evolution of the smallest eigenvalue ($V_{s}$) and variance of the EPR operators ($\Delta u^{2}+\Delta v^{2}$) of the cavity radiation for $\kappa = 0.5$, $\theta=0.25$, $A=25$, $\Omega=10\Gamma$ and $\gamma=0.75\Gamma$.](pe12.eps){height="6.5cm"}

It is unequivocally shown in Fig. \[fig9\] (please note that $A=25$ is used so that the dependence of the two can be distinctly observed) that the degree of entanglement that can be predicted by the two criteria exhibits very similar nature when $\Omega=0$. However, their nature turns out to be completely different when $\Omega\ne0$ in the longer time span as evinced in Fig. \[fig10\] where the time parameter is limited to small interval so that the relation between the two can be readily noticeable. It is worth noting that $\Delta u^{2}+\Delta v^{2}$ rapidly increases with time which leads to dying of entanglement whereas $V_{s}$ continuously decreases with time. What can be said at this juncture is that the two criteria predict similar nature of entanglement evolution for relatively smaller time scale, but they can also predict entirely different thing when there is an external driving radiation at longer time span. By the way, such a disparity between the two is not uncommon for $\eta=0$ which includes the present case [@jpb42215506].

Hillery-Zubairy criteria
