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arXiv · 2608.03871

Few-photon degenerate parametric resonance in a two-tone driven microwave resonator

Orjan Ameye·Jakob Koenig·Clinton Potts·Oded Zilberberg·Gary Steele
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Abstract

Multi-tone external driving offers a route to parametric physics without directly modulating the device. However, the validity of the parametric response in the few-photon regime remains underexplored. Here, we apply two coherent microwave tones to a Josephson-junction Kerr oscillator and stimulate degenerate parametric downconversion via four-wave mixing. Using transmission spectroscopy, we observe that the response retains the qualitative semiclassical Kerr parametric oscillator structure, including its instability lobe and bistable phase-space topology. Interestingly, we demonstrate that a conventional single-mode reduction fails to capture the system quantitatively: the predicted AC Stark shift is severely underestimated, and the reported distributions might not be fully physical when the single-photon Kerr shift $K$ exceeds the cavity linewidth $\kappa$. Instead, we show that a full three-tone quantum description accurately reproduces the experimental observables. There, quantum fluctuations of the drive tones become dynamically dominant over dissipation, and all three interacting tones operate in a deep few-photon limit where the expected semiclassical macroscopic lobes undergo fundamental renormalization due to profound mixing with quantum variance. Our results establish two-tone-driven Kerr oscillators as potential parametric amplifiers and open new horizons to explore the quantum-to-classical crossover in driven-dissipative circuits.

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Orjan Ameye, Jakob Koenig, Clinton Potts, Oded Zilberberg, Gary Steele. 2026-08-04. Few-photon degenerate parametric resonance in a two-tone driven microwave resonator. https://arxiv.org/abs/2608.03871

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