## 4 Data Analysis and Discussion
The form of the spectrum Re\(Y\)(\(f\)) (a thick line after annealing (Figure 7a)) fits well with five Lorentz curves with the following central frequencies \(f_{\rm ka}\) and the linewidths \(\delta f_{\rm ka}\), in THz: \(f_{\rm 1a}\) = 4.14, \(\delta f_{\rm 1a}\) = 0.245; \(f_{\rm 2a}\) = 4.56, \(\delta f_{\rm 2a}\) = 0.171; \(f_{\rm 3a}\) = 4.62, \(\delta f_{\rm 3a}\)= 0.102; \(f_{\rm 4a}\) = 4.68, \(\delta f_{\rm 4a}\) = 0.087; \(f_{\rm 5a}\) = 4.84, \(\delta f_{\rm 5a}\) = 0.43. A sum of three Lorentz curves is sufficient to fit the spectrum Re\(Y\)(\(f\)) (thick navy curve in Figure 7b) for the same JJ before annealing in oxygen. The fit parameters, in THz, are the following: \(f_{\rm 2b}\) = 4.54, \(\delta f_{\rm 2b}\) = 0.219; \(f_{\rm 3b}\) = 4.61; \(\delta f_{\rm 3b}\) = 0.113; \(f_{\rm 5b}\) = 4.89, \(\delta f_{\rm 5b}\) = 0.12. Comparison of the results of nonlinear fits for the same JJ before and after annealing shows that three spectral components at \(f_{\rm 2}\) = (4.55 \(\pm\) 0.01) THz; \(f_{\rm 3}\) = (4.61 \(\pm\) 0.01) THz and \(f_{\rm 5}\) = (4.86 \(\pm\) 0.03) THz practically did not change the positions of their maxima, but increased their peak values by about two, three and four times, correspondingly. In addition, two extra Lorentz curves appeared at \(f_{\rm 1}\) = 4.14 THz and \(f_{\rm 4}\) = 4.68 THz after annealing, while the curve at 4.68 THz has a narrow linewidth of around 0.09 THz. This low linewidth is a hint that the mode at \(f_{\rm 4}\) = 4.68 THz belongs to highly oxygenated YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\rm x}\)[26]. The general trend in the constituent Lorentzians in the spectra in Figure 7a,b is the intensification of the lines at \(f_{\rm 2}\), \(f_{\rm 3}\), and \(f_{\rm 5}\) and the appearance of new lines at \(f_{\rm 1}\) and \(f_{\rm 4}\) in the spectral range from 4.1 THz to 5.1 THz. This trend is in qualitative agreement with the tendency deduced from the data in Table 1 (see also [26]), where initial deoxygenation results in the splitting of the 4.65 THz line, followed by an increase in the number of splitted lines and frequency differences in splitting with further deoxygenation. It is worthwhile to compare quantitatively the absorption lines obtained by Josephson admittance spectroscopy lines in the YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\rm x}\) bicrystal thin-film JJ and those in the reflection spectra of YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\rm x}\) single crystals [26]. The narrowest line at \(f_{\rm 4}\) = 4.68 THz in the YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\rm x}\) JJ can be from the optical phonon mode with \(E\mid\mid c\), observed in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.95}\) single crystals at 4.65 THz. The lines at \(f_{\rm 3}\) = 4.62 THz, \(f_{\rm 2}\) = 4.56 THz,  
Figure 7: Real parts of dynamic conductances Re\(Y\)(\(f\)) for JJyd705101_1 (thick navy lines) recovered from experimental data in Figure 6 according to [PERSON] admittance spectroscopy: (**a**) after low-temperature annealing in atomic oxygen, (**b**) before annealing. Dashed grey lines are nonlinear fits by multiple Lorentz curves. The thin colored lines are Lorentz curves from the fits. Parameters are in the text. and \(f_{1}\) = 4.14 THz can be from the splitted collective modes at 4.59 THz, 4.41 THz, and 4.08 THz in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.7}\). The line at \(f_{5}\) = 4.84 THz in the YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) JJ can be due to the splitted collective mode at 4.83 THz in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.5}\). This comparison makes it possible to estimate the oxygen distribution in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) near the bicrystal boundary of JJs made from YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) thin films with mutually tilted \(c\)-axes. After this comparison, one can suggest some mixed composition, from YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6}\) (with no oxygen in the chains) to YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.85}\) (the chains partly filled with oxygen), in the YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) electrodes of the bicrystal JJ as fabricated.