# Detection of On-Chip Generated Weak Microwave Radiation Using Superconducting Normal-Metal SET
## 2 Experimental Section
### Josephson Junction Microwave Source  
As a local microwave radiation source, we have employed the AC-Josephson effect, linking--by the Josephson relation--the oscillation frequency \(f_{\rm J}\) to the average voltage \(V_{\rm JJ}\) across the tunnel junction [27]. Generally, the Josephson oscillations involve an infinite set of harmonics of the fundamental frequency \(f_{\rm J}=V_{\rm JJ}/\Phi_{0}\), where \(\Phi_{0}=h/2e\) is the flux quantum, but under certain conditions (see [24] for details), the oscillation amplitude of higher harmonics can be made negligibly small compared to the fundamental one, thus resulting in a quasi-monochromatic signal with the amplitude [28]  
\[V_{1}\approx\frac{V_{\rm C}}{\sqrt{1+(\beta_{\rm C}\frac{V_{\rm J}}{V_{\rm C} })^{2}}}, \tag{1}\]  
where \(\beta_{\rm C}\equiv\frac{2\pi}{\Phi_{0}}I_{\rm C}R_{\rm S}^{2}C_{\rm J}\) is the McCumber-Stewart damping parameter [29; 30], \(V_{\rm C}\equiv I_{\rm C}R_{\rm S}\) is the junction characteristic voltage, \(C_{\rm J}\) the junction capacitance and \(R_{\rm S}\) the effective shunt resistance (made up, in our case, of serial bias resistances attached to the junction, _cf._, [15; 16]). Actually, our Josephson junction source consists of a small SQUID (comprising two nominally identical Al/AlO\({}_{x}\)/Al tunnel junctions, with total normal resistance \(R_{\rm N}\approx 5\) k\(\Omega\)) which enables tuning the critical current and, therefore, the generated microwave power by applying a magnetic field. The critical current modulation period is \(\Delta B=\Phi_{0}/A\approx 5\) mT, where \(A\approx 0.4\) um\({}^{2}\) is the effective SQUID loop area. As the on-chip rf-shunting elements (see inset of Figure 3), we used serial thin film resistors made of double layer AuPd/TiO\({}_{x}\) (5/30 nm) [24; 31] with a square sheet resistance \(r\approx 80\)\(\Omega/\square\). The resistors were placed close to the device in order to minimize the capacitive \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Island Area** & **Tunnel Area** & \(R_{T}\) & \(E_{\rm C}\) & \(\Delta\) \\ (μm\({}^{2}\)) & (nm\({}^{2}\)) & (k\(\Omega\)) & (μeV) & (μeV) \\ \hline
1.4 \(\times\) 0.08 & 50 \(\times\) 50 & 110 & 140 & 210 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Typical measured values for the NISIN transistor parameters. Values of \(R_{T}\), \(E_{\rm C}\) and \(\Delta\) are measured at \(T\approx 15\) mK. contributions of the leads, \(C_{\rm L}\sim 0.1\,\)pF, to the small junctions' capacitance, \(C_{\rm J}\sim 5\,\)fF \(\ll C_{\rm L}\), which otherwise would dramatically reduce the oscillation amplitude as a result of a large effective value of \(\beta_{\rm C}\) (see Equation (1)). Figure 3 depicts one of the measured \(I\)-\(V\) curves of the SQUID circuit at \(T\approx 15\,\)mK. The device is biased with a standard transimpedance amplifier as a feedback-controlled DC voltage source (see inset of Figure 3). Using the transimpedance amplifier and 4-point connection layout made it possible to circumvent the contribution of the cryostat wiring to the DC loading curve of the source and on this way to realize an almost perfect DC voltage bias for the SQUID. Continuous quasi-monochromatic microwave oscillation (with a stable Josephson voltage \(V_{\rm JJ}=V\)) is expected in the subgap branch of the \(I\)-\(V\) curve, extending up to the voltages \(V\approx V_{\rm max}=2\Delta/e\). For Al tunnel junctions, \(V_{\rm max}\approx 400\)\(\mu\)V (\(f_{\rm max}=4\Delta/h\approx 200\,\)GHz). At larger bias voltages, the strong DC quasiparticle current (\(>65\,\)nA) leads to the overheating of the junctions and generation of recombination phonons. On the other hand, at \(V<V_{\rm min}\approx 100\)\(\mu\)V, the value of \(V_{\rm JJ}\) is unstable due to the phase retrapping effect [32], and the junction state alternates between the supercurrent and the quasiparticle branch.