Hysteretic flux response and nondegenerate gain of flux-driven josephson parametric amplifiers

Josephson parametric amplifiers (JPAs) have become key devices in quantum science and technology with superconducting circuits. In particular, they can be utilized as quantum-limited amplifiers or as a source of squeezed microwave fields. Here, we report on the detailed measurements of five flux-driven JPAs exhibiting a hysteretic dependence of the resonant frequency on the applied magnetic flux. We model the measured characteristics by numerical simulations based on the two-dimensional potential landscape of the dc superconducting quantum interference devices, which provide the JPA nonlinearity for a nonzero screening parameter βL>0 and demonstrate excellent agreement between the numerical results and the experimental data. Furthermore, we study the nondegenerate response of different JPAs and accurately describe the experimental results with our theory.