  In this experiment, we couple a superconducting Transmon qubit to a
high-impedance $645\ \Omega$ 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 ($\bar{g}=g/\omega=0.071$ 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.
