Vacuum Rabi Mode Splitting at High Drive Powers and Elevated Temperatures

The circuit QED architecture $[1,2]$ is ideal to probe the nonlinearity of a strongly coupled cavity QED system at high drive powers populating the cavity with a controllable average photon number in the range from 0.1 $<$ n $<$ 100. While in atomic cavity QED the radiation pressure exerted on the atoms by the drive tends to expel the atoms from the cavity, superconducting qubits remain at a fixed position and maintain constant coupling. This enables us to explore the cross-over from the quantum to the classical regime in the single qubit-field interaction by measuring vacuum Rabi mode splitting spectra. We also investigate the effect of thermal radiation in the cavity leading to a thermal population of excited states in the Jaynes-Cummings ladder, which was theoretically studied in Ref. $[3]$. Simulations have been carried out in order to determine the optimal set of qubit and resonator parameters needed for first experiments. \newline $[1]$ A. Blais \textit{et al.} Phys. Rev. A \textbf{69}, 062320 (2004). \newline $[2]$ A. Wallraff \textit{et al.} Nature \textbf{431}, 162 (2004). \newline $[3]$ I. Rau \textit{et al.} Phys. Rev. B \textbf{70}, 054521 (2004).