Quantum electrodynamics of a superconductor–insulator phase transition

A chain of Josephson junctions represents one of the simplest many-body models undergoing a superconductor–insulator quantum phase transition 1 , 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 parameter 3 , 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 fluctuations 5 . 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 experiment 6 – 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 magnitude 9 – 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.