LAUSR

A chain of Josephson junctions represents one of the simplest many-body models undergoing a superconductor–insulator quantum phase transition1,2. 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 parameter3,4. Little is known about the fate of this mode on entering the insulating state, where the order parameter’s amplitude remains non-zero, but the phase ordering is ‘melted’ by quantum fluctuations5. Here, we show that the phase mode survives far into the insulating regime, such that megaohm-resistance chains can carry gigahertz-frequency alternating currents as nearly ideal superconductors. The insulator reveals itself through interaction-induced broadening and random frequency shifts of collective mode resonances. Our spectroscopic experiment puts forward the problem of quantum electrodynamics of a Bose glass for both theory and experiment6–8. By pushing the chain parameters deeper into the insulating state, we achieved a wave impedance of the phase mode exceeding the predicted critical value by an order of magnitude9–14. The effective fine structure constant of such a one-dimensional electromagnetic vacuum exceeds unity, promising transformative applications to quantum science and technology.A Josephson junction array is used to show the phase mode associated with superconductivity surviving deep in the insulating regime at high frequency. This generates a device with an effective fine structure constant larger than unity.