Fig. 2
From: Probing the strongly driven spin-boson model in a superconducting quantum circuit

Spin-boson dynamics and spectra at different coupling strengths in the absence of the drive. a–c Frequency dependence of the imaginary part χ″(ωp) of the linear susceptibility (a.u.) and time evolution of the population difference P(t) (insets) for the three selected combinations of coupling and temperature shown in Fig. 1c. The position ω* and FWHM 2γ of the linear susceptibility peak in the coherent regimes (α = 0.007, α = 0.21) provide a direct measure of the renormalized qubit frequency \({{\Omega }} = \sqrt {\left( {\omega ^ \ast } \right)^2 - \gamma ^2}\). In the incoherent regime (α = 0.8), the peak position yields the relaxation rate γr. d–f Experimental transmission spectra of three flux qubit devices with different coupling junctions are compared with spectra calculated within the NIBA. The characteristic hyperbolic spectrum of the flux qubit is evident in d and recognizable in e. Its disappearance in f indicates the transition to the incoherent regime. At \({\Phi }_\varepsilon\) = Φ0/2 the spin-boson system is unbiased, which is the situation of panels a–c