The theoretical approach takes in consideration the cooperative phenomena which appear between three particle in two-photon resonance in the process of single- and two- photon decay. This type of single- and two-quanta cooperative effect between three subsystems of radiators are described by master equation which takes into account three-particle cooperative resonance in the system. The resonance between the spontaneous emissions by two- and single photon transitions of three inverted radiators from the ensemble is proposed in order to accelerate the collective decay rate of the entangled photon pairs generated by the system. This effect is accompanied with the interferences between one-photon and two-quantum collective transitions of three inverted radiators from the ensemble. The three particle collective decay rate is defined in the description of three atomic correlation functions.
The symmetry of the two types of resonances between the spontaneous and induced emissions by two- and single-photon transitions of three inverted radiators from the ensemble is studied. The condition for increasing the collective decay rate of the entangled photon pairs generated by the system relative to the dipole-forbidden transition is found. One of them corresponds to the situation when the total energy of emitted photons by two dipole-active radiators enters the two-photon resonance with the dipole-forbidden transitions of the third atom. The second effect corresponds to the scattering situation when the differences of the excited energies of two dipole-active radiators are in resonance with the dipole-forbidden transitions of the third atom. It is shown that transfer of the excited energy between two quantum oscillators off resonance takes place through a dipole-forbidden transition of the thread atom.