Probing insulating state of a Josephson junction in dc and microwave domains

A single Josephson junction in an Ohmic environment undergoes the Schmid-Bulgadaev quantum phase transition between superconducting and insulating states. Here we present a characterization of the junction's insulating state, combining conventional dc measurements and a novel technique, which probes the junction's response to microwave photons. With both techniques, we observe the junction's behavior, which is consistent with the behavior of an element dual to a superconducting Josephson junction. In the junction's response to a dc excitation, we find Coulomb blockade and Bloch oscillation effects. Accordingly, in the microwave domain, the junction responds to incoming photons as a non-linear Bloch capacitance, which we reveal through the frequency dependance of the phase shift induced by the junction to scattered photons. Our experimental technique allows for the simple characterization of insulating Josephson junctions with potential applications in quantum information science and metrology.