Plasmon decay and non-equilibrium steady states in Josephson junction chains

Josephson junction (JJ) chains combine the coherence of superconductivity with the controllability of microwave-frequency circuits, making them a powerful platform for circuit quantum electrodynamics. In this work we consider a long JJ chain that effectively realizes a multi-mode cavity with nonlinear dispersion and additional multi-mode interactions. Individual modes appearing due to the finite size of the chain can be experimentally probed via microwave spectroscopy, both in equilibrium and in driven far-from-equilibrium settings. We study the role of multi-mode interactions in degrading internal coherence -- observable as excess linewidth -- in both equilibrium and driven regimes. Focusing on two-into-two mode scattering as the leading relaxation process, we classify the relevant scattering processes and derive their expected temperature- and frequency-scaling under equilibrium conditions. For experimentally relevant parameters, we show that the equilibrium decay rate is dominated by non-resonant processes, however weakly driving a particular set of modes out of equilibrium enhances resonant scattering, leading to observable signatures in the distribution function and linewidth. Finally, in the strong non-equilibrium regime we report a crossover to a qualitatively different non-equilibrium steady state.