Extracting the current-phase relation of a monolithic three-dimensional nanoconstriction using a dc-current-tunable superconducting microwave cavity

Superconducting circuits with nonlinear elements such as Josephson tunnel junctions or kinetic inductance nanowires are the workhorse for microwave quantum and superconducting sensing technologies. For devices, which can be operated at high temperatures and large magnetic fields, nanoconstrictions as nonlinear elements are recently under intense investigation. Constrictions, however, are far less understood than conventional Josephson tunnel junctions, and their current-phase relationships (CPRs), although key for device design, are hard to predict. Here, we present a niobium microwave cavity with a monolithically integrated, neon-ion-beam patterned three-dimensional (3D) nanoconstriction. By design, we obtain a dc-current-tunable microwave circuit and characterize how the bias-current-dependent constriction properties impact the cavity resonance. Based on the results of these experiments, we reconstruct the CPR of the nanoconstriction. Finally, we discuss the Kerr nonlinearity of the device, a parameter essential for many high-dynamic-range applications and an experimental probe for the second and third derivatives of the CPR. Our platform provides a useful method to comprehensively characterize nonlinear elements integrated in microwave circuits and could be of interest for current sensors, hybrid quantum systems, and parametric amplifiers. Our findings furthermore contribute to a better understanding of nanofabricated 3D constrictions.