Flux-driven Josephson parametric amplifiers: Hysteretic flux response   and nondegenerate gain measurements
  Josephson parametric amplifiers (JPA) 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, three of them exhibiting a hysteretic dependence of the resonant frequency versus 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 (dc-SQUID), which provide the JPA nonlinearity, for a finite screening parameter $\beta_\mathrm{L}\,{>}\,0$ 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. 
Stefan Pogorzalek, Kirill G. Fedorov, Ling Zhong, Jan Goetz, Friedrich   Wulschner, Michael Fischer, Peter Eder, Edwar Xie, ...
cond-mat.supr-con cond-mat.mes-hall quant-ph