## 2 Dilute Rubidium Atoms in a Solid Argon and Neon Matrix: Experimental Results
been adopted to couple the light coming from the laser source to the crystal and a small fraction (\(\lesssim\)1%) of the beam has been focused into a silicon photodiode that acts as a laser system monitor. No control of the polarization of the source has been done. An optical fiber connects the output BK7 window to the the light-detection system that can be made of a NIR spectrometer (Ocean Optics NirQuest) or of a Silicon (Si) photodiode coupled with long-pass filters. Through these kind of sensors we can measure the fluorescence spectra in different visible and NIR regions. To minimize the background noise, the measurements have been carried out in a dark environment. We report here only the measurements relevant for the analysis of the width of the emitted spectrum, and for the comparison with the theoretical calculations that will be presented in the following section. Figure 3 shows the fluorescence spectrum in the NIR region of the Rb-Ar crystal excited at \(\lambda_{excitation}=770\) nm. At this excitation wavelength, the emission spectrum is optimized in amplitude; furthermore this \(\lambda\) is very close to the D\({}_{2}\) line of the rubidium [33]. The blue line represents the acquired data while purple curves are the Lorentzian fits of the peaks, given by:  
\[L(\lambda)=y_{0}+\frac{2A\Delta\lambda/\pi}{4(\lambda-\lambda_{c})^{2}+(\Delta \lambda)^{2}}, \tag{1}\]  
where \(\lambda_{c}\), \(A\), \(\Delta\lambda\) are, respectively, the central wavelength, the width and the area of the Lorentzian, and \(y_{0}\) is an offset. The results of the fits are listed in the Table 1.  
If we consider the three main peaks of the emission spectrum (peak 1, 2 and 3 of Table 1), their relative energy widths \(\Delta E/E=|\Delta\lambda/\lambda_{c}|\) are:  
\[ \begin{array}{c}(\Delta E/E)_{1}\sim 7\%\,,(\Delta E/E)_{2}\sim 9\%\\ (\Delta E/E)_{3}\sim 4\%\end{array}  \tag{2}\]  
We can identify these peaks as energy-shifted transitions from the ground state of the Rubidium atoms to the first excited-states group [34], with energy levels corrected by the energy shifts due to the matrix interaction (the unperturbed transition wavelengths from \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Peak** & **A (a.u.)** & **\(\lambda_{c}\) (nm)** & **\(\Delta\lambda\) (nm)** \\ \hline
1 & (70 \(\pm\) 3)\(\cdot 10^{5}\) & 927.4 \(\pm\) 0.3 & 71 \(\pm\) 10 \\
2 & (56 \(\pm\) 5)\(\cdot 10^{5}\) & 1034.9 \(\pm\) 0.3 & 92 \(\pm\) 4 \\
3 & (151 \(\pm\) 3)\(\cdot 10^{5}\) & 1154.8 \(\pm\) 0.2 & 39 \(\pm\) 10 \\
4 & (79 \(\pm\) 4)\(\cdot 10^{2}\) & 1624.7 \(\pm\) 0.4 & 37 \(\pm\) 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Peak parameters of the fits of Figure 3.  
Figure 3: Fluorescence spectrum of the Rb-Ar crystal excited with 770 nm photons. The blue line represents experimental data, while purple curves are the Lorentzian fits. ground to the first upper excited states are in the range \(\lambda\)\(\sim\)[770; 771; 772; 773; 774; 775; 776; 777; 778; 779; 780; 781; 782; 783; 784; 785; 786; 787; 788; 789; 790; 791; 792; 793; 794; 795] nm, according to the specific fine and hyperfine transition). This is very reasonable, because the transitions of the Argon atoms in the solid matrix are at a quite higher energy. We can meaningfully identify the large broadening of these peaks of the spectrum as the effect of an inhomogeneous broadening of the energy levels, for both the ground and the first electronically-excited levels, consequent (in part, at least) to the interaction of the alkali atoms with the Argon atoms of the solid matrix. Figure 4 shows the measured fluorescence emission integrated for \(\lambda_{emission}>850\) nm as a function of the excitation wavelength.