Approaching ultra-strong coupling in Transmon circuit-QED using a high-impedance resonator

In this experiment, we couple a superconducting Transmon qubit to a high-impedance $645\mathrm{\Omega }$ microwave resonator. Doing so leads to a large qubit-resonator coupling rate $g$, measured through a large vacuum Rabi splitting of $2g\simeq 910$ MHz. The coupling is a significant fraction of the qubit and resonator oscillation frequencies $\omega$, placing our system close to the ultra-strong coupling regime ($\bar{g}=g\mathrm{/}\omega =0.071$ on resonance). Combining this setup with a vacuum-gap Transmon architecture shows the potential of reaching deep into the ultra-strong coupling $\bar{g}\sim 0.45$ with Transmon qubits.