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arXiv:2606.30781

A Levitated-Magnet Vector Force Sensor for Spin-Dependent Exotic Interactions

Dorian W. P. Amaral, Lei Cong, Tim M. Fuchs, Hendrik Ulbricht, Dmitry Budker

hep-phhep-exquant-phSubmitted Jun 29, 2026• Announced Jul 1, 2026
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Abstract

We present a magnetically levitated ferromagnetic vector force sensor that enables selective searches for spin-dependent exotic interactions mediated by beyond-Standard-Model bosons. A defining feature of spin-dependent exotic interactions is that they can generate forces with distinct directional signatures set by the relative spin configuration of the interacting bodies. We show that our sensor resolves these signatures by mapping forces along different axes onto distinct translational modes with different resonance frequencies, thereby separating interaction channels within the same coupling class. As a representative example, we study parity-violating axial-vector--vector interactions mediated by a spin-1 $Z'$ boson between a sensing and a driving levitated ferromagnet. Using a matched-filter likelihood analysis, we show that a setup based on an already demonstrated experiment can probe the pure electron--electron coupling $g_A^e g_V^e$ in the previously inaccessible force range $λ\lesssim 1\,\mathrm{cm}$, corresponding to mediator masses $M_{Z'} \gtrsim 10^{-5}\,\mathrm{eV}/c^2$. Our results establish levitated ferromagnets as a promising platform for millimeter-scale searches for spin-dependent fifth forces and for resolving the multiple effective potentials associated with a given coupling class.

Comments
6 pages, 4 figures, 6 appendices

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We present a magnetically levitated ferromagnetic vector force sensor that enables selective searches for spin-dependent exotic interactions mediated by beyond-Standard-Model bosons. A defining feature of spin-dependent exotic interactions is that they can generate forces with distinct directional signatures set by the relative spin configuration of the interacting bodies. We show that our sensor resolves these signatures by mapping forces along different axes onto distinct translational modes with different resonance frequencies, thereby separating interaction channels within the same coupling class. As a representative example, we study parity-violating axial-vector--vector interactions mediated by a spin-1 Z′Z'Z′ boson between a sensing and a driving levitated ferromagnet. Using a matched-filter likelihood analysis, we show that a setup based on an already demonstrated experiment can probe the pure electron--electron coupling gAegVeg_A^e g_V^egAe​gVe​ in the previously inaccessible force range λ≲1 cmλ\lesssim 1\,\mathrm{cm}λ≲1cm, corresponding to mediator masses MZ′≳10−5 eV/c2M_{Z'} \gtrsim 10^{-5}\,\mathrm{eV}/c^2MZ′​≳10−5eV/c2. Our results establish levitated ferromagnets as a promising platform for millimeter-scale searches for spin-dependent fifth forces and for resolving the multiple effective potentials associated with a given coupling class.
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We develop a quantum model for the rotational dynamics of a freely floating levitated ferromagnetic gyroscope (LFG), emphasizing the interplay between intrinsic spin S\boldsymbol{S}S, mechanical angular momentum L\boldsymbol{L}L, and magnetic torque. The conserved total angular momentum projection along the zzz-directed magnetic field B\boldsymbol{B}B, Jz=Sz+LzJ_z=S_z+L_zJz​=Sz​+Lz​, is quantized, leading in the small-libration-amplitude limit to discrete precessional states ∣m⟩|m\rangle∣m⟩ (eigenstates of JzJ_zJz​ with eigenvalues Jz=mℏJ_z = m\hbarJz​=mℏ) and librational harmonic oscillator states ∣n⟩|n\rangle∣n⟩ (n=0,1,2,…n=0,1,2,\ldotsn=0,1,2,…). The discreteness of the energies and dynamical variables is governed by the quantum precession scale ΩQ=ℏ/IΩ_Q=\hbar/IΩQ​=ℏ/I, where III 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 JzJ_zJz​-eigenstates ∣m⟩|m\rangle∣m⟩, clarifying the relation between classical precession signals and the underlying quantized spin-rotor dynamics. We further show that radio-frequency fields can drive Δm=±1Δm = \pm 1Δm=±1 and Δn=±1Δn = \pm 1Δn=±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.