Optimizing Josephson-Ring-Modulator-based Josephson Parametric Amplifiers via full Hamiltonian control

A Josephson Parametric Amplifier (JPA) with a large saturation power is an essential ingredient to achieve efficient quantum sensing and qubit readout in superconducting quantum computing circuits. In a previous work, we showed that the saturation power of JPAs is not limited by pump depletion, but instead by the strong nonlinearity of Josephson junctions, the nonlinear circuit elements that enables amplification in JPAs [1]. Here, we present a systematic study of the nonlinearities in JPAs, we show which nonlinearities limit the saturation power, and present a strategy for optimizing the circuit parameters for achieving the best possible JPA. For concreteness, we focus on JPAs that are constructed around a Josephson Ring Modulator (JRM). We show that by tuning the external and shunt inductors, we should be able to take the best experimentally available JPAs and improve their saturation power by ~ 15dB. Finally, we argue that our methods and qualitative results are applicable to a broad range of JPAs with few-Josephson junctions like SNAILs.

[1]. G. Liu et al, Appl. Phys. Letts., 111, 202603 (2017)