Properties of superconducting circuits based on Josephson junction arrays beyond the single-mode approximation

An accurate description of SNAIL and fluxonium devices is fundamental for their use in scalable quantum processors. Both devices belong to a class of circuits consisting of an array of identical junctions forming a loop with an additional junction different from the rest. Frequently, these circuits are described by an approximate one-mode model which disregards internal array modes. As a result, the physics of array modes has remained largely unexplored, both from the perspective of fundamental understanding and potential applications. We discuss the range of validity and eventual breakdown of the one-mode model as the number of junctions and their parameters are varied. We specifically examine the case in which the odd junction has the larger Josephson energy, a scenario not captured by the one-mode model, and discuss spectral properties and potential applications of this circuit.