Mutual cooperative effects between single- and two-photon super-fluorescent processes through vacuum field

Two types of resonance between the spontaneous emissions by two- and single photon transitions of three inverted radiators from the ensemble are proposed to accelerate the collective decay rate of the entangled photon pairs generated by the system relative the dipole-forbidden transition. One of them corresponds to the situation when the total energy of emitted photons by two dipole-active radiators enter the two-photon resonance with the dipole-forbidden transition of third atom. Second effect corresponds to the scattering situation, when the difference of the excited energies of two dipole-active radiators is in the resonance with the dipole-forbidden transition of third atom. These effects are accompanied with the interferences between single- and two-quantum collective transitions of three inverted radiators from the ensemble. The three particle collective decay rate is defined in the description of the atomic correlation functions