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arXiv · 2507.22630

Parametric Amplification in Kerr Nonlinear Resonators: A theoretical review of Josephson Parametric Amplifiers

Rajlaxmi Bhoite·Shraddhanjali Choudhury
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Abstract

This paper presents a detailed theoretical review of the amplification process in Josephson Parametric Amplifiers (JPAs), which are crucial for quantum-limited signal amplification in superconducting circuits. The paper begins by outlining the principles of parametric amplification, focusing on how a strong classical pump interacts with the nonlinear Josephson medium in reflection geometry. The key dynamical equations are derived under intense pumping, leading to a nonlinear steady-state solution. Linearization around this solution allows to analyze the system response to weak signals and extract expressions for parametric gain and intermodulation gain using the input-output formalism. Numerically, the equations are solved to explore how the gain depends on frequency detuning and pump strength, which is visualized with a gain response curve. By enhancing our understanding of JPAs, this work aims to inspire continued research in the field of quantum-limited amplification.

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Rajlaxmi Bhoite, Shraddhanjali Choudhury. 2025-07-30. Parametric Amplification in Kerr Nonlinear Resonators: A theoretical review of Josephson Parametric Amplifiers. https://arxiv.org/abs/2507.22630

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