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 (SI) quantum phase transition between states with zero and infinite resistance. Apart from zero resistance, the superconducting state is necessarily accompanied by a sound-like mode due to collective oscillations of the phase of the complex-valued order parameter. Exciting this phase mode results in transverse photons propagating along the chain. 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 report momentum-resolved radio-frequency spectroscopy of collective modes in nanofabricated chains of Al/AlOx/Al tunnel junctions. We find that the phase mode survives remarkably far into the insulating regime, such that $\textrm{M}\Omega$-resistance chains carry $\textrm{GHz}$-frequency alternating currents as nearly ideal superconductors. The insulator reveals itself through broadening and random frequency shifts of collective mode resonances, originated from intrinsic interactions. By pushing the chain parameters deeper into the insulating state, we achieved propagation with the speed of light down to $8\times 10^5~\textrm{m/s}$ and the wave impedance up to $23~\textrm{k}\Omega$. The latter quantity exceeds the predicted critical impedance by an order of magnitude, which opens the problem of quantum electrodynamics of a Bose glass insulator for both theory and experiment. Notably, the effective fine structure constant of such a 1D vacuum exceeds a unity, promising transformative applications to quantum science and technology.