Combined DC and Microwave Probing of the Insulating State of a Josephson Junction.

A Josephson junction (JJ) conducts supercurrent when placed in a low-impedance environment, but undergoes a quantum phase transition to an insulating state when the environmental impedance exceeds the resistance quantum R_Q. We induce this underexplored insulating state by galvanically connecting a JJ to a high-impedance transmission line. This line, composed of thousands of large-area Josephson junctions, reaches characteristic impedances of 5*R_Q while creating a bath of individually accessible high-quality standing wave modes. In this configuration, the JJ functions as a nonlinear "Bloch" capacitive termination of the line and scatters incoming photons, resulting in measurable frequency shifts and spectral broadening. Combining microwave spectroscopy with DC excitation, we simultaneously observe charging effects such as Coulomb blockade and inelastic scattering of microwave photons. Our hybrid DC-RF setup uniquely allows us to present results detailing the intricate interplay between the low and high-frequency responses of an insulating junction, offering insights for advancing quantum theory and metrological techniques.