arXiv:2607.16592

Quantum dynamics of a levitated ferromagnetic gyroscope

Derek F. Jackson Kimball

quant-phphysics.atom-phSubmitted Jul 18, 2026• Announced Jul 21, 2026• 0 citations

Abstract

We develop a quantum model for the rotational dynamics of a freely floating levitated ferromagnetic gyroscope (LFG), emphasizing the interplay between intrinsic spin $\boldsymbol{S}$, mechanical angular momentum $\boldsymbol{L}$, and magnetic torque. The conserved total angular momentum projection along the $z$-directed magnetic field $\boldsymbol{B}$, $J_z=S_z+L_z$, is quantized, leading in the small-libration-amplitude limit to discrete precessional states $|m\rangle$ (eigenstates of $J_z$ with eigenvalues $J_z = m\hbar$) and librational harmonic oscillator states $|n\rangle$ ($n=0,1,2,\ldots$). The discreteness of the energies and dynamical variables is governed by the quantum precession scale $Ω_Q=\hbar/I$, where $I$ is the moment of inertia of the LFG. We find that the phenomenon of LFG precession persists into high-field regimes where the magnitude of the rotational angular momentum associated with precession exceeds the total intrinsic spin. We analyze the complementary quantum limits of localized semiclassical LFG orientation wave packets and exact $J_z$-eigenstates $|m\rangle$, clarifying the relation between classical precession signals and the underlying quantized spin-rotor dynamics. We further show that radio-frequency fields can drive $Δm = \pm 1$ and $Δn = \pm 1$ transitions, enabling ladder spectroscopy, tilt-angle control, and sideband-like coupling between precession and libration. The coupled dynamics also exhibit branch-point magnetic resonances where precession and librational motion become strongly coupled. These results establish a framework for using LFGs not only as ultrasensitive torque and magnetic-field sensors, but also as controllable mesoscopic quantum systems. The techniques developed here may be applied to searches for exotic, beyond-the-standard model spin-dependent interactions, ultralight dark matter, and spin-gravity couplings.

Comments: 26 pages, 10 figures

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arXiv:2607.16592

Quantum dynamics of a levitated ferromagnetic gyroscope

Derek F. Jackson Kimball

quant-phphysics.atom-phSubmitted Jul 18, 2026• Announced Jul 21, 2026• 0 citations

arXiv HTML PDF

Abstract

We develop a quantum model for the rotational dynamics of a freely floating levitated ferromagnetic gyroscope (LFG), emphasizing the interplay between intrinsic spin

\boldsymbol{S}

, mechanical angular momentum

\boldsymbol{L}

, and magnetic torque. The conserved total angular momentum projection along the

z

-directed magnetic field

\boldsymbol{B}

J_z=S_z+L_z

, is quantized, leading in the small-libration-amplitude limit to discrete precessional states

|m\rangle

(eigenstates of

J_z

with eigenvalues

J_z = m\hbar

) and librational harmonic oscillator states

|n\rangle

(

n=0,1,2,\ldots

). The discreteness of the energies and dynamical variables is governed by the quantum precession scale

Ω_Q=\hbar/I

, where

I

is the moment of inertia of the LFG. We find that the phenomenon of LFG precession persists into high-field regimes where the magnitude of the rotational angular momentum associated with precession exceeds the total intrinsic spin. We analyze the complementary quantum limits of localized semiclassical LFG orientation wave packets and exact

J_z

-eigenstates

|m\rangle

, clarifying the relation between classical precession signals and the underlying quantized spin-rotor dynamics. We further show that radio-frequency fields can drive

Δm = \pm 1

and

Δn = \pm 1

transitions, enabling ladder spectroscopy, tilt-angle control, and sideband-like coupling between precession and libration. The coupled dynamics also exhibit branch-point magnetic resonances where precession and librational motion become strongly coupled. These results establish a framework for using LFGs not only as ultrasensitive torque and magnetic-field sensors, but also as controllable mesoscopic quantum systems. The techniques developed here may be applied to searches for exotic, beyond-the-standard model spin-dependent interactions, ultralight dark matter, and spin-gravity couplings.

Comments: 26 pages, 10 figures

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quant-pharXiv:2605.00090May 4, 2026

QMU Registration of Gyroscopic Coupling in a Nonspinning Ferromagnet: Public-Trace Reproduction, a Composition Envelope, and a Material-Participation Constraint

David J. Thomson

Ahrens and Vinante recently measured gyroscopic spin-rotation coupling between two librational modes of a nonspinning, superconductively levitated hard-ferromagnet microsphere. The measured coupling provides a direct experimental relation between the magnetic moment $\mu$ and the collective intrinsic angular momentum $S$ associated with the particle magnetization. This study independently reconstructs the central experimental observable from the complete public archive. All five deposited MD5 checksums are verified, and all 315 two-channel traces are analyzed using the correlation model specified in the experimental supplement. Three of the four reconstructed Einstein--de Haas frequencies $f_I$ agree with the published central values to within $0.3%$ . Dataset 1, which contains the smallest measured quadrature ratio, reconstructs $17.4%$ above the published central value but remains consistent within $1.24$ combined standard deviations. 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For a spherical particle, the experimental closure becomes $\Gamma_{\mathrm{QMU}}=5M\,\mathrm{ccf}\,\mathrm{mchg}/(4\pi\rho R^2f_I)=5Mm_e/(4\pi\rho R^2f_Ie)$ . This expresses the measured gyroscopic coupling as a dimensionless ratio of magnetic moment and angular momentum while preserving an exact bridge to the experimentally reported quantities. Public composition reports for commercial Magnequench MQP-S-11-9-20001 powder are converted from weight percent to atomic percent and evaluated with the deliberately simplified constituent model used in the source study. The resulting composition controls give $g_{\mathrm{ctrl}}=1.3647$ -- $1.3952$ and $\Gamma_{\mathrm{ctrl}}=0.6823$ -- $0.6976$ . Within this model, agreement with the measured value requires the rare-earth share of modeled angular momentum to increase from approximately $0.48$ -- $0.50$ to approximately $0.661$ . The equivalent transition-metal participation factor is $\beta_{\mathrm{TM}}=0.468$ -- $0.516$ . The QMU identity $\Gamma_{\mathrm{QMU}}=g/2$ is an exact registration of the measured observable rather than an independent material prediction. A predictive Aether Physics Model calculation must determine the species- and phase-resolved magnetic-moment and angular-momentum population sums before comparison with the experiment. The paper therefore defines the numerical target, identifies the principal material-participation constraint, and proposes composition, phase, temperature, particle-metrology, and blind-registration experiments capable of distinguishing competing closures. The deposit includes the complete paper, Overleaf-compatible LaTeX source, publication figures, machine-readable result summaries, composition inputs, claims ledger, figure-regeneration code, and package-validation report.Ahrens and Vinante recently measured gyroscopic spin-rotation coupling between two librational modes of a nonspinning, superconductively levitated hard-ferromagnet microsphere. The measured coupling provides a direct experimental relation between the magnetic moment $\mu$ and the collective intrinsic angular momentum $S$ associated with the particle magnetization. This study independently reconstructs the central experimental observable from the complete public archive. All five deposited MD5 checksums are verified, and all 315 two-channel traces are analyzed using the correlation model specified in the experimental supplement. Three of the four reconstructed Einstein--de Haas frequencies $f_I$ agree with the published central values to within $0.3%$. Dataset 1, which contains the smallest measured quadrature ratio, reconstructs $17.4%$ above the published central value but remains consistent within $1.24$ combined standard deviations. An inverse-variance fit to the four published material factors gives $g_{\mathrm{mat}}=1.16263\pm0.02578$, corresponding to $\Gamma_{\mathrm{mat}}=g_{\mathrm{mat}}/2=0.58131\pm0.01289$. The size-scaling quantity $f_I R^2/M$ is consistent with a common material factor across the four experimental configurations, with $\chi^2=0.969$ for three degrees of freedom and $p=0.809$ under the stated independence approximation. The experimental result is registered in Quantum Measurement Units using $\mathrm{angm}=h=m_e{\lambda_C}^2F_q$, $\mathrm{magm}={e_\mathrm{emax}}^2{\lambda_C}^2F_q$, $\mathrm{mchg}=m_e/{e_\mathrm{emax}}^2$, and $\mathrm{ccf}={e_\mathrm{emax}}^2/e$. These definitions produce the exact correlations $\mathrm{magm}/\mathrm{angm}=1/\mathrm{mchg}$ and $\mathrm{ccf}\,\mathrm{mchg}=m_e/e$. The resulting dimensionless QMU registration is $\Gamma_{\mathrm{QMU}}=(\mu\,\mathrm{ccf}/\mathrm{magm})/(S/\mathrm{angm})=g/2=(\mu\,\mathrm{ccf}/S)\mathrm{mchg}$. For a spherical particle, the experimental closure becomes $\Gamma_{\mathrm{QMU}}=5M\,\mathrm{ccf}\,\mathrm{mchg}/(4\pi\rho R^2f_I)=5Mm_e/(4\pi\rho R^2f_Ie)$. This expresses the measured gyroscopic coupling as a dimensionless ratio of magnetic moment and angular momentum while preserving an exact bridge to the experimentally reported quantities. Public composition reports for commercial Magnequench MQP-S-11-9-20001 powder are converted from weight percent to atomic percent and evaluated with the deliberately simplified constituent model used in the source study. The resulting composition controls give $g_{\mathrm{ctrl}}=1.3647$--$1.3952$ and $\Gamma_{\mathrm{ctrl}}=0.6823$--$0.6976$. Within this model, agreement with the measured value requires the rare-earth share of modeled angular momentum to increase from approximately $0.48$--$0.50$ to approximately $0.661$. The equivalent transition-metal participation factor is $\beta_{\mathrm{TM}}=0.468$--$0.516$. The QMU identity $\Gamma_{\mathrm{QMU}}=g/2$ is an exact registration of the measured observable rather than an independent material prediction. A predictive Aether Physics Model calculation must determine the species- and phase-resolved magnetic-moment and angular-momentum population sums before comparison with the experiment. The paper therefore defines the numerical target, identifies the principal material-participation constraint, and proposes composition, phase, temperature, particle-metrology, and blind-registration experiments capable of distinguishing competing closures. The deposit includes the complete paper, Overleaf-compatible LaTeX source, publication figures, machine-readable result summaries, composition inputs, claims ledger, figure-regeneration code, and package-validation report.

Aug 9, 20262 citations

Controlling rotations of magnetically levitated superconductors

Fynn Köller, Dominik Maile, Joachim Ankerhold +3 more

Magnetically trapped type-I superconductors are promising candidates for precision experiments at the quantum-to-classical borderline, with applications in quantum sensing of forces and accelerations and fundamental tests of quantum physics. Here, we show how the rotational motion of micron-sized superconductors is strongly affected by (i) the diamagnetic torques due to the gradient of the trapping field and by (ii) the gyromagnetic coupling due to Einstein-de Haas and Barnett effects. We show that this allows the three-dimensional alignment of asperhical superconductors in the trap center, as required for future sensing applications and quantum experiments, and determine the resulting librational trapping frequencies. Finally, we propose an experiment to probe gyromagnetic coupling in levitated superconductors and we discuss how it can be used to control the particle rotation.Magnetically trapped type-I superconductors are promising candidates for precision experiments at the quantum-to-classical borderline, with applications in quantum sensing of forces and accelerations and fundamental tests of quantum physics. Here, we show how the rotational motion of micron-sized superconductors is strongly affected by (i) the diamagnetic torques due to the gradient of the trapping field and by (ii) the gyromagnetic coupling due to Einstein-de Haas and Barnett effects. We show that this allows the three-dimensional alignment of asperhical superconductors in the trap center, as required for future sensing applications and quantum experiments, and determine the resulting librational trapping frequencies. Finally, we propose an experiment to probe gyromagnetic coupling in levitated superconductors and we discuss how it can be used to control the particle rotation.

quant-pharXiv:2608.16184Aug 18, 20260 citations

Levitation of a YIG sphere using a magnetic Paul trap - towards strongly coupled quantum magno-mechanics

A. O. Yakymenko, S. Das, J. Twamley

Magnetic levitation offer passive levitation of massive objects for use in advanced inertia sensors, for the generation of non-classical macroscopic motional states, and towards the table-top testing of low energy gravity with quantum mechanics. Magnons, a quanta of spin wave, couple to many physical quantities and strongly to electromagnetic fields, even at room temperature. In this work we demonstrate the stable trapping of a small YIG sphere using a magnetic Paul trap. We present a classical stability analysis of a magnetic Paul trap and show the stability diagram for all mechanical degrees of freedom. We show that coupling between librational and translational modes changes the stability region. We experimentally levitate the soft magnet yttrium iron garnet at room temperature obtaining Q-factors of $\sim25$ and secular frequencies $15.8$ Hz and $17.2$ Hz. We provide numerical estimates of the achievable enhanced coupling between the center-of-mass motion and excited magnon modes, with a cooperativity above unity despite strong mechanical damping, indicating potential applications in quantum information processing, quantum interconnects and quantum memories.Magnetic levitation offer passive levitation of massive objects for use in advanced inertia sensors, for the generation of non-classical macroscopic motional states, and towards the table-top testing of low energy gravity with quantum mechanics. Magnons, a quanta of spin wave, couple to many physical quantities and strongly to electromagnetic fields, even at room temperature. In this work we demonstrate the stable trapping of a small YIG sphere using a magnetic Paul trap. We present a classical stability analysis of a magnetic Paul trap and show the stability diagram for all mechanical degrees of freedom. We show that coupling between librational and translational modes changes the stability region. We experimentally levitate the soft magnet yttrium iron garnet at room temperature obtaining Q-factors of $\sim25$ and secular frequencies $15.8$ Hz and $17.2$ Hz. We provide numerical estimates of the achievable enhanced coupling between the center-of-mass motion and excited magnon modes, with a cooperativity above unity despite strong mechanical damping, indicating potential applications in quantum information processing, quantum interconnects and quantum memories.

quant-pharXiv:2608.12752Aug 14, 2026

We develop a quantum model for the rotational dynamics of a freely floating levitated ferromagnetic gyroscope (LFG), emphasizing the interplay between intrinsic spin

\boldsymbol{S}

, mechanical angular momentum

\boldsymbol{L}

, and magnetic torque. The conserved total angular momentum projection along the

z

-directed magnetic field

\boldsymbol{B}

J_z=S_z+L_z

, is quantized, leading in the small-libration-amplitude limit to discrete precessional states

|m\rangle

(eigenstates of

J_z

with eigenvalues

J_z = m\hbar

) and librational harmonic oscillator states

|n\rangle

(

n=0,1,2,\ldots

). The discreteness of the energies and dynamical variables is governed by the quantum precession scale

Ω_Q=\hbar/I

, where

I

J_z

-eigenstates

|m\rangle

, clarifying the relation between classical precession signals and the underlying quantized spin-rotor dynamics. We further show that radio-frequency fields can drive

Δm = \pm 1

and

Δn = \pm 1

\mu

and the collective intrinsic angular momentum

S

associated with the particle magnetization. This study independently reconstructs the central experimental observable from the complete public archive. All five deposited MD5 checksums are verified, and all 315 two-channel traces are analyzed using the correlation model specified in the experimental supplement. Three of the four reconstructed Einstein--de Haas frequencies

f_I

agree with the published central values to within

0.3%

. Dataset 1, which contains the smallest measured quadrature ratio, reconstructs

17.4%

above the published central value but remains consistent within

1.24

combined standard deviations. An inverse-variance fit to the four published material factors gives

g_{\mathrm{mat}}=1.16263\pm0.02578

, corresponding to

\Gamma_{\mathrm{mat}}=g_{\mathrm{mat}}/2=0.58131\pm0.01289

. The size-scaling quantity

f_I R^2/M

is consistent with a common material factor across the four experimental configurations, with

\chi^2=0.969

for three degrees of freedom and

p=0.809

under the stated independence approximation. The experimental result is registered in Quantum Measurement Units using

\mathrm{angm}=h=m_e{\lambda_C}^2F_q

\mathrm{magm}={e_\mathrm{emax}}^2{\lambda_C}^2F_q

\mathrm{mchg}=m_e/{e_\mathrm{emax}}^2

, and

\mathrm{ccf}={e_\mathrm{emax}}^2/e

. These definitions produce the exact correlations

\mathrm{magm}/\mathrm{angm}=1/\mathrm{mchg}

and

\mathrm{ccf}\,\mathrm{mchg}=m_e/e

. The resulting dimensionless QMU registration is

\Gamma_{\mathrm{QMU}}=(\mu\,\mathrm{ccf}/\mathrm{magm})/(S/\mathrm{angm})=g/2=(\mu\,\mathrm{ccf}/S)\mathrm{mchg}

. For a spherical particle, the experimental closure becomes

\Gamma_{\mathrm{QMU}}=5M\,\mathrm{ccf}\,\mathrm{mchg}/(4\pi\rho R^2f_I)=5Mm_e/(4\pi\rho R^2f_Ie)

. This expresses the measured gyroscopic coupling as a dimensionless ratio of magnetic moment and angular momentum while preserving an exact bridge to the experimentally reported quantities. Public composition reports for commercial Magnequench MQP-S-11-9-20001 powder are converted from weight percent to atomic percent and evaluated with the deliberately simplified constituent model used in the source study. The resulting composition controls give

g_{\mathrm{ctrl}}=1.3647

1.3952

and

\Gamma_{\mathrm{ctrl}}=0.6823

0.6976

. Within this model, agreement with the measured value requires the rare-earth share of modeled angular momentum to increase from approximately

0.48

0.50

to approximately

0.661

. The equivalent transition-metal participation factor is

\beta_{\mathrm{TM}}=0.468

0.516

. The QMU identity

\Gamma_{\mathrm{QMU}}=g/2

is an exact registration of the measured observable rather than an independent material prediction. A predictive Aether Physics Model calculation must determine the species- and phase-resolved magnetic-moment and angular-momentum population sums before comparison with the experiment. The paper therefore defines the numerical target, identifies the principal material-participation constraint, and proposes composition, phase, temperature, particle-metrology, and blind-registration experiments capable of distinguishing competing closures. The deposit includes the complete paper, Overleaf-compatible LaTeX source, publication figures, machine-readable result summaries, composition inputs, claims ledger, figure-regeneration code, and package-validation report.

\sim25

and secular frequencies

15.8

Hz and

17.2

Hz. We provide numerical estimates of the achievable enhanced coupling between the center-of-mass motion and excited magnon modes, with a cooperativity above unity despite strong mechanical damping, indicating potential applications in quantum information processing, quantum interconnects and quantum memories.