Analysis of Josephson junction arrays beyond the single-mode approximation

SNAIL and fluxonium devices belong to a group of superconducting circuits that consist of an array of identical Josephson junctions forming a loop with an additional junction that is distinct from the others. An accurate description of such circuits is fundamental for their use in quantum processors as they continue to be scaled up. These circuits are often studied using an approximate one-mode model which disregards higher-energy array modes. As a result, the physics arising from such array modes has remained largely unexplored. We discuss diagnostics to test the range of validity of the one-mode model and we analyze the impact of the array modes on the low-energy physics of the system. We further examine the parameter regime in which the odd junction has the larger Josephson energy, a scenario that goes beyond the conventional one-mode model. We discuss the symmetry, spectral and decoherence properties of the circuit in this parameter regime with a view to potential applications.