Understanding the saturation power of Josephson Parametric Amplifiers made from SQUIDs arrays

We report on the implementation and detailed modelling of a Josephson Parametric Amplifier (JPA) made from an array of eighty Superconducting QUantum Interference Devices (SQUIDs), forming a non-linear quarter-wave resonator. This device was fabricated using a very simple single step fabrication process. It shows a large bandwidth (45 MHz), an operating frequency tunable between 5.9 GHz 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 non-linear 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.