Gaussian R\'enyi-2 correlations in a nondegenerate three-level laser

Quantum correlation is a key component in various quantum information processing tasks. Decoherence process imposes limitations on achieving these quantum tasks. Therefore, understanding the behavior of quantum correlations in dissipative-noisy systems is of paramount importance. Here, on the basis of the Gaussian R\'{e}nyi-2 entropy, we analyze entanglement and quantum discord in a two-mode Gaussian state $\rho_{AB}$. The mode $A$($B$) is generated within the first(second) transition of a nondegenerate three-level cascade laser. Using realistic experimental parameters, we show that both entanglement and discord could be generated and enhanced by inducing more quantum coherence. Under thermal noise, entanglement is found more fragile having a tendency to disappear rapidly. While, quantum discord exhibits a freezing behavior, where it can be captured within a wide range of temperature. Surprisingly, we find that entanglement can exceed quantum discord in contrary to the expectation based on the assumption that the former is only a part of the later. Finally, we show numerically as well as analytically that optimal quantum discord can be captured by performing Gaussian measurements on mode $B$. The obtained results suggest that nondegenerate three-level lasers may be a valuable resource for some quantum information tasks, especially, for those do not require entanglement.