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Three-particle cooperative emission in single- and two-photon exchanges through the vacuum field

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.