------------------------

In earlier communication, on account of the relation of the criterion introduced by Hillery and Zubairy [@prl96050503] with the correlation of the photon number, the generated entanglement has been tipped to be quantifiable via simultaneous two-photon count measurement [@pra79063815]. In search of more appropriate and easy means of detecting entanglement, the degree of entanglement that can be predicted by the logarithmic negativity and HZ criteria has been compared earlier for nondegenerate three-level laser when $\Omega=0$, $\theta=0$ and $\gamma=\Gamma$. It was shown that both criteria predict the manifestation of entanglement at steady state, even though the degree of nonclassicality cannot be compared since HZ-criteria has no upper limit. In this contribution, upon changing the above parameters, the comparative evolution of the entanglement is investigated.

According to HZ criteria, one can say that there is entanglement if $$\begin{aligned}
\label{p43}|\langle\hat{a}(t)\hat{b}(t)\rangle|>\sqrt{\langle\hat{N}_{a}(t)\rangle\langle\hat{N}_{b}(t)\rangle},\end{aligned}$$ where $\langle\hat{N}_{a}(t)\rangle=\langle\hat{a}^{\dagger}(t)\hat{a}(t)\rangle$ and $\langle\hat{N}_{b}(t)\rangle=\langle\hat{b}^{\dagger}(t)\hat{b}(t)\rangle$ are the pertinent photon numbers corresponding to the involved modes, and $\langle\hat{a}(t)\hat{b}(t)\rangle$ is the intermodal correlation. Since the operators are already put in the normal order, Eq. can be expressed in terms of $c$-number variables associated with the normal ordering as $$\begin{aligned}
\label{p44}\langle\alpha(t)\beta(t)\rangle^{2}>\langle\alpha^{*}(t)\alpha(t)\rangle\langle\beta^{*}(t)\beta(t)\rangle.\end{aligned}$$

For nondegenerate three-level cascade laser, based on the assumption that there is no interaction among 