Hunting for Dark Matter with a Spinning Magnet

Author: Denis Avetisyan

Researchers are employing a highly sensitive torsional oscillator to search for evidence of ultralight axions, a leading candidate for dark matter.

The study demonstrates that future iterations of levitated FMTO experiments, leveraging optimized configurations, enhanced vibration isolation, and superconducting shielding, are projected to significantly improve sensitivity to axion-electron coupling-potentially matching or exceeding the constraints currently established by both laboratory-based comagnetometers and astrophysical observations of red-giant cooling and solar axions, as indicated by the projected curves and current limits shown for <span class="katex-eq" data-katex-display="false">g_{aee}</span> versus <span class="katex-eq" data-katex-display="false">m_a</span>. — The study demonstrates that future iterations of levitated FMTO experiments, leveraging optimized configurations, enhanced vibration isolation, and superconducting shielding, are projected to significantly improve sensitivity to axion-electron coupling-potentially matching or exceeding the constraints currently established by both laboratory-based comagnetometers and astrophysical observations of red-giant cooling and solar axions, as indicated by the projected curves and current limits shown for $g_{aee}$ versus $m_a$ .

This study details the development and initial results from a levitated ferromagnetic torsional oscillator designed to detect axion-electron interactions, establishing new constraints on potential coupling strengths.

Despite comprising a significant portion of the universe, the nature of dark matter remains elusive, motivating searches for weakly interacting candidates across a broad mass range. This paper details a novel experimental approach-detailed in ‘Search for Ultralight Axion Dark Matter with a Levitated Ferromagnetic Torsional Oscillator’-utilizing a highly sensitive levitated torsional oscillator to detect ultralight axion dark matter through its predicted coupling to electron spins. Initial data analysis, employing a likelihood-based statistical framework, yields no evidence of axion-induced signals and establishes constraints on the axion-electron coupling, with limits reaching g_aee < 6e-5 at 90% confidence. Can future improvements-including cryogenic operation and enhanced magnetic shielding- unlock the sensitivity needed to definitively probe this compelling dark matter candidate?

The Universe’s Missing Mass: A Search for the Axion

The universe, as currently understood, presents a significant discrepancy: visible matter accounts for only a small fraction of the total mass. This realization has led physicists to posit the existence of dark matter, a substance that doesn’t interact with light, rendering it invisible to traditional observation methods. Evidence for dark matter’s presence comes from a variety of sources, including galactic rotation curves, gravitational lensing, and the cosmic microwave background. These observations consistently indicate a mass component far exceeding what can be accounted for by stars, gas, and dust alone. Consequently, the search for dark matter has become a central focus of modern physics, pushing the boundaries of theoretical frameworks and inspiring innovative experimental approaches to detect this elusive component of the cosmos. The very nature of dark matter remains unknown, necessitating the development of new physics beyond the Standard Model to explain its properties and interactions.

Quantum chromodynamics, the theory describing the strong nuclear force, unexpectedly predicts a violation of charge-parity (CP) symmetry – a phenomenon known as the Strong CP Problem. However, experimental evidence indicates this violation is vanishingly small. Physicist Roberto Peccei and Frank Wilczek proposed a dynamic solution in 1977, postulating the existence of a new particle, the axion. This remarkably light, neutral particle arises from a new symmetry breaking in the quantum chromodynamics sector, effectively canceling the problematic CP-violating term. Crucially, the axion’s predicted properties – its extremely weak interactions and low mass – not only resolve the Strong CP Problem, but also position it as a compelling and increasingly investigated candidate to constitute the elusive dark matter that permeates the universe.

The axion, a particle conceived as a solution to the perplexing ‘Strong CP Problem’ in quantum chromodynamics, has unexpectedly positioned itself as a frontrunner in the search for dark matter. The Strong CP Problem concerns the observed absence of a violation of charge-parity (CP) symmetry in strong interactions, a phenomenon not naturally predicted by the Standard Model. The axion’s proposed mechanism elegantly addresses this issue, and calculations reveal that, if axions exist with the predicted properties, they would have been created in vast quantities during the early universe. This naturally leads to an abundance that precisely matches the observed amount of dark matter – a coincidence that has captivated physicists. Current experiments, employing powerful magnetic fields and sensitive detectors, are actively searching for these elusive particles, hoping to confirm their existence and finally illuminate the composition of the universe’s missing mass.

Detecting the Subtle Whisper of Axions

Haloscopes and Helioscopes function on the principle that axions, if they exist, will convert into detectable photons within a strong magnetic field. The conversion probability is frequency-dependent, dictated by the axion mass and its velocity distribution; therefore, these detectors scan a range of microwave frequencies, searching for a resonant signal. Haloscopes are typically laboratory-based experiments utilizing superconducting magnets to generate the necessary field strength, while Helioscopes aim to detect axions produced within the sun, requiring directional sensitivity and often utilizing existing magnetic fields like those at CERN. The expected signal is extremely weak, necessitating low-noise amplification and careful shielding from environmental electromagnetic interference to distinguish potential axion conversions from background noise.

Light-Shining-Through-A-Wall experiments operate on the principle that axions, if they exist, may be converted into photons within a strong magnetic field. These experiments utilize two cavities separated by an opaque barrier, with a magnetic field applied to each. Axions produced in the first cavity, if present, can pass through the barrier and potentially convert into detectable photons in the second cavity. The barrier prevents direct photon transmission, serving to isolate the signal from background noise and verifying that any detected photons originate from axion conversion. The low expected interaction rate necessitates the use of high-power lasers and sensitive photon detectors to maximize the probability of observing an axion signal.

Axion detection via nuclear spin interaction leverages the predicted coupling between axions and the magnetic moments of atomic nuclei. These experiments, often employing Nuclear Magnetic Resonance (NMR) techniques, search for subtle shifts in NMR spectra induced by axion-nuclear interactions. Specifically, axions can induce an effective precession of nuclear spins, altering the Larmor frequency and creating a detectable signal. Current approaches utilize highly sensitive magnetometers and shielded environments to minimize background noise and maximize the probability of detecting these minute spectral changes. The sensitivity of these NMR-based searches is dependent on factors including the strength of the axion-nucleon coupling, the density of target nuclei, and the achievable signal-to-noise ratio.

Digital lock-in scanning revealed torsional oscillation modes below 10 Hz, with resonance frequency and quality factor determined by Lorentzian fits, and a calibrated transfer function relating bias magnetic field amplitude to optical spot displacement was established using a reference field <span class="katex-eq" data-katex-display="false">B_{cal}</span> at frequency <span class="katex-eq" data-katex-display="false">f_{cal}</span>. — Digital lock-in scanning revealed torsional oscillation modes below 10 Hz, with resonance frequency and quality factor determined by Lorentzian fits, and a calibrated transfer function relating bias magnetic field amplitude to optical spot displacement was established using a reference field $B_{cal}$ at frequency $f_{cal}$ .

Isolating the Signal: Shielding and Precision Measurement

Minimizing external magnetic interference is paramount in axion detection due to the extremely weak interaction strength expected from these hypothetical particles. Magnetic shielding, employing multiple layers of μ-metal and, critically, superconducting materials, is therefore essential. These materials exhibit the Meissner effect, actively expelling magnetic fields and significantly reducing environmental noise. While complete shielding is impractical, the system is designed to attenuate external fields to levels below those induced by the anticipated axion-electron interaction. Measurements confirm an attenuation factor of 1.7 x 10^-3, demonstrating the effectiveness of the shielding in isolating the experiment from external magnetic disturbances and enabling the detection of exceedingly faint signals.

Ferromagnetic Torsional Oscillators (FTOs) and Comagnetometers are utilized to detect the extremely weak magnetic fields predicted to be generated by the interaction between axions and electrons. The FTO operates by measuring the resonant frequency of a mechanically oscillating ferromagnetic pendulum, which shifts in the presence of an external magnetic field. Comagnetometers employ two distinct atomic species, exploiting differences in their magnetic resonance frequencies to amplify the detected signal. Both devices are chosen for their ability to measure magnetic fields with high precision at low frequencies, crucial for detecting the expected signature of axion-electron coupling, which manifests as a time-varying magnetic field. These instruments effectively serve as highly sensitive magnetometers, optimized to probe the predicted strength of the $ga_{ee}$ coupling constant.

The sensitivity of axion detection experiments utilizing devices like the Ferromagnetic Torsional Oscillator and Comagnetometer is fundamentally limited by the $\hbar$ inherent to quantum mechanics, establishing a ‘Quantum Limit’ on measurable magnetic fields. Beyond this fundamental limit, practical sensitivity is further constrained by the ‘Coherence Time’ of the quantum states employed in the measurement; longer coherence times allow for more precise determination of the induced magnetic field. This study achieved a current upper limit on the axion-electron coupling strength, $g_{a_{ee}}$ , approaching existing limits established by comagnetometer experiments, demonstrating the efficacy of the employed techniques within these sensitivity constraints.

A quality factor (Q) of 10⁵ was achieved in the torsional oscillator used for axion detection. This high Q-factor directly impacts the instrument’s sensitivity by maximizing the bandwidth limited by thermal noise; a higher Q allows for the detection of weaker signals within a given bandwidth. The thermal-noise limited sensitivity is inversely proportional to the Q-factor, meaning a Q of 10⁵ results in a correspondingly high sensitivity, crucial for detecting the extremely faint magnetic fields expected from axion-electron interactions. This parameter is a key contributor to the overall performance of the instrument and enables the current limits on the axion-electron coupling strength $g_{a_{ee}}$ .

Experimental results demonstrate attenuation of the expected axion signal due to the implementation of magnetic shielding. A measured attenuation factor of 1.7 x 10^-3 indicates that the shielding, while effective in reducing background noise, simultaneously reduces the strength of the signal expected from axion-electron interactions. This attenuation is a direct consequence of the shielding material’s interaction with the oscillating magnetic field produced by the axion interaction, and must be accounted for in data analysis to accurately determine the axion-electron coupling constant, $g_{a_{ee}}$ .

Data-driven limits on the axion-electron coupling strength <span class="katex-eq" data-katex-display="false">g_{aee}</span> as a function of axion mass <span class="katex-eq" data-katex-display="false">m_a</span> (bottom axis) or Compton frequency <span class="katex-eq" data-katex-display="false">f_c</span> (top axis) are presented, showing the median and <span class="katex-eq" data-katex-display="false">1\sigma/2\sigma</span> bands from simulations alongside existing limits from prior comagnetometer experiments (Blochet al., 2020) and accounting for potential attenuation of the axion-induced field <span class="katex-eq" data-katex-display="false">B_a</span> due to innermost magnetic shielding. — Data-driven limits on the axion-electron coupling strength $g_{aee}$ as a function of axion mass $m_a$ (bottom axis) or Compton frequency $f_c$ (top axis) are presented, showing the median and $1\sigma/2\sigma$ bands from simulations alongside existing limits from prior comagnetometer experiments (Blochet al., 2020) and accounting for potential attenuation of the axion-induced field $B_a$ due to innermost magnetic shielding.

Beyond Confirmation: Implications for Cosmology and Fundamental Physics

The enduring puzzle of dark matter may find resolution alongside a decades-old problem in particle physics if axions are confirmed to exist. These hypothetical particles not only present a compelling dark matter candidate, accounting for the universe’s missing mass, but also elegantly address the Strong CP Problem – a theoretical inconsistency concerning why the strong nuclear force doesn’t violate charge-parity symmetry. The Standard Model of particle physics allows for this violation, yet experiments show no evidence of it; axions naturally arise as a solution, effectively canceling out the problematic term. Thus, a single detection would simultaneously illuminate the nature of dark matter and validate a sophisticated theoretical framework, representing a significant advancement in understanding the fundamental forces and constituents of the universe. This convergence makes the search for axions particularly compelling, as success promises a deeper, more consistent picture of reality.

The theoretical ‘Axion Wind Interaction’ proposes a subtle coupling between axions – prime candidates for dark matter – and standard model particles, creating a tantalizing pathway to explore physics beyond current understanding. This interaction doesn’t rely on the traditional electromagnetic or strong force couplings, but instead suggests axions create a fleeting, directional ‘wind’ detectable through its influence on particle spins. Researchers posit that observing this interaction could reveal properties of axions previously inaccessible, and potentially link them to other undiscovered fundamental particles-perhaps even mediating interactions with dark energy or providing insights into the matter-antimatter asymmetry of the universe. Consequently, the Axion Wind Interaction isn’t simply about confirming dark matter’s existence; it’s a potential bridge to a more complete and nuanced model of the cosmos, offering a unique probe of the hidden sector and its connection to the visible universe.

The search for dark matter is undergoing a paradigm shift with innovative experiments focusing on the subtle interactions between axions and electron spins. These novel methods, differing significantly from traditional direct detection approaches, exploit the predicted coupling between axions and magnetic moments of electrons. By precisely measuring changes in electron spin resonance or seeking minute shifts in energy levels, researchers aim to identify the ‘fingerprint’ of passing axions. This technique offers a unique advantage: it’s sensitive to a different range of axion masses and interaction strengths than other detectors, potentially unveiling regions of parameter space previously unexplored. Successful detection through these spin-based experiments won’t just confirm the existence of axions, but will also provide crucial information regarding their local density, velocity distribution, and ultimately, a detailed map of dark matter’s distribution within our galaxy – painting a clearer picture of the universe’s hidden mass.

The FMTO system utilizes a levitated magnet assembly, stabilized by pyrolytic graphite, to detect faint magnetic fields by monitoring torsional motion with a camera and centroid-tracking, employing bias and calibration coils aligned with its sensitive axis <span class="katex-eq" data-katex-display="false">\vec{\xi}</span> to characterize the response to the axion-wind effective magnetic field <span class="katex-eq" data-katex-display="false">\vec{B}_{a}</span>. — The FMTO system utilizes a levitated magnet assembly, stabilized by pyrolytic graphite, to detect faint magnetic fields by monitoring torsional motion with a camera and centroid-tracking, employing bias and calibration coils aligned with its sensitive axis $\vec{\xi}$ to characterize the response to the axion-wind effective magnetic field $\vec{B}_{a}$ .

The pursuit of detecting ultralight axion dark matter, as detailed in this study, exemplifies a rigorous reduction of complexity. Researchers meticulously crafted a ferromagnetic torsional oscillator, stripping away extraneous noise to isolate a potential signal. This echoes John Stuart Mill’s sentiment: “It is better to be a dissatisfied Socrates than a satisfied fool.” The experiment’s sensitivity hinges not on adding more instrumentation, but on refining the existing setup – minimizing interference to reveal the subtle interaction between axions and electrons. Each layer of magnetic shielding, each calibration step, represents a further paring down, seeking truth through elegant simplicity. The focus remains on what’s left after meticulous subtraction-a potential glimpse into the universe’s hidden mass.

Further Refinements

The pursuit of ultralight axion dark matter, as detailed in this work, inevitably confronts the limitations inherent in translating theoretical elegance into experimental reality. The sensitivity achieved with the levitated torsional oscillator represents a demonstrable advance, yet the signal remains elusive. Future iterations will not be measured by increments of complexity, but by ruthless pruning of systematic uncertainties – a reduction to the essential elements of interaction. The current reliance on magnetic shielding, while necessary, introduces its own subtle distortions, and a path toward mitigating or circumventing this dependency warrants serious consideration.

A productive avenue for investigation lies not simply in scaling the experiment – larger oscillators, longer run times – but in a re-evaluation of the underlying assumptions regarding axion-electron coupling. The explored parameter space, though constrained, remains vast. It is conceivable that the interaction manifests in a manner less readily detectable by spin-dependent means, prompting a broadening of experimental techniques. A deliberate parsimony in theoretical modeling, favoring simplicity over elaborate constructions, might prove surprisingly fruitful.

Ultimately, the search for dark matter demands a willingness to confront the possibility of a fundamentally different universe than the one currently envisioned. The continued refinement of this torsional oscillator, therefore, should be guided not by a desire to confirm expectations, but by a commitment to observing what is, rather than what is expected to be.

Original article: https://arxiv.org/pdf/2601.04576.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

The Universe’s Missing Mass: A Search for the Axion

Detecting the Subtle Whisper of Axions

Isolating the Signal: Shielding and Precision Measurement

Beyond Confirmation: Implications for Cosmology and Fundamental Physics

Further Refinements

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