Quantum electrodynamics of a superconductor-insulator phase transition
A chain of Josephson junctions implements one of the simplest many-body models undergoing a superconductor-insulator quantum phase transition between states with zero and infinite resistance. This phenomenon is central to our understanding of interacting bosons and fermions in one dimension. Apart from zero resistance, the superconducting state is always accompanied by a sound-like mode due to collective oscillations of the phase of the complex-valued order parameter. Surprisingly little is known about the fate of this mode upon entering the insulating state, where the order parameter's amplitude remains non-zero, but the phase ordering is “melted” by quantum fluctuations. Here we present momentum-resolved radio-frequency spectroscopy of collective modes in nanofabricated chains of Al/AlOx/Al tunnel junctions. Our key finding is that the GHz-frequency modes survive far into the insulating regime, i.e. an insulator can superconduct AC currents. The insulating state manifests itself by a weak decoherence of collective modes with an unusual frequency dependence: longer wavelengths decohere faster, in fact suggesting the absence of DC transport. Owing to an unprecedentedly large kinetic inductance per unit length, the observed phase mode represents microwave photons with a remarkably low speed of light (below 8x105 m/s) and high wave impedance (above 23 kΩ). The latter exceeds the transition value for the Bose glass insulator, expected in this system, by an order of magnitude, which may challenge theory to revisit the finite-energy condensate dynamics near the transition. More generally, the high impedance translates into a fine structure constant exceeding a unity, opening access to previously impossible regimes of quantum electrodynamics.