## 3 Results
Moreover, the transposition of the dominant inner resonances, owing its presence to the alteration of the value of \(R\), is of low importance as compared to the transposition of the resonances observed in the case with \(\hbar T_{e}=0.01\) meV (Figure 4). However, the amplitude of the resonances is slightly decreased as the distance between the particles is increased. Finally, and most importantly, as we note by comparing Figure 4 to Figure 5, when the tunneling  
Figure 4: The dispersion (**a**,**c**,**e**) and the absorption (**b**,**d**,**f**) spectra for \(\hbar\Omega_{a}=3\) meV, \(\omega_{12}=\Delta=0\) and \(\hbar T_{e}=0.01\) meV, for various interparticle distances (\(R=100\) nm (blue solid curve), \(20\) nm (red dashed curve), and \(15\) nm (green dashed-dotted curve)). The rest parameters used are \(a=7.5\) nm, \(\varepsilon_{S}=6\varepsilon_{Q}\), \(\varepsilon_{env}=\varepsilon_{0}\), \(\hbar\omega_{01}=1.4\) eV, \(s_{a}=2\), \(\hbar\Gamma_{10}=0.025\) meV, \(\hbar\Gamma_{20}=0.000025\) meV, \(\Gamma_{12}=0\), \(\hbar\gamma_{01}=0.22\) meV, \(\hbar\gamma_{12}=0.1\) meV, \(\hbar\gamma_{02}=0.001\) meV, and \(\hbar T_{e}=0.01\) meV. Figure 5: The dispersion (**a**,**c**,**e**) and the absorption (**b**,**d**,**f**) spectra for the same parameters as in Figure 4, but with \(\hbar T_{e}=0.5\) meV. Also, \(R=100\) nm (blue solid curve), \(20\) nm (red dashed curve), and \(15\) nm (green dashed-dotted curve). rate coefficient increases, the double SQD molecule susceptibility seems to have an even more important contribution to the spectral profile of the total susceptibility \(\chi_{tot}^{(1)}\). In Figure 6, we investigate the optical response of the two counterparts, as well as the total optical response of the system, for a high electron-tunneling rate (\(\hbar T_{e}=5\) meV). Here, as the interparticle distance decreases, we note an infinitesimal transposition of the resonances, while their intensity is slightly increased, exhibiting an inverse trend with respect to the one observed in Figure 5, for \(\hbar T_{e}=0.5\) meV. In addition, the distance between the inner resonances is doubled. Furthermore, the double SQD molecule contribution almost entirely defines the spectral profile of \(\text{Im}[\chi_{tot}^{(1)}]\), as shown in Figure 6, while the MNP mainly adds a shift to the spectral profile due to the contribution of the double SQD molecule, both co-shaping the profile of the \(\text{Re}[\chi_{tot}^{(1)}]\) spectrum (Figure 6e). In the next three figures, we study the off-resonant case, with \(\hbar\Delta=-1\) meV, for various values of the tunneling rate coefficient (Figure 7: \(\hbar T_{e}=0.01\) meV, Figure 8: \(\hbar T_{e}=0.5\) meV, and Figure 9: \(\hbar T_{e}=5\) meV), where we take \(\hbar\omega_{12}=1\) meV. After carefully studying all the possible cases, it becomes evident that, for \(\Delta\
eq 0\), the spectral profiles lose their symmetry. By comparing Figure 7a,b with the corresponding Figure 4 (for the same electron-tunneling rate, yet with \(\Delta=\omega_{12}=0\)), we observe that, for \(\hbar T_{e}=0.01\) meV, the general profile of the dispersion spectrum of the one figure roughly resembles the profile of the absorption spectrum of the other figure. The rest of the trends that are followed are similar to the ones presented in Figure 4, the most important of them being the significant transposition of the resonances when the center-to-center distance is modified. In the case of an average electron-tunneling rate (\(\hbar T_{e}=0.5\) meV), for \(\hbar\Delta=-\hbar\omega_{12}=-1\) meV, which is presented in Figure 8, we note that the typical six-resonance pattern arises on the spectra of the SQDs' susceptibility, as seen in Figure 8a,b. These patterns usually appear in three-level-system spectra, unless we are in a dark state with exactly resonant transitions or at two-photon resonance. Furthermore, the profile of the total susceptibility is ascribed both to the contributions of the coupled SQDs, as well to the MNP, as seen in Figure 8c,d.