Hunting Dark Matter with Quantum Shadows

Author: Denis Avetisyan

A new wave of experiments is harnessing the subtle effects of quantum mechanics to search for axions, a leading candidate for dark matter.

A Mach-Zehnder interferometer is leveraged to detect the subtle Berry phase induced by axions, a phenomenon predicted to manifest as a measurable shift in interference patterns.

This review details emerging techniques utilizing Aharonov-Bohm and Berry phases in superconducting circuits and photonic interferometers to improve axion detection sensitivity.

Despite the compelling evidence for dark matter, its fundamental nature remains elusive, motivating exploration of diverse detection strategies. This work, ‘Searching for axions with quantum interferometry’, investigates novel approaches to detecting axions-a prime dark matter candidate-by harnessing quantum phase measurements in experimentally feasible setups. We demonstrate that axion-photon interactions can induce both Aharonov-Bohm and Berry phases in superconducting circuits and photonic interferometers, potentially reaching axion-photon couplings of $g_{aγγ}^{\mathrm{min}}\sim 7.8\times10^{-{14}}~\mathrm{GeV}^{-1}$ for axion masses around $10^{-{10}}~\mathrm{eV}$ . Could these quantum phase observables unlock a new era of sensitivity in the search for weakly interacting dark matter and beyond?

The Echo of Symmetry: Unraveling the Strong CP Problem and Dark Matter

The Standard Model of particle physics, while remarkably successful in describing fundamental forces and particles, encounters a perplexing issue with the strong interaction – one of the four fundamental forces of nature. Theoretical calculations predict a violation of Charge-Parity (CP) symmetry within the strong force, meaning that particles and their antimatter counterparts should behave differently under combined charge conjugation and parity transformations. However, experimental observations demonstrate no such violation. This discrepancy, known as the Strong CP Problem, suggests a missing piece in the Standard Model, or a fundamental misunderstanding of the strong interaction itself. Physicists have proposed various solutions, including the introduction of new particles and interactions, to reconcile the theory with experimental results and explain why the strong force appears to conserve CP symmetry despite theoretical predictions to the contrary. The persistence of this problem highlights the limitations of current understanding and motivates ongoing research into the fundamental laws governing the universe.

Observations across multiple scales – from galactic rotation curves to the cosmic microwave background – reveal a startling discrepancy: the visible matter in the universe accounts for only a small fraction of its total mass. This unseen mass, dubbed Dark Matter, exerts gravitational influence but does not interact with light, rendering it invisible to telescopes. Cosmological models estimate that roughly 85% of the universe’s mass is comprised of this enigmatic substance, implying a fundamental gap in our understanding of the cosmos. Its presence is inferred through its gravitational effects on visible matter and the large-scale structure of the universe, prompting extensive searches for its constituent particles and a continued refinement of theoretical models attempting to explain its nature and origin.

The axion presents a remarkably elegant solution to two of the most perplexing problems in modern physics. Theorized as a pseudo-Nambu-Goldstone boson, its existence not only naturally explains the strong CP problem – the baffling absence of charge-parity (CP) violation in the strong nuclear force – but also provides a compelling candidate for dark matter. The strong CP problem arises because the Standard Model allows for a term that should cause a measurable electric dipole moment in the neutron, which has never been observed; the axion’s properties effectively cancel this term. Simultaneously, because axions are predicted to be lightweight and weakly interacting, they would have been produced prolifically in the early universe, accumulating to a density that could account for a substantial fraction – or even all – of the observed dark matter. This dual functionality makes the axion a particularly attractive and intensely studied particle, representing a potential bridge between the seemingly disparate realms of particle physics and cosmology.

The pursuit of axion properties represents a pivotal frontier in modern physics, holding the potential to reshape cosmological models and refine the Standard Model. Determining the axion’s mass, its coupling strength to ordinary matter, and its potential self-interactions is not merely an exercise in particle detection; it’s a quest to illuminate the composition of dark matter, which constitutes approximately 85% of the universe’s mass. Current research leverages increasingly sensitive experiments – from resonant cavities chilled to near absolute zero to searches for axion-induced photons in strong magnetic fields – to probe the theoretical parameter space. A confirmed detection would not only solve the Strong CP Problem by providing a natural explanation for the absence of certain particle interactions, but also offer a concrete window into a hidden sector of the universe, potentially revealing connections to other unresolved mysteries like the matter-antimatter asymmetry and the nature of neutrino masses. Therefore, unraveling the characteristics of this elusive particle is paramount to achieving a complete and accurate picture of the cosmos.

A THz Mach-Zehnder interferometer can detect the Berry phase induced by axions and their associated quasiparticles.

Whispers in the Quantum Foam: Methods for Axion Detection

Axion detection is fundamentally challenged by the exceedingly weak predicted coupling strength between Axions and photons. Theoretical models suggest an interaction that produces extremely small magnetic field fluctuations, necessitating measurement sensitivities far beyond conventional techniques. Current experimental setups aim to detect signals on the order of $10^{-{15}}$ Tesla or smaller, requiring highly sensitive magnetometers and significant noise reduction strategies. The predicted interaction rate is also highly dependent on the Axion mass, which remains unknown, further complicating detection efforts and necessitating broad frequency searches to cover the possible parameter space. This weak interaction, combined with the uncertainty in Axion mass, defines the primary difficulty in experimentally verifying the existence of these particles.

The radio-frequency Superconducting Quantum Interference Device (rf-SQUID) functions as an exceptionally sensitive magnetometer, making it well-suited for detecting the faint magnetic fields predicted to be generated by Axion-Photon interactions. These interactions, while theoretically established, produce extremely weak signals; the rf-SQUID’s operation, based on the quantum mechanical properties of superconducting loops, allows for the measurement of magnetic fields on the order of $10^{-{18}}$ Tesla or lower. Specifically, the SQUID detects changes in magnetic flux by measuring the critical current through a Josephson junction, providing a quantifiable signal proportional to the induced magnetic field. The high sensitivity and low noise characteristics of the rf-SQUID, particularly when cryogenically cooled, enable the detection of the subtle magnetic signatures expected from even weak Axion couplings.

Mach-Zehnder Interferometers (MZIs) provide an alternative detection method to rf-SQUIDs by directly measuring the phase shift imparted on photons interacting with an axion field. An MZI splits a coherent photon beam into two paths, allowing them to propagate through a region with a strong static magnetic field – the environment where axion-photon interactions are predicted. The presence of axions induces a phase shift proportional to the integral of the magnetic field along each path, creating interference patterns at the output. This phase shift, though extremely small, can be precisely measured by analyzing the interference fringes, allowing for the detection of even weak axion signals. The sensitivity of MZI-based detection scales with the path length and the strength of the applied magnetic field, necessitating both long interaction lengths and high-field environments.

Mach-Zehnder Interferometers (MZIs) are utilized in axion detection by measuring the Berry phase, a geometric phase shift induced on photons interacting with a static magnetic field and, hypothetically, axions. Magnetic Field Rotation (MFR) techniques are coupled with MZIs to continuously rotate the polarization of photons propagating through the interferometer, maximizing sensitivity to the small phase shifts caused by the axion-induced Berry phase. The Berry phase manifests as a shift in the interference pattern of the MZI, directly proportional to the strength of the axion field and the rotation rate of the magnetic field. Precise measurement of this interference shift, through careful control of the MZI and MFR parameters, allows for the identification of the axion signature despite extremely weak interactions. $\Delta \phi = \in t_C A \cdot dl$ , where $\Delta \phi$ is the Berry phase, and the integral represents the circulation of the vector potential $A$ around the closed path $C$ .

An rf-SQUID loop can detect the <span class="katex-eq" data-katex-display="false"> ext{axion}</span>-induced Aharonov-Bohm phase, providing a pathway for axion detection. — An rf-SQUID loop can detect the $ext{axion}$ -induced Aharonov-Bohm phase, providing a pathway for axion detection.

Echoes of Collective Behavior: Axion Quasiparticles and THz Interferometry

Axion quasiparticles offer a distinct detection strategy for Axion-like particles (ALPs) by leveraging collective spin-wave excitations within a material. Unlike traditional ALP detection methods which focus on individual particle interactions, this approach examines the macroscopic behavior of these excitations. These quasiparticles emerge from the coherent alignment of numerous electron spins and exhibit properties influenced by the underlying material’s topology. Detection relies on observing the effects of these collective excitations rather than individual axion events, providing a potentially higher signal-to-noise ratio and broadening the scope of detectable ALP parameters, particularly at lower masses where individual axion detection becomes increasingly challenging.

Axion quasiparticles, arising as collective excitations within topological materials, exhibit a coupling to the electromagnetic field that differentiates their detection from methods targeting individual axions. This coupling manifests as a frequency-dependent polarization rotation in applied electromagnetic radiation. Unlike single axion searches which rely on extremely weak signals from individual particle interactions, the collective nature of the quasiparticles amplifies the electromagnetic response, offering a potentially more robust detection pathway. The signal’s dependence on the material’s topological properties and the quasiparticle’s dispersion relation provides a unique spectral signature, allowing for discrimination from background noise and conventional electromagnetic phenomena. This distinct signature is crucial for developing targeted detection strategies using terahertz interferometry.

Terahertz (THz) interferometers are employed for the detection of axion quasiparticle effects due to their sensitivity to minute phase shifts in electromagnetic radiation. These instruments operate by splitting a THz beam, directing each portion through a sample potentially hosting these quasiparticles, and then recombining the beams for interference. The presence of axion quasiparticles induces a measurable phase difference due to their coupling to the electromagnetic field, even when individual axion detection is impractical. Specifically, the interferometers are designed to maximize sensitivity in the frequency range relevant to the predicted properties of these quasiparticles, typically around 10¹² Hz, and are capable of resolving phase shifts on the order of $10^{-6}$ radians, which is sufficient to observe the predicted subtle effects.

Detection of axion quasiparticles would not only offer further validation of axion existence, but also enable more precise characterization of their fundamental properties. Current research indicates that the proposed detection methods, utilizing Terahertz interferometry, are projected to improve existing limits on the axion-photon coupling constant by a factor of 10 to 100 at axion masses around $10^{-{10}}$ eV. This represents a significant advancement in the search for these weakly interacting particles and will allow for a more detailed understanding of their interactions with electromagnetic fields.

Calculations predict a Berry phase contribution of 0.15π within representative topological materials operating in the Terahertz (THz) regime. This Berry phase arises from the geometric properties of the electronic band structure and significantly influences the quasiparticle dynamics. Specifically, the predicted value represents the accumulated phase shift experienced by the quasiparticle wavefunction as it traverses a closed loop in momentum space, impacting the observed THz signal and serving as a key indicator for detection. This contribution is crucial for interpreting experimental results and distinguishing the signal from background noise, enabling more sensitive searches for Axion-like particles via quasiparticle detection.

Measurements of the Aharonov-Bohm phase using an rf-SQUID loop demonstrate sensitivity to the <span class="katex-eq" data-katex-display="false">axion-photon</span> coupling. — Measurements of the Aharonov-Bohm phase using an rf-SQUID loop demonstrate sensitivity to the $axion-photon$ coupling.

Beyond the Horizon: Exploring the Landscape of Axion-Like Particles

Initially conceived as a solution to the strong CP problem in quantum chromodynamics, the search for dark matter candidates has expanded beyond the original axion to include a broader landscape of Axion-Like Particles, or ALPs. This shift acknowledges the theoretical possibility that nature may contain particles sharing key characteristics with axions – namely, very weak interactions with standard model particles and the potential to constitute dark matter – but differing in mass and coupling strength. By widening the scope to encompass this ‘ALP forest’, researchers significantly increase the probability of detection; while axions occupy a specific parameter space, ALPs could exist across a vast range of masses and interaction strengths, effectively multiplying the opportunities for experimental confirmation. This expanded search doesn’t necessitate entirely new detection strategies, as the fundamental principles – leveraging the interaction between these particles and photons – remain consistent, but it demands greater experimental flexibility and a willingness to explore a much wider range of potential signals.

The enduring quest for axions has naturally expanded to include a broader family of particles known as axion-like particles (ALPs), due to a crucial shared characteristic: interaction with photons. This similarity is far from merely conceptual; it allows researchers to leverage the same sophisticated detection techniques originally developed for axion searches. These methods, often relying on sensitive magnetometers and resonant cavities, are predicated on observing the subtle effects of photon-ALP interactions. Specifically, when an ALP encounters a magnetic field, it can convert into a photon, or vice versa, creating a detectable signal. Because ALPs share this fundamental interaction pathway with axions, existing experimental infrastructure and data analysis pipelines remain directly applicable, significantly accelerating the search for these elusive particles and broadening the scope of potential discoveries within the dark matter landscape.

Detecting axion-like particles hinges on their exceptionally weak interactions, necessitating innovative approaches to amplify signals. The Aharonov-Bohm phase, a quantum mechanical phenomenon, offers a pathway to achieve this enhancement by allowing interactions to be detected even without a direct force exchange. However, the sensitivity of current radio-frequency Superconducting Quantum Interference Device (rf-SQUID) setups isn’t uniform across all potential ALP masses; limitations arise from several sources. Below an energy of $4 \times 10^{-{15}} \text{ eV}$ , low frequency noise obscures subtle signals, while between $4 \times 10^{-{15}} \text{ eV}$ and $7 \times 10^{-{10}} \text{ eV}$ , the coherence time of the SQUID restricts sensitivity. Above $7 \times 10^{-{10}} \text{ eV}$ , the detector bandwidth becomes the limiting factor, preventing the capture of higher-frequency interactions. Overcoming these constraints is paramount to fully exploring the landscape of ALPs and unlocking their potential to reveal new physics.

The confirmed existence of Axion-Like Particles (ALPs) would represent a profound leap beyond the Standard Model of particle physics, immediately necessitating a re-evaluation of established theoretical frameworks. Currently, the Standard Model fails to account for phenomena like dark matter and the observed matter-antimatter asymmetry in the universe; ALPs present a compelling candidate to address these mysteries, potentially constituting a significant portion of dark matter itself. Beyond cosmology, detecting ALPs could unlock insights into the nature of the vacuum, the existence of extra dimensions, and the unification of fundamental forces. Investigations into ALP properties – their mass, coupling strengths, and interactions with other particles – would establish a new realm for precision measurements, driving innovation in detector technology and opening pathways to explore physics at energy scales currently inaccessible through conventional means. This detection isn’t merely confirmation of a particle’s existence, but the initiation of a new era in fundamental research, potentially reshaping ΛCDM cosmology and our understanding of the universe’s deepest secrets.

The pursuit of axions, as detailed in this study, resembles less a construction project and more the tending of a garden. Researchers cultivate sensitivity within superconducting circuits and photonic interferometers, hoping to coax a signal from the void. It’s a delicate dance with quantum phases, a willingness to accept that the desired outcome isn’t built, but grown from the inherent uncertainties of the system. As Henry David Thoreau observed, “It is not enough to be busy; so are the ants. The question is: What are we busy with?” This work isn’t simply about detecting dark matter; it’s about refining the instruments to perceive the subtle whispers of the universe, knowing full well that even the most elegant design is merely a temporary compromise against the inevitable entropy of time.

The Horizon Beckons

The pursuit of axions, as detailed within, is not a tightening of tolerances, but a yielding to the inevitable complexity of any system attempting to grasp the unseen. Each interferometer, each superconducting loop, is less a detector and more a resonant cavity, amplifying not just a signal, but the background hum of its own imperfections. The current explorations into Berry and Aharonov-Bohm phases are not destinations, but the charting of increasingly subtle contours on a landscape perpetually shifting beneath one’s feet.

The real challenge lies not in squeezing more sensitivity from existing architectures, but in accepting that every refinement introduces new avenues for decoherence, for spurious signals mimicking the desired whisper from the dark. The search will inevitably drift from a quest for a specific frequency, a definitive detection, towards a mapping of the noise itself – understanding the system’s internal weather patterns as much as the external influences. It is a humbling endeavor.

Future work will not be defined by breakthroughs, but by increasingly sophisticated techniques for disentangling signal from the ever-present tangle of self-interference. The ultimate instrument will not find the axion, but become a mirror reflecting the fundamental limitations of measurement itself – a testament to the beautiful, frustrating fact that the universe rarely yields its secrets cleanly.

Original article: https://arxiv.org/pdf/2604.13181.pdf

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

The Echo of Symmetry: Unraveling the Strong CP Problem and Dark Matter

Whispers in the Quantum Foam: Methods for Axion Detection

Echoes of Collective Behavior: Axion Quasiparticles and THz Interferometry

Beyond the Horizon: Exploring the Landscape of Axion-Like Particles

The Horizon Beckons

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