the otherwise induced strong coupling of the upper and lower energy levels by pumping. However, in this contribution, it is 