The paper proposes to unify the two-photon laser and induced cooperative scattering Raman lasing in which the flying ensemble of two-level excited radiators are coupled with the bimodal cavity field in nonlinear two-photon and scattering interactions. It discusses the situation in which the induced two-quantum lasing takes place together with the cooperative scattering conversion of photons between the pump, Stokes, and anti-Stokes cavity modes. The proposed master equation describes cooperative energy exchanges between Raman and two-photon lasing processes by portions of energies multiple to the energy of the entangled photon pair.

The generators of such emission and absorption processes belonging to the symmetries of Raman conversion and two-photon cooperative generation are unified. The first symmetry belongs to $su\left(2\right)$ algebra connected to the scattering conversion in the Stokes, pump, and anti-Stokes modes of cavity (Opt. Commun.,285(5) (2012) 686–692). The second one belongs to multi-mode $su(1,1)$ symmetry which quantifies the cooperative process belonging to two-photon emission in cavity/fiber mode components of field (see Opt. Commun. 247(4–6) (2005) 381–392). The bimodal collective photon operators are introduced describing the emission or absorption acts of the fixed portion of energy from the cavity equal to the transition energy between the states of each excited atom. A key impact of the study focuses on the statistical properties of the bimodal field and their detection possibilities are proposed for the description of the time evolution of quantum correlations between the field components of Raman conversion and two-photon emission.

该论文提出将双光子激光和诱导协同散射拉曼激光统一起来，其中两能级激发辐射体的飞行系综在非线性双光子和散射相互作用中与双模腔场耦合。它讨论了诱导双量子激光与泵浦、斯托克斯和反斯托克斯腔模式之间光子的协同散射转换一起发生的情况。提出的主方程描述了拉曼和双光子激光过程之间的协作能量交换，其能量是纠缠光子对能量的倍数。

属于拉曼转换和双光子协同生成对称性的这种发射和吸收过程的发生器是统一的。第一个对称性属于$秒你\left(2\right)$代数连接到腔的斯托克斯、泵浦和反斯托克斯模式中的散射转换（Opt. Commun.,285(5) (2012) 686–692）。第二个属于多模$秒你(1,1)$对称性量化属于场的腔/光纤模式分量中的双光子发射的协作过程（参见 Opt. Commun. 247(4-6) (2005) 381-392）。引入了双峰集体光子算子，描述了来自腔的固定部分能量的发射或吸收行为，该部分能量等于每个激发原子状态之间的跃迁能量。该研究的一个关键影响集中在双峰场的统计特性上，并提出了它们的检测可能性，以描述拉曼转换和双光子发射的场分量之间的量子相关性的时间演化。