Quantum correlations in a coherently pumped cascade three-level laser in the presence of dephasing

This study considers the quantum correlations between two field modes produced by a coherently pumped cascade three-level laser, taking into account the inevitable dephasing processes. The photon-photon quantum correlations are investigated by applying the stationary solutions of the various expectation values of the product of cavity mode operators. In the relatively weak coherent pumping regime, it is found that the stationary entanglement and squeezing between the two field modes increase with the coherent pumping amplitude, while in the relatively strong coherent pumping regime, they decrease. We also show that the quantification of quantum correlations through Gaussian quantum discord, entanglement, and squeezing shows a similar evolution pattern. Moreover, we show that the degree of quantum correlations is increased by the atomic injection rate and decreased by the dephasing processes.