Fig. 3
From: Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits
Temperature-induced renormalization. a Zoom on a even–odd pair of transmission peaks for sample A at temperature ranging from 23 to 150 mK. The even mode (gray) does not move while the odd mode (blue is at 25 mK, red at 130 mK) shifts down in frequency when warming up, showing a downward renormalization of the junction frequency \({\omega }_{{\rm{J}}}^{* }\). b ZPF of the small junction \(\langle {\phi }_{{\rm{J}}}^{2}\rangle\) as a function of the temperature for three samples (A, B, and C ranging from dark to light blue), extracted from Eq. (2). ZPF are stronger in sample A, which is associated to a smaller ratio \({E}_{{\rm{J,bare}}}/{E}_{{\rm{c}}}\) (large nonlinearity). The measured quantum to classical crossover is in good agreement with theory (full lines). The inset displays the corresponding renormalized junction frequency \({f}_{{\rm{J}}}^{* }={\omega }_{{\rm{J}}}^{* }/2\pi\) of the three samples. The full lines are the SCHA predictions while the dashed lines represent what would be the temperature evolution of these frequencies if ZPF were omitted from \(\langle {\phi }_{{\rm{J}}}^{2}\rangle\), using the same values of \({E}_{{\rm{J,bare}}}\)
