Cooperative and dipole-dipole effects in the fluorescent spectra of two identical three-level atoms at high photon densities

We have studied stimulated three-photon processes arising from the interaction of a system of two-identical three-level atoms with a strong pump field and a weak signal field simultaneously. The atoms consist of an upper excited state and two lower states and they interact through their dipole-dipole and cooperative radiative interactions, respectively. The strong laser field, whose frequency mode ωb is initially populated, depletes the metastable state by bringing the electrons into the excited state from where the electrons emit photons and decay through the signal field into the lower ground states of the system. Using the Green function method in the limit of high photon densities of the laser field, the spectral functions for the signal field have been calculated describing stimulated three-photon processes of the symmetric and antisymmetric modes, respectively, which arise from the dipole-dipole and cooperative radiative interactions between the atoms. The stimulated three-photon excitations near the frequency ω≈ω21 − 2ωb describe physical processes where one-photon of the signal field with frequency ω21 is absorbed while simultaneously two photons of the laser field are emitted. At resonance and in the absence of the dipole-dipole interaction, the spectra consist of a doublet whose peaks are symmetrically located from frequency ω = ω21 − 2ωb, while the magnitude and sign of the intensity of the peaks depend on the value of the relative Rabi frequency ηb. For ηb = 3, the intensity of the doublet takes negative values and it becomes positive for ηb⩾5. As the value of ηb increases the magnitude of the intensity of the doublet decreases and it becomes nearly constant for values of ηb between 50 and 100. The single atom spectra consist of a doublet having a constant negative intensity independent of ηb. The difference between the single and two-atom spectra is attributed to the cooperative radiative interaction between the two atoms. In the presence of detunings, the symmetry in the positions and intensities of the two sidebands vanishes. In the presence of the dipole-dipole interaction and at resonance, the spectra consist of three sidebands whose position, line shape, and sign as well as magnitude of the intensities depend entirely on the strength of the dipole-dipole interactions between the atoms. In the presence of detunings, asymmetries arise, enhancing certain spectral peaks while diminishing the intensity of others. The computed spectra are graphically presented for different values of ηb, dipole-dipole interactions, and detunings. Comparison between the single and two-atom spectra is made and discussed in detail.