injected atoms, the photon number correlation is found to have the form [@pra74043816] $$\begin{aligned}
\label{p45}g(n_{a},n_{b})=1+{\langle\alpha(t)\beta(t)\rangle^{2}\over\langle\alpha^{*}(t)\alpha(t)\rangle\langle\beta^{*}(t)\beta(t)\rangle}.\end{aligned}$$ Hence upon comparing Eqs. and , one can readily see that the HZ inseparability criterion can be restated as $$\begin{aligned}
\label{p46}g(n_{a},n_{b})>2.\end{aligned}$$

It is obvious to see from Eq. that $g(n_{a},n_{b})>2$ for all parameters under consideration. It is also clearly indicated that the evolution of the generated entanglement exhibits oscillatory nature. At this juncture, it is essential to note that for earlier time span $g(n_{a},n_{b})$ goes to infinity in connection with the mean photon number in one of the modes rapidly close to zero. In earlier report, similar behavior of $g(n_{a},n_{b})$ has been explained in relation to the correlation involved in the criteria [@jpb42215506]. In light of this, it is possible to infer that except near the beginning of lasing operation, the two criteria unequivocally assert that the system under consideration generates entangled light. The overlap between these predictions may be utilized in detecting entanglement using the simultaneous photon count measurement in case the usual homodyne detection is found to be practically challenging.

Conclusion
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Detailed analysis of the time evolution of the entanglement generated from a correlated emission laser is presented. Aiming at searching for 