nature for certain parameters under consideration. It is worth noting that, since the injection of the atoms is launched at $t=0$, entanglement would not be expected at the beginning when the cavity is taken to be initially at vacuum state. Moreover, it is not difficult to see that the degree of entanglement increases rapidly and then starts to fluctuate with time. The increment of the degree of entanglement at early stages of the lasing process can be directly linked to the increment of the atoms that participate in the correlated emission. Similar increment behavior at early stages of lasing operation was observed for various schemes of three-level laser under different conditions using various entanglement criteria [@pra72022305; @pra79013831; @pra444688; @oc283781].

Nevertheless, in order to trace the origin of the fluctuation, it appears natural referring back to Eq. . In Eq. , if $\Omega=0$, the term under square root reduces to $\sqrt{4(\chi^{2}-e^{-2\theta})}$. This indicates that, in Eqs. , and , the exponential term that contains time would be complex valued which leads to oscillation if $\gamma/\Gamma<e^{-\theta}$. In case of $\theta=0$ and $\gamma=\Gamma$, generally the oscillation in the entanglement evolution is not observed as large volume of earlier works asserted [@pra72022305; @pra79013831; @pra444688; 