Resistively shunted Josephson junctions in the quantum regime

We perform spectroscopy of resistively shunted Josephson junctions in a superconducting circuit QED experiment. We investigate a range of parameters for the junction impedance E_J/E_C ≈ 0.1-10, covering the Cooper-pair box to the light transmon. The galvanically connected resistive shunt R is varied over several orders of magnitude, R ≈ 0.01-100 R_Q, where R_Q = h/(2e)² ≈ 6.5 kΩ. Our setup avoids issues of previous experiments including Joule heating, DC noise, and implementation of a resistor as a finite transmission line. The data hints at a new phase diagram for the damped Josephson junction. Instead of attempting to prove the existence of the Schmid transition line, we turn our attention to an experiment that tests for the existence of two different phases (capacitive and inductive response). We clarify the role of a dissipative high impedance element on the dynamics of a Josephson junction in the quantum regime and set the stage for a better understanding of phenomena such as dual Shapiro steps, also known as Bloch oscillations.