Fig. 3: Second harmonic generation.
From: Strong coupling between a single-photon and a two-photon Fock state
a The amplitude of the SHG versus the external flux bias δΦext and the SHG frequency. The efficiency \(\eta \equiv {S}_{21}^{(2\omega )}/{S}_{21}^{(\omega )}\) of the SHG is about 0.1 at the point where the SHG amplitude is maximized (ω1/2π = 4.9 GHz and δΦext = −45 mΦ0), which qualitatively agrees with the theoretical result in Supplementary Fig. 2. b Theoretical calculation corresponding to the plot in (a). c The amplitude of the SHG versus the average photon number \({\overline{n}}_{1}\) in the resonator. The signal frequency applied at the n = 1 mode of the resonator is ω1/2π = 4.9 GHz (at δΦext = −45 mΦ0). The red solid curve is the theoretical fit. The average photon number in (c) is determined by contrasting the experimental data—plotting the maximum second harmonic generation (SHG) amplitude against input power—with the theoretical simulation outlined in Supplementary Eq. (35), as depicted in (c). The power applied in (a and b) corresponds to an average photon number \({\overline{n}}_{1}\simeq 0.25\) in the resonator.
