Designing pump-efficient Josephson parametric amplifiers with high saturation power

Circuit QED based quantum information processing relies on low noise amplification for signal readout. In the realm of superconducting circuits, this amplification is often achieved via Josephson parametric amplifiers (JPA). In the past, these amplifiers exhibited low power added efficiency (PAE), which is roughly the fraction of pump power that is converted to output signal power. This is relevant because high saturation power amplifiers with very low PAE put a high heat load on the cryostat and limit the number of amplifiers that a dilution refrigerator can host. Here, we numerically investigate upper bounds on PAE by directly integrating the device equations of motion. We focus on a class of parametric amplifiers that consists of a capacitor shunted by a nonlinear inductive block. We first identify that amplifiers with inductive blocks composed of repeating elements must have monotonic current-phase relations in order to avoid exciting high-frequency modes. Using this design rule, we propose two circuit designs for JPA inductive blocks. We find that there is considerable room to improve PAE as compared to state of the art devices. For example, for degenerate amplifiers with power gain of 20 dB, the PAE is ~0.1% for typical JPAs, 37.9% for our simpler circuit JPAs, and 42.6% for our more complex circuit JPAs. Finally, we investigate practical implementations of these circuits which consider manufacturing tolerances and the effect of stray inductance in real circuits.