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arXiv:2608.03440

Suppressing Cavity Frequency Noise Using a Kerr Nonlinearity

J. P. van Soest, S. Meilof, G. L. Bhai, M. Villiers, C. A. Potts, G. A. Steele

quant-phSubmitted Aug 4, 2026• Announced Aug 5, 2026• 0 citations
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Abstract

Resonance-frequency fluctuations can limit the sensitivity and stability of superconducting microwave cavities used for qubit readout, optomechanical displacement sensing, and magnetic flux detection. Here, we demonstrate the suppression of resonance-frequency fluctuations by locking a noisy nonlinear superconducting microwave cavity to a strong pump tone. The Kerr nonlinearity of this system, whereby the resonance frequency depends on the intracavity field amplitude, gives rise to an intrinsic feedback mechanism that enables passive stabilization without active external feedback. Using two-tone spectroscopy, we experimentally characterize the intrinsic nonlinear feedback mechanism and investigate its temporal stability through Allan deviation analysis. The frequency fluctuations of the locked cavity mode are reduced by nearly two orders of magnitude, reaching the $1/f$ noise floor, without continuous frequency tracking or active control. Kerr locking provides a general approach for self-stabilizing nonlinear microwave resonators by suppressing low-frequency cavity noise while preserving sensitivity to signals outside the locking bandwidth. This approach may benefit a broad range of systems, including SQUID-based resonators, optomechanical devices, and parametric amplifiers.

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Resonance-frequency fluctuations can limit the sensitivity and stability of superconducting microwave cavities used for qubit readout, optomechanical displacement sensing, and magnetic flux detection. Here, we demonstrate the suppression of resonance-frequency fluctuations by locking a noisy nonlinear superconducting microwave cavity to a strong pump tone. The Kerr nonlinearity of this system, whereby the resonance frequency depends on the intracavity field amplitude, gives rise to an intrinsic feedback mechanism that enables passive stabilization without active external feedback. Using two-tone spectroscopy, we experimentally characterize the intrinsic nonlinear feedback mechanism and investigate its temporal stability through Allan deviation analysis. The frequency fluctuations of the locked cavity mode are reduced by nearly two orders of magnitude, reaching the 1/f1/f1/f noise floor, without continuous frequency tracking or active control. Kerr locking provides a general approach for self-stabilizing nonlinear microwave resonators by suppressing low-frequency cavity noise while preserving sensitivity to signals outside the locking bandwidth. This approach may benefit a broad range of systems, including SQUID-based resonators, optomechanical devices, and parametric amplifiers.
Superconducting optomechanical circuits enable frequency mixing of optical and mechanical modes, facilitating the generation of microwave frequency combs. However, such optomechanical combs suffer from frequency fluctuations, requiring their stabilization for applications in precision sensing and signal processing. Here, we investigate the sideband injection locking of microwave frequency combs in a niobium-based superconducting optomechanical circuit. By strongly driving the device with a blue-detuned pump to induce parametric instability and introducing an additional tone near individual comb peaks, we study how the locking range varies with the power, the frequency position, and the sweep direction of the injection tone. The locking responses show interesting features such as injection hysteresis, which cannot be explained by existing models. Numerical simulations of the classical optomechanical equations implementing a cubic mechanical nonlinearity show that the nonlinearity contributes to broadening the locking range. We also characterize the Allan deviations and phase noise of the injection-locked combs for different injection frequencies, demonstrating enhanced stability performance. Our results lay the foundation for the utilization of optomechanical combs for applications in nanomechanical sensing and cryogenic microwave pulse generation.
Environmental noise coupling to mechanical experiments often introduces low-frequency fluctuations to the resonators, adding noise to measurements and reducing signal to noise. To counter these fluctuations, we demonstrate a dynamic feedback system implemented by the locking of a microwave drive to the noisy cavity. A homodyne interferometer scheme monitors the cavity resonance fluctuations due to low-frequency noise, which is mitigated by frequency-modulating (FM) the microwave generator. The feedback has a bandwidth of 400400400 Hz, with a reduction of cavity fluctuations by 84%84\%84% integrating up to a bandwidth of 222 kHz. Moreover, the cavity resonance frequency fluctuations are reduced by 73%73\%73%. This scheme can be scaled to enable multi-tone experiments locked to the same feedback signal. As a demonstration, we apply the feedback to an optomechanical experiment and implement a cavity-locked, multi-tone mechanical measurement. As low-frequency cavity frequency noise can be a limiting factor in many experiments, the multi-tone microwave locking technique presented here is expected to be relevant for a wide range of fields of research.
Microwave cavities are commonly used in many experiments, including optomechanics, magnetic field sensing, magnomechanics, and circuit quantum electrodynamics. Noise, such as variations in the magnetic field or mechanical vibrations, can cause fluctuations of the natural frequency of the cavity, creating challenges in operating them in experiments. To overcome these challenges, we demonstrate a dynamic feedback system implemented by the locking of a microwave drive to the noisy cavity. A homodyne-interferometer scheme monitors the cavity resonance fluctuations due to low-frequency noise, which is mitigated by frequency modulating the microwave generator. The feedback has a bandwidth of 400 Hz, with a reduction of cavity fluctuations by $85\mathrm{%}$ integrating up to a bandwidth of 2 kHz. Moreover, the cavity resonance frequency fluctuations are reduced by $73\mathrm{%}$. This scheme can be scaled to enable multitone experiments locked to the same feedback signal. As a demonstration, we apply the feedback to an optomechanical experiment and implement a cavity-locked multitone mechanical measurement. As low-frequency cavity frequency noise can be a limiting factor in many experiments, the multitone microwave locking technique presented here is expected to be relevant for a wide range of microwave-cavity experiments.
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We successfully demonstrate low-frequency noise suppression in the resonant-frequency fluctuations of a cavity-embedded Cooper-pair transistor (cCPT) driven at single-photon occupancy. In particular, we report a reduction in the resonant-frequency fluctuations caused by the internal charge noise over a bandwidth of approximately 1.4kHz1.4\phantom{\rule{0.2em}{0ex}}\text{kHz}1.4kHz when the cavity is driven at an average photon number n=10n=10n=10 and a bandwidth of 11 Hz for an average n=1n=1n=1. The gate-dependent tunability of the cCPT allows us to implement a feedback scheme derived from the Pound-Drever-Hall locking technique. This reduces fluctuations due to intrinsic charge noise, which otherwise interfere with the operation of the cCPT as a near quantum-limited electrometer. Our technique can be generalized to achieve frequency stabilization in tunable microwave resonators that play a vital role in today's quantum computing architectures, thereby moderating the limitations in detection caused by the intrinsic 1/f1/f1/f noise on such circuit devices. The work discusses the various aspects relating to the operation of a fully functional feedback loop down to the single-photon level.
We develop a theory of parametric resonance in tunable superconducting cavities. The nonlinearity introduced by the superconducting quantum interference device (SQUID) attached to the cavity and damping due to connection of the cavity to a transmission line are taken into consideration. We study in detail the nonlinear classical dynamics of the cavity field below and above the parametric threshold for the degenerate parametric resonance, featuring regimes of multistability and parametric radiation. We investigate the phase-sensitive amplification of external signals on resonance, as well as amplification of detuned signals, and relate the amplifier performance to that of linear parametric amplifiers. We also discuss applications of the device for dispersive qubit readout. Beyond the classical response of the cavity, we investigate small quantum fluctuations around the amplified classical signals. We evaluate the noise power spectrum both for the internal field in the cavity and the output field. Other quantum-statistical properties of the noise are addressed such as squeezing spectra, second-order coherence, and two-mode entanglement.