in a strong driving limit ($\Omega>>\Gamma$) [@jpb41055503]. In the following, upon varying the values of the rate of dephasing ($\gamma/\Gamma$) and the deviation of the phase fluctuation ($\theta$), the time evolution of the entanglement that can be detected by the logarithmic negativity is studied.

![\[fig5\] Plots of the time evolution of the smallest eigenvalue ($V_{s}$) of the cavity radiation for $\kappa = 0.5$, $\theta=0$, $A=10$, $\Omega=10\Gamma$ and different values of $\gamma/\Gamma$.](pe6.eps){height="6.5cm"}

![\[fig6\] Plots of the time evolution of the smallest eigenvalue ($V_{s}$) of the cavity radiation for $\kappa = 0.5$, $\theta=0.25$, $A=10$, $\Omega=10\Gamma$ and different values of $\gamma/\Gamma$.](pe7.eps){height="6.5cm"}

![\[fig7\] Plots of the time evolution of the smallest eigenvalue ($V_{s}$) of the cavity radiation for $\kappa = 0.5$, $\gamma=\Gamma$, $A=10$, $\Omega=10\Gamma$ and different values of $\theta$.](pe5.eps){height="6.5cm"}

![\[fig8\] Plots of the time evolution of the smallest eigenvalue ($V_{s}$) of the cavity radiation for $\kappa = 0.5$, $\gamma=0.75\Gamma$, $\theta=0.25$, $\Omega=10\Gamma$ and different values of $A$.](pe10.eps){height="6.5cm"}

In line with earlier discussion, the term under square root in Eq. would not be negative for large $\Omega$. As a result, as clearly evinced in Figs. \[fig5\], \[fig6\], \[fig7\] and \[fig8\], the degree of entanglement does not exhibit oscillatory nature in the strong driving limit. It is, 