Observation of attractor transitions in active magnon-polaritons under microwatt drives

Abstract: Magnon-polaritons provide a room-temperature platform for investigating nonlinear cavity quantum electrodynamics in the microwave domain, but experimentally observing controlled transitions among distinct nonlinear attractors remains challenging in conventional passive systems, where strong external driving is usually required. Here we report the observation of attractor transitions in an active magnon-polariton formed by a self-oscillating microwave cavity coupled to a yttrium iron garne (YIG) sphere. The feedback loop supplies an internal microwave drive, while Kerr frequency pulling and Suhl-mediated magnon-magnon scattering produce an enhanced effective nonlinearity. Stability analysis using experimentally calibrated parameters reveals a rich fixed-point (FP) landscape with multiple unstable-FP phases and a triple-point region. By tuning gain across these phases, we observe the first experimental evidence of explosive growth of bistability, followed by transitions to multifrequency limit cycles, comb-like/fractal spectra, and broadband chaotic dynamics at microwatt powers. Near a critical point, magnetic-field-triggered switching between nonlinear emission states produces spectral shifts up to 162 times the bare gyromagnetic response. By enabling low-power attractor transitions and attractor-switching-amplified spectral response, active magnon-polaritons open opportunities for nonlinear microwave signal generation, high-precision sensing, and neuromorphic computing.

• The paper demonstrates nonlinear attractor transitions in active magnon-polaritons using a self-oscillating cavity that operates at microwatt power levels.
• The paper employs a van-der Pol oscillator model with Kerr nonlinearity and Suhl instability to reveal bistable, limit-cycle, and chaotic regimes.
• The paper highlights implications for microwave signal generation, ultrahigh magnetic sensing, and neuromorphic computing through low-power dynamic control.

Observation of Attractor Transitions in Active Magnon-Polaritons under Microwatt Drives

Background and Motivation

The study addresses nonlinear dynamics in hybrid cavity quantum electrodynamics (QED) systems at microwave frequencies, specifically focusing on magnon-polariton (MP) platforms based on yttrium iron garnet (YIG) spheres coupled to microwave cavities. Conventional passive MP systems face limitations in revealing rich nonlinear behaviors due to high external drive thresholds, particularly for nonlinear attractor transitions. This work investigates a feedback-driven, self-oscillating cavity architecture that supplies internal drive and mitigates photon losses, enabling robust nonlinear dynamics at microwatt power levels.

Theoretical Model and Stability Landscape

Both active and passive MP systems are modeled with a cavity photon mode ($a$) coupled to a magnon mode ($m$) with intrinsic Kerr nonlinearity ($K$), magnon damping ($\gamma$), and photon damping ($\kappa$). The active system incorporates a linear gain ($G$) and nonlinear gain saturation ($\Gamma|a|^2$), emulating a van-der Pol (vdP) oscillator. Unlike the externally driven passive system, the active MP features self-sustaining oscillations with zero detuning between cavity and drive.

Stability analysis reveals that the active MP exhibits a diverse fixed-point landscape with multiple unstable phases, triplet points, and regimes devoid of stable fixed points. This topology contrasts sharply with the passive system, which only shows bistability under strong detuning and high photon occupation. The active topology favorably facilitates transitions to time-dependent nonlinear attractors, including limit cycles and chaos, at orders-of-magnitude lower photon numbers.

Experimental Realization

A microstrip-line cavity with a bipolar junction transistor gain element (BJT) and a 1-mm YIG sphere is fabricated on chip. Magnetic tuning of the YIG sphere yields a magnon mode with a gyromagnetic ratio of $28.2$ MHz/mT and a damping rate of $10.3$ MHz. The cavity, under increasing BJT voltage, transitions from passive to active (vdP oscillator) operation, with a dramatic increase in quality factor ($Q_L$) and emission power ($m$0 dBm at $m$1 GHz). Critically, the active cavity provides a self-oscillating internal drive, eliminating the need for external microwave sources.

Low-Power Nonlinear Dynamics and Attractor Transitions

Positioning the YIG sphere at the optimal coupling point, nonlinear transitions are observed at drive powers no greater than $m$2 dBm ($m$3 $m$4W). Under a $m$5 dBm drive, bistable transitions manifest as abrupt frequency blue-shifts and switching, with up- and down-sweeps revealing strong memory effects. Notably, these phenomena appear at negative magnon-cavity detuning, diverging from prior reports.

Increasing drive to $m$6 dBm induces frequency bending and multifrequency sidebands, indicative of transitions to multifrequency limit-cycle attractors. These behaviors arise from the confluence of enhanced Kerr nonlinearity and magnon-magnon scattering (Suhl instability), with a fitted Kerr coefficient of $m$7 $m$8Hz, substantially greater than expected for bulk YIG spheres.

Route to Chaos and Explosive Bistability

At powers above $m$9 dBm, the active MP undergoes transitions to chaotic states, fractal spectra, comb-like structures, and broadband chaos. Under $K$0 dBm, explosive bistability is observed: oscillator frequencies jump to higher states with detuning, producing frequency shifts up to $K$1 MHz, far exceeding previous theoretical predictions that required drive powers above $K$2 mW. Detailed scanning reveals path-dependent progression through multifrequency limit cycles, fractals, combs (with up to $K$3 sidebands), and chaos.

At even higher powers ($K$4 dBm and $K$5 dBm), ultrahigh magnetic sensitivity is demonstrated, with emission peak shifts up to $K$6 times the bare gyromagnetic response. Abrupt transitions between multimode and single-mode emission occur within magnetic field changes below $K$7 G, revealing strong nonlinear magnetic responsiveness.

Power-Dependent Phase Diagrams and Attractor Control

Critical detuning at which attractor transitions appear shifts deeper into negative values with increased power. Stability phase diagrams in parameter space ($K$8, $K$9) show deterministic transitions from conventional bistable regimes (2 stable + 1 unstable FP) to triplet and 2S+3U unstable fixed-point phases, consistent with multifrequency and chaotic attractor emergence. Slight increases in drive can yield nondeterministic phase boundaries, underscoring environmental sensitivity and phase fragmentation near noise regimes. Ultimately, elevated drive powers expand the chaotic and multifrequency attractor domains.

Implications and Outlook

This study achieves deeply nonlinear active magnon-polariton dynamics utilizing microwatt internal drives, which is several orders of magnitude lower than previous approaches. The feedback-based architecture obviates external microwave generators, facilitating compactness and scalability. The collective action of Kerr and Suhl nonlinearities is critical in accessing chaotic attractors at low power.

Implications include:

• Nonlinear Microwave Signal Generation: Efficient access to combs and chaos enables novel sources for communications, metrology, and signal processing.
• High-Precision Magnetic Sensing: Attractor-switching-amplified spectral response with ultrahigh field sensitivity paves the way for ultrasensitive quantum magnetometry.
• Neuromorphic Computing: Rich nonlinear dynamics and attractor transitions may be exploited for hardware-efficient logic gates and memory in spintronic neuromorphic architectures.
• Quantum Information: Self-oscillating active hybrid systems open new regimes for squeezing, entanglement, and cavity-assisted quantum state engineering.

Further theoretical development is warranted to characterize intermediate attractor states and multi-mode nonlinear networks. The quantumness of active MP—squeezing, entanglement, and fluctuation-driven transitions—remains a fertile research area. Integration of active MP platforms with advanced chip-scale architectures may enable ultralow-power quantum sensors and computing elements.

Conclusion

Active magnon-polariton systems implemented via chip-scale self-oscillating cavities enable robust, low-power access to rich nonlinear attractor transitions encompassing bistability, multifrequency limit cycles, frequency combs, fractals, and chaos. Enhanced effective Kerr nonlinearity and Suhl instability promote deeply nonlinear dynamical phases, with strong power-dependent control of instability regimes. The approach represents an efficient route to nonlinear microwave functionalities, offering broad prospects in sensing, computation, and quantum technology (2604.27668).