Introducing coherent time control to cavity magnon-polariton modes

Cavity magnon-polaritons (CMPs) arise from strong coupling between microwave photons in a cavity and magnon excitations, offering a platform that links quantum information processing with spintronics. Early CMP-based devices such as gradient memories and microwave–optical transducers demonstrate the potential for quantum networking. Prior studies largely relied on steady-state, single-tone spectroscopy, revealing coupling strengths, dissipation channels, temperature dependencies, and phenomena like level attraction. Yet, flexible information processing demands nanosecond, on-demand control of the CMP. Time-resolved experiments have been scarce and typically limited to pulsing the cavity alone, without simultaneous coherent control of both subsystems. This work addresses that gap by establishing independent, phase-coherent time-domain control over the cavity and magnon components, enabling switching between beat and normal modes, dynamic control of magnon-Rabi oscillations, and in situ energy extraction.

Three complementary models underlie CMP physics: coupled harmonic oscillators (intuitive description of mode hybridization and normal/beat modes), a classical electromagnetic model (phase correlations and backaction via Faraday’s and Ampère’s laws), and a quantum picture (framework for coupling magnons to superconducting qubits). Spectroscopy has identified loss channels, temperature dependence of dissipation and coupling, and dissipative coupling leading to level attraction. Devices include gradient memories and microwave–optical transducers critical for quantum internet architectures. Time-resolved studies with YIG waveguides or CMPs have been limited and primarily cavity-driven; simultaneous coherent control of both cavity and magnon had not been demonstrated. These gaps motivate the present time-domain control experiments.

Theoretical model: The YIG Kittel mode (uniform FMR) is treated as a macrospin with dynamic magnetization m(t)=m0 e^{-iω_m t} governed by the Landau–Lifshitz–Gilbert equation. The cavity is modeled as an RLC resonator with ω_c=1/√(LC). Electromagnetic backaction couples the subsystems: the precessing magnetization induces cavity currents (Faraday) and cavity currents produce rf magnetic fields driving the FMR (Ampère). Near resonance, the dynamics reduce to coupled-oscillator eigenvalue equations: (ω_c−ω)(ω_m−ω)−g^2=0, with complex ω_c=ω_c−iβω_c, ω_m=ω_m−iαω_m, ω_m=γH|(H+M0). Driven dynamics are modeled by adding coherent drive tones to both cavity and magnon lines, F_cm=A_cm cos(ω0 t+φ_cm). Numerical integration combines driven segments (pulses) and free evolution to simulate experiments. Experimental platform: A copper reentrant cavity resonating at ω_c/2π=6.58 GHz hosts a 0.5 mm diameter YIG sphere near the magnetic antinode. A dedicated stripline with a second microwave port directly addresses the magnon mode; its rf field, the cavity rf field, and the static bias field are mutually orthogonal to minimize crosstalk. The setup comprises independent cavity and magnon manipulation lines and a cavity reflection recording line. A single microwave source provides the carrier, while an AWG with two synchronized DAC sets generates 250 MHz IF IQ pulses that are up-converted via identical IQ mixers, preserving relative phase and envelope. Typical manipulation pulses are 10 ns to prepare initial states without driving to steady state; in one energy-extraction experiment, a 40 ns cavity pulse is used. Calibration and acquisition: Cable delays between lines are calibrated by simultaneous Gaussian test pulses; a 7 ns relative delay is found. Residual sub-nanosecond uncertainties, magnetic field drifts, and small reflections necessitate experimental sweeps of phase offset and power ratio for each protocol. The reflected cavity signal is down-converted, filtered, digitized, and digitally down-converted to extract amplitude and phase. A voltage-controlled attenuator and amplifier on the magnon line adjust the relative excitation amplitude. Protocols: (1) System characterization via spectroscopy (avoided crossing) and time-domain single cavity pulse to observe magnon-Rabi oscillations and extract coupling and decay rates. (2) Two-pulse preparation with simultaneous, phase- and amplitude-matched cavity and magnon pulses to generate normal modes (no energy exchange) at resonance; detuning reintroduces beating. (3) Mode composition mapping by sweeping phase offset and power ratio; fitting free-evolution time traces to Pc(t)=P0[(1−Λ)+(1+Λ)cos^2(gt+φ0)]e^{−t/τ}, where Λ∈[−1,1] indicates normal mode (Λ=−1) versus beat mode (Λ=1). (4) Dynamic control: start in a normal mode, inject a short magnon pulse to turn on Rabi oscillations transiently, then apply an anti-phase magnon pulse to remove added energy and return to a normal mode within the same decay. (5) Active energy extraction: after a cavity pulse, during the second cavity→magnon energy transfer, apply an anti-phase magnon pulse to destructively interfere and rapidly de-excite the system. Sample details: YIG sphere from Ferrisphere Inc.; open-ended 50 Ω stripline on Rogers TMM10i (35 μm Cu, 0.64 mm thickness). All measurements are performed in the linear response regime.

• Strong coupling: Spectroscopy reveals an avoided crossing with coupling strength g/2π=24.6 MHz. Time-domain Rabi oscillations with a single cavity pulse confirm g, with oscillation period T_R=2π/g≈40.6 ns at resonance.
• Decay rates: Measured decay time τ≈77.6 ns agrees with 1/κ_cp≈75.8 ns at the crossing point, consistent with equal hybridization and identical decay rates κ_ap/2π=2.1 MHz.
• Normal mode preparation: Phase- and amplitude-matched simultaneous pulses to cavity and magnon suppress Rabi oscillations on resonance, yielding a pure exponential decay indicative of normal modes. Off-resonance, mismatch reintroduces oscillations.
• Mode composition control: By sweeping phase offset and power ratio between pulses, the parameter Λ governing free evolution spans from +1 (beat mode) to −1 (normal modes). Normal modes occur near phase offsets of ~180° and 360° for matched powers; experimentally observed regions are shifted by ~30° due to sub-0.1 ns timing mismatch and affected by small crosstalk and detuning. Experimental maps agree with analytic predictions and simulations including imperfections.
• Dynamic coherent control within a single decay: Starting from a normal mode, a short magnon pulse turns on Rabi oscillations (energy exchange). A subsequent anti-phase magnon pulse of reduced amplitude (accounting for losses) removes the added energy by destructive interference and returns the system to a normal mode, halting the oscillations; simulations reproduce the traces.
• Rapid energy extraction: After a cavity pulse, an anti-phase magnon pulse applied during the second energy transfer to the magnon reduces the reflected cavity power by ~20 dB within a few nanoseconds, effectively de-exciting the CMP; simulations show similar suppression, with experimental floor limited by ADC dynamic range and pulse reflections.

The study demonstrates simultaneous, phase-coherent, nanosecond control of both subsystems of a cavity magnon-polariton, directly addressing the need for on-demand manipulation beyond steady-state spectroscopy. Preparing arbitrary superpositions between normal and beat modes by tuning relative phase and amplitude enables control over energy exchange and storage in hybrid light–matter states. The ability to dynamically switch Rabi oscillations on and off and to extract energy coherently within a single relaxation window showcases a toolbox for CMP-based information processing. These capabilities connect to regimes previously identified in two-tone spectroscopy, including dissipative coupling and level attraction, and may be leveraged for protocols related to entanglement generation and coherent state engineering. The time-control paradigm extends to other strongly coupled hybrid platforms, including opto- and electromechanical polaritons, suggesting a general approach for coherent control in hybrid quantum systems.

This work introduces coherent time-domain control of cavity magnon-polaritons by independently pulsing the cavity and magnon with stable, controllable phase and amplitude. The authors realize on-demand transitions between beat and normal modes, dynamically modulate magnon-Rabi oscillations, and coherently extract energy via anti-phase driving. Measurements quantitatively agree with coupled-oscillator theory and numerical simulations. These results provide core building blocks for CMP-based quantum networking interfaces and magnonic quantum information processing. Future research directions include exploiting time-domain control in regimes of level attraction and non-Hermitian dynamics, integrating with superconducting qubits for quantum state transfer and entanglement, implementing more complex pulse shaping for optimal control, and extending the protocols to optomagnonic and electromechanical systems.

Experimental imperfections affect precise mode preparation: sub-nanosecond timing mismatches (<0.1 ns) between lines shift optimal phase conditions; residual direct crosstalk between lines and small magnetic field drifts induce slight detuning and power asymmetries. A weak additional magnon mode near 234 mT perturbs traces but is not central to protocols. The ADC dynamic range and pulse reflections limit observation of deep post-extraction suppression and obscure very small residual oscillations. Experiments are in the linear regime; nonlinear effects and higher-excitation dynamics are not explored.