## 3 Results  
Here, we investigate the characteristics associated with the absorption and the dispersion spectra of a probe field applied to an SQD-MNP hybrid structure, under the interaction with a strong pump field, for various interparticle distances. In the following paragraphs, we consider a linearly polarized strong pump field. Its polarization is taken parallel to the interparticle axis \((s_{a}=2)\), while its Rabi frequency \(\hbar\Omega_{a}\) is set equal to 3 meV. The weak probe field Rabi frequency is considered to be 100 times lower than the pump field Rabi frequency. The SQD dielectric constant is \(\varepsilon_{S}=6\varepsilon_{0}\), while for the modeling of the MNP we take the experimental values of the dielectric function referring to gold [57]. The radius \(a\) of the MNP is 7.5 nm. The hybrid structure is considered to be surrounded by vacuum and hence, \(\varepsilon_{env}=\varepsilon_{0}\). For the SQD, we consider values typical for InAs/GaAs SQDs that have been used in previous studies [38; 42; 46]. As far as the dephasing and decay rates related to the double-SQD molecule are concerned, we respectively have \(\hbar\gamma_{01}=0.22\) meV, \(\hbar\gamma_{12}=0.1\) meV, \(\hbar\gamma_{02}=0.001\) meV, and \(\hbar\Gamma_{10}=0.025\) meV, \(\hbar\Gamma_{20}=0.000025\) meV, and \(\Gamma_{12}=0\). Finally, the energy gap associated with the \(\ket{1}\leftrightarrow\ket{2}\) transition is \(\hbar\omega_{12}=1.4\) eV and the dipole moment element \(\mu\) of the \(\ket{0}\leftrightarrow\ket{1}\) transition is equal to \(0.65\cdot e\) nm. More specifically, in Figures 4-10, we present the spectra of the asymmetric double SQD molecule susceptibility, \(\chi^{(1)}_{SQD}\), the MNP susceptibility, \(\chi^{(1)}_{MNP}\), and the total susceptibility of the hybrid structure, \(\chi^{(1)}_{tot}\), as a function of the pump-probe field detuning \(\delta\), for several values of the distance \(R\) that separates the SQD from the MNP (\(R=100\) nm: blue solid curve, 20 nm: red dashed-dotted curve, and 15 nm: green dashed-dotted curve). In Figure 4, the dispersion and the absorption spectra of the probe field are presented for \(\Delta=\omega_{12}=0\), in the case of a quite low value of the tunneling rate \(\hbar T_{e}=0.01\) meV, as seen in Figure 4a,c,e and b,d,f, respectively. First, we observe that, at exact resonance, the absorption/dispersion associated with the double SQD molecule exhibits a symmetric/antisymmetric profile for every value of the tunneling rate coefficient. In Figure 4, since the tunneling rate tends to zero, the spectra of the SQD optical susceptibility, as seen in Figure 4a,b, are identical to the ones plotted for a single SQD-MNP hybrid [36]. As the value of \(R\) decreases, the sideband resonances are transposed away from the spectral center. For the set of parameters used in Figures 4-6 (\(\Delta=\omega_{12}=0\)), the MNP contribution outweighs the contribution of the double SQD molecule, introducing a slope to the spectra of the total susceptibility due to the presence of the first term in the expression of the MNP susceptibility, which is in accordance with the mathematical expression of Equation (28). Figure 3: A dressed-state representation indicating the possible excitation pathways, in the case with \(\omega_{12}=\Delta\). (**a**) refers to the off-resonance case, with a positive pump-field detuning \((\Delta>0)\), while (**b**) refers to the exact-resonance case \((\Delta=0)\). The susceptibility spectra presented in Figure 5 refer to the case of the non-negligible electron-tunneling rate \(\hbar T_{e}=0.5\) meV. Here, we observe a set of inner resonances arising around the positions \(\pm\hbar\sqrt{\Omega_{a}^{2}+T_{e}^{2}}\), as well as a set of outer resonances, placed at \(\pm 2\hbar\sqrt{\Omega_{a}^{2}+T_{e}^{2}}\), which are hardly noticeable due to their low amplitude.