ations in single-photon switches, single-photon transistors, and so on [@Chen2013; @Shomroni2014; @Baur2014; @Zhou2013].

The intrinsic linewidth broadening with increasing driving power when $\langle n\rangle \gg 1$ is explained by the dephasing of $|f\rangle \leftrightarrow |g\rangle$ from the fluctuations of the photon inside the cavity [@Schuster2005]. This is contrast to the linewidth narrowing with increasing driving power in ATS driven with classical control fields [@Abdumalikov2010]. The upper branch of the spectrum is broadened in the vicinity of 12.4 GHz, probably due to an unwanted low quality mode in the environment, which is difficult to remove at high (above 10 GHz) frequencies. Figure 3(d) shows the reflection power when $\langle n\rangle \approx 35$. The red line is fitted by a double-Gaussian curve of the form $A\exp{(-2\big(\delta\omega/\Delta\omega}\big)^2)$, where the fitting parameter $\Delta\omega/2\pi$ is found to be $121$ MHz at 11.876 GHz and $186$ MHz at 12.655 GHz. The linewidths are about twice the coupling strength $g_0$, which can be mainly determined by the Poisson photon distribution of coherent states formed inside the resonator [@Schuster2005].

Finally, we change the coupling strength $g_{0}$ between the transition $|e\rangle \leftrightarrow |f\rangle$ and the resonator by tuning the magnetic field inside the device $\alpha$-loop [@Fedorov2010]. We confirm that the splitting in the reflection spectrum of the coupled system around the transition frequency $\omega_{fe}$ is also twice the coupling strength $g_{0}$.

In conclusion, we engineer an interaction between a superconducting artificial atom and a resonator and observe the vacuum-induced (quantized) Autler-Townes doublet by direct measurement of the reflection spectrum from the atom. Furthermore, we study the transition of the quantum-to-classical Autler-Townes doublet with changing the number of photons inside the resonator. Our work is an important step towards the control of propagating microwaves in a transmissi