Figure 5: Two-level system vacuum Rabi mode splitting.

(a) Colour plot of the measured reflection S₁₁ of a weak coherent probe tone ω_p as a function of the drive power P_d (P₀=1 mW) for drive detunings Δ_r,d/2π=−6.5 MHz (left) and Δ_r,d/2π=5.6 MHz (right). In these plots, blue (yellow) colour corresponds to high (low) reflectivity. Measurements were taken for a fridge temperature T_f=11 mK. The black dashed curve shows the theoretically TLS-resonator frequency tuning for a theoretical model with coherent TLS-resonator coupling g_0,tls/2π=0.9 MHz and input attenuation . The white dashed curve is a plot of the same theoretical model including the AC Stark tuning of the TLS but with the resonator and TLS otherwise decoupled. (b) Measured spectrum (blue curve) and double Lorentzian fit (red curve) for Δ_r,d/2π=−6.5 MHz and three different drive powers corresponding to the vertical green dashed lines in a. From top to bottom the drive powers are P_d/P₀=−59.5, −46 and −43 dB. As indicated, the estimated bare TLS-resonator detuning for each of these drive powers from the fit model is from top to bottom δ_tls,r/2π=−1.5, −0.5 and 0.6 MHz.