Imaging non-Gaussian output fields produced by Josephson parametric amplifiers: theory*

Josephson parametric amplifiers (JPA) have facilitated significant improvements in the~readout~fidelity of superconducting qubits [1]. Understanding and detailed characterization of current designs is necessary in order to improve the current generation of quantum-limited amplifiers with the goal of obtaining larger gain, bandwidth and dynamic range. In this talk, we theoretically explore the impact of terms going beyond the standard ``stiff-pump'' approximation in the description of JPAs. In particular we consider the impact of usually neglected nonlinear corrections on the properties of the JPA. ~Using the maximum entropy principle [2], we show how to reconstruct the filtered output state of a JPA. This reconstruction allows us to quantify the non-gaussianity of the output field and the noise properties of the JPA. \\[4pt] [1] Jeffrey, E. et al., PRL~\textbf{112}, 190504~(2014)\\[0pt] [2] Buzek, V. et al., PRA~\textbf{54}, 804 (1996)