A Quantum Model for a Graphene Josephson Junction Parametric Amplifier for Quantum-Noise-Limited Microwave Amplification

We present a quantized theoretical framework for the description of a reflection-type resonant microwave parametric amplifier using graphene Josephson junctions. We focus on the regime of interest for parametric amplification and apply a coefficient method combined with a two-photon loss model to analyze the quantum-noise-limited microwave amplification process. Based on the constructed quantum model, we investigate the amplification performance by predicting the reflection magnitude over the narrow gain bandwidth and compare our results to recent experimental data from the literature. The theoretical and experimental reflection magnitudes are in good agreement.