Understanding the Saturation Power of Josephson Parametric Amplifiers Made from SQUID Arrays

We report on the implementation and detailed modeling of a Josephson parametric amplifier (JPA) made from an array of eighty superconducting quantum interference devices (SQUIDs), forming a nonlinear quarter-wave resonator. This device is fabricated using a very simple single-step fabrication process. It shows a large bandwidth (45 MHz), an operating frequency tunable between 5.9 and 6.8 GHz, and a large input saturation power (-117 dBm) when biased to obtain 20 dB of gain. Despite the length of the SQUID array being comparable to the wavelength, we present a model based on an effective nonlinear LC series resonator that quantitatively describes these figures of merit without fitting parameters. Our work illustrates the advantage of using array-based JPA since a single-SQUID device showing the same bandwidth and resonant frequency would display a saturation power 15 dB lower.