Systematic Approach for Tuning Flux-driven Josephson Parametric Amplifiers for Stochastic Small Signals

Many experiments operating at millikelvin temperatures with signal frequencies in the microwave regime are beginning to incorporate Josephson Parametric Amplifiers (JPA) as their first amplification stage. While there are implementations for a wideband frequency response with a minimal need for tuning, designs using resonant structures with small numbers of Josephson elements still achieve the best noise performance. In a typical measurement scheme involving a JPA, one needs to control the resonance frequency, pump frequency and pump power to achieve the desired amplification and noise properties. In this work, we propose a straightforward approach for operating JPAs with the help of a look-up table (LUT) and online fine-tuning. Using the proposed approach, we demonstrate the operation of a flux-driven JPA with 20 dB gain around 5.9 GHz, covering approximately 100 MHz with 20 kHz tuning steps. The proposed methodology was successfully used in the context of a haloscope axion experiment.