## 5 Experimental Results and Discussion
### Characterization of Individual SEBs  
The case of a single SEB is the simplest from the physics standpoint, yet it is the most challenging from the measurement perspective because of its very small admittance and thus low expected SNR. To perform a reflectometry measurement of one SEB (a micrograph of representative device is shown in Figure 1b) we used a matching \(\Pi\) network discussed in Section 3, Figure 7a. Here it is composed of the match improving capacitor, \(C_{IN}\) = 39 pF, a 560 nH inductor and a pad capacitance, \(C_{pad}\). The response of the MN measured at a low temperature (about 50 mK) is shown in Figure 7b (solid line) along with the simulated response curve based on the model in Figure 7a. The values of the inductor's DC resistance (\(R_{DC}\)) and skin-effect resistance (\(R_{SE}\)) are adjusted for experimentally obtained temperature dependence of the coil resistance. The value of the parallel capacitor of the inductor, \(C_{L}\), is not changed, and the resistor that accounted for loss in \(C_{L}\) is adjusted from its room temperature value (\(R_{C}\) = 61 \(\Omega\)) to obtain best fit to the data. The value of \(C_{pad}\) = 901 fF is calculated from the resonant frequency using the parasitics listed above. The results of reflectometry measurements of a single SEB are presented in Figure 8 where the magnitude (Figure 8a) and phase (Figure 8b) of the reflected signal are plotted as a function of gate bias \(V_{g}\). After significant curve averaging resulting in the SNR improvement (by a factor \(\approx\)55), delta-function like features emerged in both the magnitude and phase of the reflected signal. To compare experimental results with the theory (2) we calculated the oscillations in magnitude and phase of SEB admittance (Figure 8c,d). Next, this simulated admittance response is passed through the MN depicted in Figure 7, and the results are plotted as black curves in Figure 8a,b. The SEB parameters used for simulations are based on the following considerations. First, the value of the gate capacitance \(C_{g}\) = 2.88 aF is extracted from the period of oscillations, \(\Delta V_{g}\) in Figure 8: \(C_{g}\) = \(e/\Delta V_{g}\). To evaluate directly immeasurable SEB parameters (\(R_{J}\), \(C_{J}\)) we measured the resistance of an SET fabricated along with SEB with the same junction design \(R_{T}\)\(\sim\)45 k\(\Omega\). The value of the junction capacitance is obtained by comparing the experiment with the simulations, with the value of \(C_{J}\) = 65 aF providing the best fit for the experiment. The simulations of SEB admittance oscillations (Figure 8c,d) using (1) show that despite significant oscillations of \"intrinsic\" (i.e., occurring within the device) SEB admittance in both magnitude and phase, the measured signals exhibited much smaller deviations from constant values corresponding to blockaded states. The observed relative magnitude variation of \(|\Gamma/\Gamma_{0}|<\) 0.7% along with \(\Delta\Theta<\) 0.3\({}^{\circ}\) correlated well with the simulated response. The reason for such small variations from average values is due to the fact that change in the dynamic capacitance, \(C_{Dym}<\) 100 aF (see Figure 2) the maximal values of Sisyphus conductance (\(<\)100 nS) even at a low temperature of 50 mK are occurring in parallel with much larger pad capacitance (\(C_{pad}\) = 901 fF) with an absolute value of admittance of \(\sim\)1 mS at the frequency of the experiment. Note that the choice of \(C_{IN}\) = 39 pF brought the \(\Pi\)-network close to the matching point. The use of the \(L\)-\(C_{pad}\) section alone, without \(C_{IN}\), would have resulted in the magnitude of oscillations \(|\Gamma/\Gamma_{0}|<\) 0.01% and \(\Delta\varphi<\) 0.025 degrees, respectively. Despite close matching, the signal in Figure 8a,b could only be obtained after massive curve averaging (in fact, single scan yielded a noise exceeding signal by a factor of \(\sim\)14).