Fig. 3: Strong charge-photon coupling at the charge sweet spot.

a Normalized amplitude of feedline transmission ∣A/A₀∣² as a function of drive frequency f_d and DQD detuning ε. An avoided crossing - the signature of the strong coupling regime–is observed when the DQD-charge transition matches the bare resonator frequency. b ∣A/A₀∣² as a function of drive frequency f_d and the voltage V_flux applied to the resonator coil, which tunes the resonator frequency f_r. During the measurement, the DQD is kept at ε = 0. An avoided crossing is observed around V_flux = 504 mV, when the bare resonator frequency f_r matches the DQD charge transition (f_r = f_q = 2t_c/h). Higher resonator modes are visible near the half-flux point (black arrows)⁶⁶. c ∣A/A₀∣² as a function of f_d at the resonance condition, highlighting the vacuum-Rabi splitting 2g₀/2π. A fit to the master equation model is represented by a solid orange line (see Methods). All the extracted values are reported in Supplementary Table 1. 2g₀ and Γ are indicated (2t_c/h = 4.149 GHz). d Simulation of ∣A/A₀∣² using input-output theory with the parameters g₀/2π = 154 MHz, Γ/2π = 80 MHz, t_c/h = 2.018 GHz extracted from fitting a line-cut of b at V_flux = 504 mV (reported in Supplementary Fig. 8b).