# Fully Superconducting Josephson Bolometers for Gigahertz Astronomy
## 5 Performance Deduced from the Experimental Data
### JES Bolometer Experimental Deduced Performance  
Additionally for the JES, the noise equivalent power is limited by thermal fluctuations between the electron and phonon systems in \(A\)[44]. Other limitations to the resolution can arise from the measurement of the superconducting to normal-state transition, which we assume it is optimized to be sub-dominant. The values of \(NEP_{TFN,JES}\) can be extracted by substituting in Equation (16) the measured parameters of the JES, such as \(I_{C,0}\), \(R(T)\) characteristics, \(\Delta_{A}\) and \(\Sigma_{A}\) (see previous sections for details). We note that the performance can be extracted at any value of \(I\), since the operation in the dissipationless superconducting state ensures that \(T_{e}(I)=T_{bath}\) (see Figure 5b,c).  
As expected, \(NEP_{TFN,JES}\) can be in situ finely controlled by tuning \(I\). In particular, it decreases monotonically by increasing the amplitude of bias current, as shown in Figure 6a. Notably, the current bias modulates the device sensitivity over about 6 orders of magnitude. Furthermore, the extracted data indicate that the JES [34] reaches best sensitivities several orders of magnitude better than nano-TES bolometers [33] and all other sensors proposed and realized [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 35; 36; 37; 48] so far. Specifically, the JES showed unprecedented values of \(NEP_{TFN,JES}\) as low as \(\sim\)\(1\times 10^{-25}\) W/\(\sqrt{\text{Hz}}\) for the highest bias current \(I=370\) nA (\(I_{C,0}/I\simeq 1.5\)) corresponding to a working temperature of about 18 mK. This sensitivity arises from the extremely suppressed heat exchange of \(A\) with all the thermal sinks (the phonons and the lateral electrodes) due to the combination of very low working temperature and operation deeply in the superconducting state.  
The JES time constant (\(\tau_{1/2}\)) can be calculated by the combination of Equations (13) and (18). As for the TES, it is proportional to the ratio between the electron heat capacitance and  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**nano-TES** & \(T_{C}\) **(mK)** & \(\alpha\) & \(NEP_{TFN,nano-TES}\) **(W/\(\sqrt{\text{Hz}}\))** & \(\tau\) **(\(\mu\)s)** & \(\tau_{eff}\) **(ns)** \\ \hline Sample 1 & 128 & 2742 & \(5.2\times 10^{-20}\) & 6 & 10 \\ Sample 2 & 139 & 121 & \(6.7\times 10^{-20}\) & 5 & 200 \\ \hline \end{tabular}
\end{table}
Table 1: Performance of nano-TES bolometers deduced from the experimental data reported in Section 4.  
the electron-phonon heat conductance in \(A\)[44]. Figure 6a shows the dependence of the JES time constant deduced from the experimental data on the amplitude of \(I\). As expected, \(\tau_{1/2}\) is monotonically suppressed by rising \(I\), since the thermalization of \(A\) is exponentially suppressed by decreasing the working temperature. In particular, \(\tau_{1/2}\) varies between \(\sim\)1 us at \(I_{C,0}/I\simeq 42\) and \(\sim 100\) ms at \(I_{C,0}/I\simeq 1.5\).  
The tunability of the JES properties allows to choose between moderate sensitivity/fast response and extreme sensitivity/slow response by simply varying the bias current within the same structure. As a consequence, the same bolometer could fulfill the requirements of different applications.