Optomagnonic LG Rotational System

• The paper demonstrates a hybrid system where Laguerre–Gaussian beams, rotational mirrors, and YIG magnons interact to enable tunable slow–fast light conversion.
• It employs radiation-torque and magneto-optical couplings to generate interference-controlled Fano resonances and precise group-delay switching.
• The architecture leverages optimized experimental parameters to realize stationary quantum correlations including entanglement, Gaussian steering, and geometric discord.

Searching arXiv for the specified papers to ground the article in the cited literature. The optomagnonic–Laguerre–Gaussian rotational system is a hybrid cavity platform in which structured optical fields carrying orbital angular momentum (OAM) interact simultaneously with rotational mechanical motion and magnon excitations in yttrium iron garnet (YIG). In the formulation of "Tunable Rotation-Associated Slow-to-Fast Light Conversion via Optomagnonic Coupling" (Liu et al., 17 Mar 2026), the system integrates cavity photons, a rotational mechanical mode of a rear spiral-phase mirror, and magnons hosted by a YIG microsphere inside the cavity, enabling tunable slow-to-fast and fast-to-slow light conversion. In the double-cavity realization studied in "Gaussian geometric discord, entanglement and EPR-steering of two rotational mirrors in a double Laguerre-Gaussian cavity optomechanics in the presence of YIG sphere" (Chabar et al., 2024), two spatially separated rotating mirrors are correlated through shared optical and magnonic fields, yielding stationary entanglement, directional Gaussian steering, and Gaussian geometric discord. Taken together, these works define an optomagnonic LG rotational architecture in which OAM-enhanced radiation torque and magneto-optical coupling jointly supply frequency tunability, interference control, and access to both classical dispersion engineering and stationary Gaussian quantum correlations.

1. Physical architecture and operating principle

In the single-cavity configuration, the cavity supports Laguerre–Gaussian optical modes carrying OAM indexed by the topological charge $l$ and radial index $p$. Spiral phase elements, specifically a partially transmissive input coupler and a fully reflective rear mirror, enforce OAM conservation and mode stability by adding or removing fixed units of OAM upon reflection. The rear mirror acts as a rotational mechanical element described by angular displacement $\phi$ and angular momentum $L_z$, while a YIG microsphere placed inside the cavity hosts a Kittel-mode magnon whose frequency is tunable as $\omega_m=\gamma H$ through an external bias field $H$ (Liu et al., 17 Mar 2026).

The central physical mechanism is the coexistence of two optically driven interactions. First, the LG intracavity field exerts a radiation torque on the rotating mirror because each photon carries $l\hbar$ of OAM. This produces an optorotational coupling that can be described as an OAM-dependent dispersive interaction $-\hbar g_\phi a^\dagger a \phi$, and it also admits a rotational Doppler interpretation with a qualitative scaling $$\delta_{\mathrm{rot}}\propto l\,\Omega_{\mathrm{rot}}$$. Second, the optical mode couples to magnons in YIG through a non-resonant Brillouin-light-scattering mechanism mediated by the magneto-optical effect, captured effectively by a term proportional to $a^\dagger a(m+m^\dagger)$. The resulting platform therefore combines photons, phonons, and magnons in a single cavity (Liu et al., 17 Mar 2026).

The double-LG cavity realization generalizes this structure to two independent LG cavities intersecting at a common region containing a YIG sphere. Each cavity contains one fixed mirror and one perfectly reflective rotating mirror, so there are two rotational mechanical modes, denoted $p$0 and $p$1, with small angular displacements $p$2 and conjugate angular momenta $p$3. The YIG sphere supports a shared magnon mode $p$4 that couples to both cavity fields through a beam-splitter-like photon–magnon interaction $p$5. In this geometry, the two mirrors are spatially separated yet can become correlated through the common optical and magnonic channels (Chabar et al., 2024).

A common simplification is to treat the rotational effect only as a Doppler frequency shift. The single-cavity study explicitly distinguishes the conceptual Doppler picture from the dynamical model: rotation is modeled as a harmonic mode at frequency $p$6 with coupling $p$7, while the Doppler picture is used to clarify how OAM and rotation rate combine to tune the optical response (Liu et al., 17 Mar 2026).

2. Hamiltonian structure and linearized dynamics

For the single-cavity system, the rotating-frame Hamiltonian driven by a strong control field and a weak probe field is written as (Liu et al., 17 Mar 2026)

$p$8

with $p$9 and $\phi$0. The rotational mode obeys $\phi$1, the magnon frequency is $\phi$2, and the control and probe amplitudes are determined by the cavity decay rate and input powers. The effective cavity detuning,

$\phi$3

contains both rotational and magnonic static backaction shifts (Liu et al., 17 Mar 2026).

The analysis proceeds by linearizing around the strong control-field steady state,

$\phi$4

and then writing the fluctuation equations in matrix form as $\phi$5 for the six-component vector $\phi$6. The anti-Stokes probe-sideband amplitude $\phi$7 determines the transmitted probe response, while the composite backaction term $\phi$8 collects both rotational and magnonic susceptibilities. This formalism is the basis for the calculated Fano resonances, transparency features, and group-delay spectra (Liu et al., 17 Mar 2026).

In the double-cavity YIG configuration, the full Hamiltonian contains two optical cavity modes, two torsional oscillators, one magnon mode, radiation-torque couplings $\phi$9, and optomagnonic couplings $L_z$0. After linearization, the theory is expressed in terms of optical, magnonic, and mechanical quadratures and summarized by a $L_z$1 drift matrix $L_z$2, with dynamical equation $L_z$3 for

$L_z$4

For stable parameter sets, the steady-state covariance matrix $L_z$5 exists and is obtained from the Lyapunov equation

$L_z$6

where $L_z$7 is the diffusion matrix determined by optical vacuum noise, magnon vacuum noise, and mechanical Brownian torque noise (Chabar et al., 2024).

The two formulations share the same structural logic: a driven nonlinear system is displaced to its steady state, linearized in fluctuations, and then analyzed either in the frequency domain for probe transmission and group delay or in the covariance-matrix formalism for stationary Gaussian correlations. This suggests that the optomagnonic LG rotational system is less a single device than a class of hybrid OAM-enabled cavity platforms.

3. Probe transmission, Fano resonances, and slow–fast light conversion

The single-cavity study uses the input–output relation $L_z$8 to define the probe transmission coefficient

$L_z$9

with group delay

$\omega_m=\gamma H$0

The paper also defines $\omega_m=\gamma H$1, with $\omega_m=\gamma H$2 and $\omega_m=\gamma H$3 characterizing absorption and dispersion, respectively (Liu et al., 17 Mar 2026).

Asymmetric Fano line shapes arise from interference between a narrow transparency pathway, associated with the rotational phonon or magnon resonance, and the broad cavity continuum. When $\omega_m=\gamma H$4 or $\omega_m=\gamma H$5 is detuned away from exact resonance with $\omega_m=\gamma H$6 or $\omega_m=\gamma H$7, the indirect pathway encoded in the susceptibility term $\omega_m=\gamma H$8 interferes with the direct photonic path in $\omega_m=\gamma H$9, producing the characteristic dispersive asymmetry. The paper gives the phenomenological Fano form

$H$0

with the asymmetry parameter controlled by the phase and amplitude relation between the direct cavity response and the indirect rotational or magnonic response (Liu et al., 17 Mar 2026).

The numerically reported spectra exhibit two transparency minima in probe absorption at $H$1 for the rotation-associated channel and $H$2 for the magnon-associated channel. Around these features, the dispersion can be tuned between positive and negative slope, corresponding to positive and negative group delay. In the paper’s terminology, slow light corresponds to $H$3, while fast light corresponds to $H$4 (Liu et al., 17 Mar 2026).

The principal result is bidirectional light-speed conversion controlled by continuous tuning. Changing the cavity-control detuning from $H$5 to $H$6 flips the magnon-associated group delay from $H$7 to $H$8. Continuous scans reveal multiple switching points: for rotation, conversion occurs at $H$9 and $l\hbar$0; for magnons, at $l\hbar$1 and $l\hbar$2. The same section reports additional tuning routes: varying $l\hbar$3 from $l\hbar$4 to $l\hbar$5 changes the magnon-associated $l\hbar$6 from $l\hbar$7 to $l\hbar$8; changing $l\hbar$9 from $-\hbar g_\phi a^\dagger a \phi$0 to $-\hbar g_\phi a^\dagger a \phi$1 yields a change from $-\hbar g_\phi a^\dagger a \phi$2 to $-\hbar g_\phi a^\dagger a \phi$3; reducing the control power $-\hbar g_\phi a^\dagger a \phi$4 from $-\hbar g_\phi a^\dagger a \phi$5 to $-\hbar g_\phi a^\dagger a \phi$6 flips $-\hbar g_\phi a^\dagger a \phi$7 from $-\hbar g_\phi a^\dagger a \phi$8 to $-\hbar g_\phi a^\dagger a \phi$9. Distinct control-power thresholds for slow-to-fast conversion, approximately $$\delta_{\mathrm{rot}}\propto l\,\Omega_{\mathrm{rot}}$$0 for rotation and approximately $$\delta_{\mathrm{rot}}\propto l\,\Omega_{\mathrm{rot}}$$1 for magnons, indicate separable control channels (Liu et al., 17 Mar 2026).

These results are significant because the magnon degree of freedom removes the fixed-frequency constraint of a purely optomechanical rotational mode. The system can therefore realize multi-frequency dynamic switching rather than a single mechanically locked transparency window.

4. Double-cavity quantum-correlation regime

The double-LG cavity realization shifts emphasis from probe dispersion to stationary Gaussian correlations between two rotational mirrors. The relevant reduced covariance matrix for the mechanical subsystem has the partitioned form

$$\delta_{\mathrm{rot}}\propto l\,\Omega_{\mathrm{rot}}$$2

from which three classes of nonclassical correlations are extracted: logarithmic negativity $$\delta_{\mathrm{rot}}\propto l\,\Omega_{\mathrm{rot}}$$3, Gaussian quantum steering, and Gaussian geometric discord (GGD) (Chabar et al., 2024).

The logarithmic negativity is defined as

$$\delta_{\mathrm{rot}}\propto l\,\Omega_{\mathrm{rot}}$$4

where $$\delta_{\mathrm{rot}}\propto l\,\Omega_{\mathrm{rot}}$$5 is the smallest symplectic eigenvalue of the partially transposed mechanical covariance matrix. Steering from $$\delta_{\mathrm{rot}}\propto l\,\Omega_{\mathrm{rot}}$$6 to $$\delta_{\mathrm{rot}}\propto l\,\Omega_{\mathrm{rot}}$$7 and from $$\delta_{\mathrm{rot}}\propto l\,\Omega_{\mathrm{rot}}$$8 to $$\delta_{\mathrm{rot}}\propto l\,\Omega_{\mathrm{rot}}$$9 is quantified by conditional symplectic spectra of the Schur complements $a^\dagger a(m+m^\dagger)$0 and $a^\dagger a(m+m^\dagger)$1, respectively. GGD is evaluated in standard form and remains nonzero for separable Gaussian states, so it probes nonclassical correlations beyond entanglement (Chabar et al., 2024).

The reported parameter dependencies are structured and nontrivial. Entanglement is thermally fragile: for representative cases, $a^\dagger a(m+m^\dagger)$2 remains positive near ambient temperature $a^\dagger a(m+m^\dagger)$3 under favorable settings but typically disappears by approximately $a^\dagger a(m+m^\dagger)$4. By contrast, GGD is strongly resilient to thermal noise and can remain large after both entanglement and steering vanish. The paper explicitly states that stationary entanglement is fragile under thermal effects, whereas the GGD demonstrates strong resilience to thermal noise and can be further enhanced by increasing the mass of the rotating mirrors (Chabar et al., 2024).

Magnon detuning plays a central role. $a^\dagger a(m+m^\dagger)$5 is maximized near $a^\dagger a(m+m^\dagger)$6, described as the blue sideband condition and associated with anti-Stokes cooling of the rotational modes. The LG OAM $a^\dagger a(m+m^\dagger)$7 enhances the radiation-torque coupling because $a^\dagger a(m+m^\dagger)$8, but the paper also reports that $a^\dagger a(m+m^\dagger)$9 can peak around an optimal $p$00 and then decrease for very large $p$01, which it attributes to increased backaction and susceptibility to instability or noise. Photon–magnon coupling is also nonmonotonic: $p$02 vanishes when $p$03, reaches a maximum near $p$04, and then decreases again as $p$05 exceeds unity (Chabar et al., 2024).

The strongest quantitative entanglement reported is $p$06, exceeding related prior work cited in that paper where $p$07. Steering is directionally asymmetric, with $p$08 typically larger than $p$09. As the ratio $p$10 is varied, the system moves through no-way steering, one-way steering, and two-way steering regimes; near $p$11, two-way steering is obtained, while appreciable mismatch favors one-way steering (Chabar et al., 2024).

A recurrent misconception in hybrid cavity systems is that the disappearance of entanglement implies the disappearance of all useful quantum correlations. The double-cavity results explicitly contradict that inference: GGD can remain significant at temperatures for which both $p$12 and steering have already vanished (Chabar et al., 2024).

5. Tunability and experimentally accessible parameter regimes

The two papers examine distinct but complementary parameter regimes. The single-cavity slow/fast-light study adopts a long cavity with a spiral-phase rear mirror and a YIG microsphere, whereas the double-cavity study focuses on shorter microcavity-like scales optimized for stationary Gaussian correlations.

Subsystem or parameter	Single-cavity light-conversion regime	Double-cavity correlation regime
Cavity length	$p$13	$p$14
Optical wavelength	$p$15	near the near-IR $p$16 typical)
Optical decay	$p$17	$p$18
OAM charge	$p$19	$p$20
Rotor frequency	$p$21	$p$22
Rotor damping	$p$23	$p$24 (order)
Magnon frequency / coupling	$p$25, $p$26	$p$27
Mirror size / mass	$p$28	$p$29
Control or input power	$p$30 unless swept	$p$31

The single-cavity paper states that spiral phase plates and chiral photonic elements can generate and sustain high-charge LG beams, with $p$32 up to approximately $p$33 demonstrated, and that high-$p$34 optical microcavities at $p$35 with $p$36 are realistic. It also notes that microfabricated torsional mirrors can provide $p$37 in the $p$38 range with $p$39, and that YIG microspheres offer low-damping magnons with $p$40 and optomagnonic couplings $p$41 (Liu et al., 17 Mar 2026).

The double-cavity paper emphasizes experimentally accessible parameters including $p$42, $p$43, $p$44, ambient temperature up to $p$45, and mirror masses in the tens of nanograms. It further states that optical LG modes with $p$46 up to a few hundred and mW powers are standard, and that current technology supports high-OAM LG beams, low-loss microcavities, and high-coherence YIG magnons (Chabar et al., 2024).

Across both studies, tunability is provided by four control knobs: cavity-control detuning $p$47 or $p$48, input power, OAM charge $p$49, and magnetic bias field through $p$50 or $p$51. A plausible implication is that the architecture is especially attractive when a single fixed mechanical resonance is insufficient, because one can redistribute functionality between photonic, rotational, and magnonic susceptibilities instead of relying on a single avoided-crossing condition.

6. Stability, limitations, and research directions

Both studies are explicitly confined to stable linearized regimes. In the single-cavity case, linear stability is assessed by the eigenvalues of the dynamical matrix $p$52; the steady state is asymptotically stable if and only if all eigenvalues satisfy $p$53, which the paper notes is equivalent to the Routh–Hurwitz conditions but is evaluated numerically because of algebraic complexity. In the double-cavity case, stability of the drift matrix $p$54 is likewise checked through the Routh–Hurwitz criterion before solving the Lyapunov equation for the covariance matrix (Liu et al., 17 Mar 2026); (Chabar et al., 2024).

The dominant limitations are also closely aligned. The single-cavity paper identifies cavity loss $p$55, magnon damping $p$56, and mechanical damping $p$57 as the main decoherence channels, and notes that thermal noise in the rotational mode can blur dispersion features at high temperatures. Optical absorption in YIG and magneto-optical dephasing can limit $p$58 and add excess noise. It also emphasizes trade-offs: increasing $p$59 enhances tunability but broadens effective linewidths and reduces peak $p$60; increasing $p$61 boosts $p$62 but may complicate mode matching and increase scattering loss; increasing $p$63 strengthens interference but risks instability and self-oscillation (Liu et al., 17 Mar 2026).

The double-cavity paper places comparable emphasis on the assumptions of the linearized Gaussian regime, Markovian optical and magnon baths, high-$p$64 approximation for Brownian torque noise, rotating-wave approximations, and idealized symmetric cavities with perfectly reflecting rotating mirrors. It identifies thermal noise at room temperature, alignment of LG phase fronts, and absorption or scattering in YIG as practical constraints, while proposing pre-cooling, optimization of cavity finesse and linewidths, stabilized high-$p$65 beam profiles, and precise bias-field tuning as mitigation strategies (Chabar et al., 2024).

The forward-looking extensions are stated most explicitly in the single-cavity work: multimode magnons, higher-order LG modes with larger $p$66 or different $p$67, polarization engineering, and non-Hermitian or PT-symmetric designs could further tailor Fano asymmetries and group delay. The same paper identifies potential applications in reconfigurable optical buffering, phase control in photonic networks, and coherent transduction across microwave–optical domains leveraging magneto-optical pathways (Liu et al., 17 Mar 2026). The double-cavity study suggests a complementary trajectory in which the same hybrid ingredients are used not primarily for group-delay engineering but for mechanically encoded entanglement, directional EPR steering, and thermally robust discord between remote torsional elements (Chabar et al., 2024).

Viewed together, these results define the optomagnonic–Laguerre–Gaussian rotational system as a hybrid OAM-enabled cavity paradigm with two experimentally distinct but conceptually unified operating modes: tunable interference-driven control of probe dispersion and group delay, and magnon-assisted generation of stationary Gaussian correlations between rotational mechanical subsystems.