Decay of plasmonic waves in Josephson junction chains

Abstract

We study the damping of plasma waves in linear Josephson junction chains as well as in two capacitively coupled chains. In the parameter regime where the ground capacitance can be neglected, the theory of the antisymmetric mode in the double chain can be mapped onto the theory of a single chain. We consider two sources of relaxation: the scattering from quantum phase slips (QPS) and the interaction among plasmons related to the nonlinearity of the Josephson potential. The contribution to the relaxation rate $1/\tau$ from the nonlinearity scales with the fourth power of frequency $\omega$, while the phase-slip contribution behaves as a power law with a non-universal exponent. In the parameter regime where the charging energy related to the junction capacitance is much smaller than the Josephson energy, the amplitude of QPS is strongly suppressed. This makes the relaxation mechanism related to QPS efficient only at very low frequencies. As a result, for chains that are in the infrared limit on the insulating side of the superconductor-insulator transition, the quality factor $\omega \tau$ shows a strongly non-monotonic dependence on frequency, as was observed in a recent experiment.

arXiv comment14 pages, 4 figures

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Cited by in corpus (13)

• Quantum electrodynamics of a superconductor-insulator phase transition
• Inelastic scattering of a photon by a quantum phase-slip
• Critical fluorescence of a transmon at the Schmid transition
• Microwave spectroscopy of a weakly-pinned charge density wave in a superinductor
• Photon-instanton collider implemented by a superconducting circuit
• Superconductivity from a melted insulator
• Inelastic decay from integrability
• Theory of coherent phase modes in insulating Josephson junction arrays
• Plasmon localization and relaxation, and thermal transport in one-dimensional conductors
• Highlighting superconductivity in an insulator
• Nonequilibrium plasmon liquid in a Josephson junction chain
• Quantum simulation of the microscopic to macroscopic crossover using superconducting quantum impurities
• Photon-instanton scattering in a superconducting circuit: Beyond the very high impedance regime