## 5 Experimental Results and Discussion
### Comparison of Performance between SEB Array and DC-Decoupled SET
One can also speculate that these lines correspond to signatures of SEBs visible in FFT of Figure 18b with inverse periods of 16-18 V\({}^{-1}\) (first harmonic) and 32-26 V\({}^{-1}\) (second harmonic), since the physical layout for SEBs in this experiment is exactly the same as in for the device with three SEBs discussed above (Figures 10-12). However, the closeness of the second harmonic of the signal \(2\times 8.5=17\) V\({}^{-1}\) generated by the DCD SET makes it impossible to accurately identify the SEB signature in FFT. To further investigate SEBs and perform an accurate comparison, in the next experiment both DCD SETs are \"muted\" by shorting their source and drain electrodes thus making both of SETs grounded for AC. This converts the measured sample into just an array of 4 SEBs. The experiment is then repeated, and comparative performance of the two configurations (two SETs plus four SEBs) vs. four SEBs is presented in Figure 19a,b where the respective derivatives are plotted for the two cases. 2D map of phase derivative oscillations \(d\Theta|dV_{g}\) is shown in Figure 19c where only lines of negative slopes are observed as expected for SEBA with DC grounded sources, and a typical oscillation \"frequency\" of about 20 V\({}^{-1}\). It is clear that the four SEBs device yields much weaker (by more than an order of  
Figure 17: **(a) Simplified circuit diagram of the DC decoupled-SET (DCD SET). Either one or both junctions are isolated with one or two non-leaky capacitors. (b) Circuit diagram of the experiment: two SETs and four SEBs are connected together to a single MN, with the SETs in counter-parallel configuration, and SEBs in parallel configuration. The lower SET in the diagram is a ”DC-decoupled.” (c) The electron micrograph of the structure used in the experiment. Four SEBs are clearly visible near \(V_{gs}\) electrode The SET on the left is fully floating; the SET on the right is source-coupled to the \(V_{gT}\) source (=AC ground). **  
magnitude) signal in magnitude of reflection but exhibited noticeable signal strength in phase of the reflected signal. Taking into account sensitivity scaling \(\sim N^{1/2}\) a nine times larger SEBA (\(N\geq 4\times 9\)) is needed to reach the phase sensitivity, and \(N\geq 4\times 400\) SEBA is needed to reach the magnitude sensitivity of a single DCD SET. (Here we also took into consideration the doubling of the sensitivity in the maxima for the two SETs, counterbalanced by approximately two times smaller \(C_{g}\) coupling to the SETs). This confirms the trends discussed in Section 2 (Figure 3e). Figure 18: Experimental results from 4 SEBs and 2 DCD SETs obtained at T = 1.45 K (**a**) Oscillations of \(R\) and \(\Theta\) as a function of the sensing gate, \(V_{gS}\). (**b**) Fast Fourier spectra of the magnitude and phase of the reflected signal over \(\pm 4\) V \(V_{gS}\) range. Two lower frequency components in magnitude stem from the SETs, while smaller peaks marked by green arrows point to the 1 st and 2 nd harmonics of signals stemming from 4 SEBs charging. (**c**) 2D maps of \(dR/dV_{g}\) and \(d\Theta/dV_{g}\) oscillations. Phase derivative plot reveals the presence of a much weaker signal (faint steep lines in \(d\Theta/dV_{g}\) map) that corresponds to charging in the SEBs. There is a visible random telegraph noise near \(V_{gS}=-0.62\) V, likely due to random trap charging near the “fully floating” DCD SET.