Hysteretic Flux Response and Nondegenerate Gain of Flux-Driven Josephson Parametric Amplifiers

For quantum information processing with superconducting circuits, efficient amplification of weak microwave signals is often required. For this purpose, Josephson parametric amplifiers (JPAs) are commonly used, due to their quantum-limited noise performance. The authors show that flux-driven JPAs exhibit hysteresis, even for negligible screening parameters, and that their amplification properties depend strongly on the resonator characteristics. These phenomena are important for a full understanding of the magnetic field response and parametric amplification in JPAs, and thus their application.