We discuss the fundamental noise limitations of a ferromagnetic torque sensor based on a levitated magnet in the tipping regime. We evaluate the optimal magnetic field resolution taking into account the thermomechanical noise and the mechanical detection noise at the standard quantum limit. We find that the energy resolution limit, pointed out in recent literature as a relevant benchmark for most classes of magnetometers, can be surpassed by many orders of magnitude. Moreover, similarly to the case of a ferromagnetic gyroscope, it is also possible to surpass the standard quantum limit for magnetometry with independent spins, arising from spin-projection noise. Our finding indicates that magnetomechanical systems optimized for magnetometry can achieve a magnetic field resolution per unit volume several orders of magnitude better than any conventional magnetometer. We discuss possible implications, focusing on fundamental physics problems such as the search for exotic interactions beyond the standard model.
We discuss the fundamental noise limitations of a ferromagnetic torque sensor based on a levitated magnet in the tipping regime. We evaluate the optimal magnetic field resolution taking into account the thermomechanical noise and the mechanical detection noise at the standard quantum limit. We find that the energy resolution limit, pointed out in recent literature as a relevant benchmark for most classes of magnetometers, can be surpassed by many orders of magnitude. Moreover, similarly to the case of a ferromagnetic gyroscope, it is also possible to surpass the standard quantum limit for magnetometry with independent spins, arising from spin-projection noise. Our finding indicates that magnetomechanical systems optimized for magnetometry can achieve a magnetic field resolution per unit volume several orders of magnitude better than any conventional magnetometer. We discuss possible implications, focusing on fundamental physics problems such as the search for exotic interactions beyond the standard model.
Levitated ferromagnetic systems are expected to have significant potential in precision magnetic field sensing by leveraging mechanical isolation to minimize mechanical contact and associated noise. Here, we report the implementation of a high-sensitivity magnetometer based on a levitated ferromagnetic torsion oscillator, incorporating a centroid tracking method for superior measurement resolution and noises reduction. The device, featuring a compact sensor volume of (2.5mm)3 and operating under room temperature, attains a remarkable magnetic sensitivity of {391±59fT⋅Hz−1/2}. This capability enables precise detection of weak magnetic fields and provides a novel platform for exploring exotic interactions beyond the Standard Model. These results demonstrate that the levitated torsion oscillator system not only serves as a powerful tool for high-precision magnetic sensing but also holds promise for advancing breakthroughs in fundamental physics.
Levitated systems have great potential in quantum sensing and exploring fundamental physics at the macroscopic scale. Of particular interest are recent works suggesting that a levitated ferromagnet can beat the standard quantum limit of magnetometry, a benchmark for quantum sensors. In this work, we show how a microscopic theory capturing atomic-scale spin-lattice interactions can be used to fully explain the emergence of collective precession dynamics of a levitated ferromagnet and the origin of its enhanced magnetometric sensitivity beyond that of independent spins. Our theory further takes us to two innovative experimental designs of immediate interest: measurement of the celebrated Berry phase with a precessing ferromagnetic needle and the use of its nutation motion to sense a low-frequency oscillating magnetic field. With a microscopic theory established for levitated ferromagnetic needles, future studies of macroscopic quantum effects and the associated quantum-classical transition also become possible.
Levitated mechanical oscillators are emerging ultrasensitive sensors with tremendous potential in both applied and fundamental physics. Levitated ferromagnets, with internal spin noises rapidly averaged, promise ultrahigh magnetic sensitivity. Here, we demonstrate a milligram-scale diamagnetically levitated ferromagnet system operating at room temperature. Through optimized geometry and multi-channel dissipation control, we achieve a magnetic sensitivity of 23~fT/Hz at frequency of 100-Hz level. We anticipate that a ferromagnetic magnetometer with subfemtotesla sensitivity is within reach, after modest technical improvements. This platform establishes a high-performance magnetometer for biomagnetic field detection and beyond-standard-model force searches.
Levitated systems have great potential in quantum sensing and exploring quantum effects at the macroscopic scale. Of particular interest are recent works suggesting that a levitated ferromagnet can beat the standard quantum limit of magnetometry. This work offers a theoretical model to analyze and understand critical features of the precessing dynamics of a levitated ferromagnetic needle, indeed much like a macrospin, in the presence of a weak magnetic field. The dynamics from the atomic scale reveals how the standard quantum limit is surpassed, thus verifying sensing advantages when compared with a collection of independent spins. Our theory further takes us to two additional experimental designs of immediate interest: measurement of the celebrated Berry phase with a precessing ferromagnetic needle and the use of its nutation motion to sense a low-frequency oscillating magnetic field. With a microscopic theory established for levitated ferromagnetic needles, future studies of macroscopic quantum effects and the associated quantum-classical transition also become possible.
It was recently demonstrated that a multitude of realizations of several magnetic sensing technologies satisfy the energy resolution limit, which connects a quantity composed by the variance of the magnetic field estimate, the sensor volume and the measurement time, and having units of action, with ℏ. A first-principles derivation of this limit is still elusive. We here present such a derivation based on quantum thermodynamic arguments. We show that the energy resolution limit is a result of quantum thermodynamic work necessarily associated with quantum measurement and Landauer erasure, the work being exchanged with the magnetic field. We apply these considerations to atomic magnetometers, diamond magnetometers, and SQUIDs, spanning an energy resolution from 10^{0}ℏ to 10^{7}ℏ. This connection between quantum thermodynamics and magnetometry can help advance quantum sensing technologies towards even more sensitive devices.
We develop a quantum model for the rotational dynamics of a freely floating levitated ferromagnetic gyroscope (LFG), emphasizing the interplay between intrinsic spin S, mechanical angular momentum L, and magnetic torque. The conserved total angular momentum projection along the z-directed magnetic field B, Jz=Sz+Lz, is quantized, leading in the small-libration-amplitude limit to discrete precessional states ∣m⟩ (eigenstates of Jz with eigenvalues Jz=mℏ) and librational harmonic oscillator states ∣n⟩ (n=0,1,2,…). The discreteness of the energies and dynamical variables is governed by the quantum precession scale ΩQ=ℏ/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 Jz-eigenstates ∣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=±1 and Δn=±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.