Table 1 Parameters of three samples. The bare Josephson energy \({E}_{{\rm{J,bare}}}^{{\rm{AB}}}\) is inferred using the Ambegaokar–Baratoff law. \({E}_{{\rm{J}}}^{* }\) is the measured value of the renormalized Josephson energy. As a consistency check, the bare value \({E}_{{\rm{J,bare}}}^{{\rm{th}}}\) is also extracted from the fit of \({E}_{{\rm{J}}}^{* }\) using the SCHA. \({C}_{{\rm{sh}}}\) is the capacitance shunting the small Josephson junction (see Supplementary Note 9). \(C\), \({C}_{{\rm{g}}}\), and \(L\) are obtained from the dispersion relation of the chain (see Supplementary Note 10)
From: Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits
Sample | A | B | C |
|---|---|---|---|
Small junction | |||
Area [\(\mu {m}^{2}\)] | 315 × 195 | 370 × 190 | 440 × 185 |
\({C}_{{\rm{J}}}\) [fF] | 2.7 \(\pm\) 0.3 | 3.2 \(\pm\) 0.3 | 3.7 \(\pm\) 0.4 |
\({C}_{{\rm{sh}}}\) [fF] | 3.0 \(\pm\) 0.5 | 2.4 \(\pm\) 0.4 | 5.1 \(\pm\) 1.0 |
\({E}_{{\rm{J}}}^{* }\)[GHz] | 1.8 \(\pm\) 0.1 | 3.1 \(\pm\) 0.2 | 5.7 \(\pm\) 0.3 |
\({E}_{{\rm{J,bare}}}^{{\rm{AB}}}\) [GHz] | 3.7 \(\pm\) 0.2 | 5.8 \(\pm\) 0.3 | 6.8 \(\pm\) 0.5 |
\({E}_{{\rm{J,bare}}}^{{\rm{th}}}\) [GHz] | 3.7 | 5.5 | 8.2 |
Nonlinearity \({E}_{{\rm{J,bare}}}/{E}_{{\rm{c}}}\) | 0.27 | 0.40 | 0.93 |
Renormalization \({E}_{{\rm{J}}}^{* }/{E}_{{\rm{J,bare}}}\) | 0.49 | 0.56 | 0.70 |
Chain | |||
\(C\) [fF] | 144 | 144 | 144 |
\({C}_{{\rm{g}}}\) [fF] | 0.189 | 0.192 | 0.181 |
\(L\) [nH] | 0.66 | 0.60 | 0.61 |
\({E}_{{\rm{J}}}/{E}_{{\rm{c}}}\) | 460 | 506 | 498 |
