Searching for Ultra-Light Axions with Twisted Cavity Resonators of Anyon Rotational Symmetry with Bulk Modes of Non-Zero Helicity

arXiv:2208.01640 · hep-ph, astro-ph.IM, physics.ins-det, quant-ph · Submitted 2022-08-01 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Searching for Ultra-Light Axions with Twisted Cavity Resonators of Anyon Rotational Symmetry with Bulk Modes of Non-Zero Helicity".

Mira: The gist: This work presents a new class of electromagnetic resonators called “anyon cavity resonators” that exhibit bulk resonant modes with non-zero electromagnetic helicity in vacuo,

Kai: First, who's behind it and why it matters.

Title and authors: Kai: So what this paper actually shows us is that these twisted triangular cavities have a mechanism to naturally couple to ultralight dark matter axions without needing an external magnetic field, which we saw in the previous segment.

Mira: Exactly. The authors use twisted hollow structures made from equilateral triangular cross-sections to make this anyon cavity resonator, and those things have bulk resonant modes with non-zero electromagnetic helicity in a vacuum, which connects them to axions through amplitude modulations <ref:2208.01640#pg1>.

Lev: The core idea is that these helical modes are what actually do the work here, and they have a non-zero overlap between the electric and magnetic field eigenvectors integrated over the whole cavity volume <ref:2208.01640#pg1>.

Kai: That’s what gives them that helicity, which then allows them to couple to axions through amplitude modulations <ref:2208.01640#pg2>. It’s about using the structure itself to generate the coupling.

Mira: And they show that in the upconversion limit, these helical modes couple to axions by adding amplitude modulated sidebands through a process called the axion-photon chiral anomaly <ref:2208.01640#pg2>.

Lev: So, for someone listening who just wants the gist, this means we use an existing cavity structure and tune its shape to create a non-zero helicity to pull out those tiny axions.

Kai: It’s interesting because it means you can use low-loss superconducting resonators here, which is something we’ve been trying to do for dark matter searches <ref:2208.01640#pg2>.

Mira: Exactly. The coupling strength is proportional to this normalized mode helicity of a monochromatic field, mam equals one over root two times Q p omega a over omega p alpha Hp <ref:2208.01640#pg2>. That means maximizing that helicity directly boosts the signal you get back from the axion search.

Lev: And they show sensitivity calculations using a complex Poynting theorem to give an SNR, which is good because it gives us a concrete number for how sensitive this setup could be in the ultra-light regime, say around ten to twelve gigaparsecs <ref:2208.01640#pg1>.

Kai: The experimental feasibility part of the paper is pretty cool; they’ve shown that they can three dee print these linear resonators and they match their predicted frequencies really well <ref:2208.01640#pg3>.

Mira: It also shows that if you achieve a high enough Q factor, an ultra-stable oscillator built off one of these anyon cavity devices could be used for the most sensitive search for ultralight dark matter in that mass range.

Lev: The paper does mention their limitation: the sensitivity calculation assumes the axion frequency is within the bandwidth of that specific resonant mode, which should be fine if we are talking about ultralight axions <ref:2208.01640#pg1>.

The paper's summary: Kai: So to wrap up what they suggest is focusing on maximizing the mode helicity Hp by designing the geometry itself <ref:2208.01640#pg3>. They mention that for specific shapes, like the equilateral cross-section, this helicity can approach one and tune in frequency as you change the twist angle phi <ref:2208.01640#pg3>.

Mira: That maximization of Hp is what directly boosts your signal strength according to equation number twenty-two <ref:2208.01640#pg3>. It's a geometric optimization for the physics.

Lev: And they also suggest using superconducting materials because their inherent properties help reduce surface losses, which is crucial for keeping things sensitive in this kind of experiment.

Kai: And they suggest using this setup as an ultra-stable oscillator locked tightly to the cavity for the best results. It’s about stability for detection.

Mira: The main implication is that by focusing on these helical modes and using geometry to maximize them, we can set limits on those extra axion-photon coupling terms, ga gamma gamma plus ga mm using only a single mode <ref:2208.01640#pg3>.

Lev: That means we don't need dual-mode excitation or a massive volume magnet to constrain the strength of this coupling. That’s a big reduction in experimental complexity for testing new physics.

Kai: It really shifts the focus from needing huge magnets to getting better control over these specific cavity geometries and materials.

Mira: So, if you can build that ultra-stable oscillator, it could be one of the most sensitive tools we have for searching ultralight dark matter axions by focusing on this unique helicity property.

Lev: But remember, they also flag that the sensitivity calculation assumes the axion frequency is right in the resonant mode bandwidth, which should hold up in this ultra-light regime <ref:2208.01640#pg1>.

The paper's improvements: Kai: So we've been looking at this paper "Searching for Ultra-Light Axions with Twisted Cavity Resonators of Anyon Rotational Symmetry with Bulk Modes of Non-Zero Helicity." It’s basically about these new cavity designs that can naturally couple to ultralight dark matter axions without needing an external magnetic field.

Mira: That coupling comes from the axion mixing with neutral pions, and that mixing is what introduces a non-zero Zilch term into the equations of motion <ref:2208.01640#pg2>.

Kai: So in short, this paper on "Searching for Ultra-Light Axions with Twisted Cavity Resonators of Anyon Rotational Symmetry with Bulk Modes of Non-Zero Helicity" shows that we can search for ultralight dark matter axions by focusing on electromagnetic fields with non-zero helicity inside these twisted triangular cavities.

Mira: It really points toward using superconducting resonators to reduce losses because they have this inherent property of coupling low-mass axions via amplitude modulation through a parametric interaction.

Lev: The limitation mentioned is that the sensitivity calculation assumes the axion frequency is within the bandwidth of that specific resonant mode, which should hold up in the ultra-light regime, but we need to make sure that holds up when we go into those extremely low frequencies.

Kai: So for us on hardware, it means designing these hollow twisted structures and getting a high enough Q factor is the main challenge before we can build an ultra-stable oscillator.

Kai: We're ready to move on from this paper and see what other cool things are being published out there.

Conclusion: Kai: So we’ve been looking at "Searching for Ultra-Light Axions with Twisted Cavity Resonators of Anyon Rotational Symmetry with Bulk Modes of Non-Zero Helicity." It’s about these new cavity designs that can naturally couple to ultralight dark matter axions without needing an external magnetic field.

Mira: Right. The authors use twisted hollow structures made from equilateral triangular cross-sections to make this anyon cavity resonator, and those things have bulk resonant modes with non-zero electromagnetic helicity in a vacuum, which connects them to axions through amplitude modulations.

Lev: From an engineering standpoint, the crucial part for us is seeing if this works in practice. The paper explores two configurations: a linear twisted resonator with arbitrary twist angle phi and a ring resonator similar to a Möbius strip with only discrete twists like phi equals Z pi over three.

Kai: And what's interesting about that is that the linear case allows for any twist angle, which means we can tune the resonance frequency by changing that geometry, and they show how the twist angle phi affects things.

Mira: It seems they found that for specific modes, like those in sixty degree or one hundred twenty degree twisted triangular waveguide cavities, the helicity approaches near unity. That's a big deal because it directly relates to the signal strength we can get from an axion interaction.

Lev: And they show that this helicity is maximized for the equilateral case of the cross-section, which is pretty helpful if we want to design something practical with three dee printing, since those three discrete phi values are three dee printed and match their predicted frequencies.

Kai: So what they're saying is that if we get a high enough Q factor from these devices, an ultra-stable oscillator built off one of these anyon cavity devices could lead to the most sensitive search for axion dark matter in the ultra-light mass range.

Mira: And they are using a complex Poynting theorem to calculate the sensitivity, and they show that if you are in the ultra-light regime, like ten-twenty-two eV to ten-fourteen eV, this calculation holds true.

Lev: The paper also mentions that the signal to noise ratio can be calculated using a formula involving ga gamma gamma beta p alpha Q p one plus four Q squared p over ten thousand t alpha over one four p rho ac three omega p square root Sam.

Kai: It's important for us to remember that this search doesn't require an external magnetic field because the axion couples to photons through the chiral anomaly, which is described by a modification to Maxwell’s equations.

Mira: That coupling comes from the axion mixing with neutral pions, and that mixing is what introduces a non-zero Zilch term into the equations of motion, which is what allows this interaction.

Lev: From an error correction side, if we were to run this on real hardware, the overhead would land on controlling that ultra-stable oscillator locked tightly to the cavity as shown in Figure six. That’s where most of your control complexity will be.

Kai: It really points toward using these hollow twisted triangular devices and getting a high Q factor as the main challenge before we can build that ultra-stable oscillator for axion dark matter detection.

Mira: And the real potential here is setting limits on ga gamma gamma plus ga mm using only a single mode without needing dual-mode excitation or a large volume magnet.

Lev: If we look at that, it sets constraints on how strongly the axion couples to photons, which is pretty powerful for constraining new physics beyond the Standard Model.

Kai: So for us on hardware, it means designing these hollow twisted structures and getting a high enough Q factor is the main challenge before we can build that ultra-stable oscillator.

Mira: And the real potential here is setting limits on ga gamma gamma plus ga mm using only a single mode without needing dual-mode excitation or a large volume magnet.

Lev: If we look at that, it sets constraints on how strongly the axion couples to photons, which is pretty powerful for constraining new physics beyond the Standard Model.

Kai: We're ready to move on from this paper and see what other cool things are being published out there.

J. F. Bourhill, E. C. I. Paterson, M. Goryachev, M. E. Tobar

Quantum Technologies and Dark Matter Labs, Department of Physics, University of Western Australia

hep-ph, astro-ph.IM, physics.ins-det, quant-ph

Submitted: 2022-08-01

Updated: 2026-10-13

Comments: An erratum has been submitted to Physical Review D; this is the corrected article. Correctly treating both axion frequency components gives AM for real field overlap and PM for imaginary overlap (helicity). Sensitivity curves are numerically unchanged if the assumed noise is interpreted as phase noise, requiring sufficiently low residual oscillator and readout phase noise

Journal ref: Phys. Rev. D 108, 052014, 2023

DOI: 10.1103/PhysRevD.108.052014

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 80/100

The gist: The gist: This work presents a new class of electromagnetic resonators called “anyon cavity resonators” that exhibit bulk resonant modes with non-zero electromagnetic helicity in vacuo, which

Key concepts

Anyon Cavity Resonators: These are novel electromagnetic resonators created by forming twisted hollow structures using equilateral triangular cross-sections. Unlike standard cavities, these structures support bulk resonant modes that possess non-zero electromagnetic helicity in a vacuum, which is key for axion coupling.
Electromagnetic Helicity (Hp): Helicity measures the handedness of an electromagnetic wave's electric and magnetic fields. In this resonator design, the bulk modes exhibit non-zero helicity (Hp), meaning the electric and magnetic field eigenvectors have a non-zero overlap, which is crucial for coupling to axions.
Axion Coupling Mechanism: The paper shows that these helical modes naturally couple to ultralight dark matter axions through the axion-photon chiral anomaly. This coupling occurs via amplitude modulation of the resonator's single mode, allowing for a search using only the cavity's inherent properties without needing an external magnetic field.
Axion-Photon Chiral Anomaly: This is a quantum electrodynamic effect where axions mix with neutral pions and subsequently couple to photons. This interaction term modifies the photon's equations of motion, providing the mechanism through which the non-zero helicity modes in the cavity can interact with dark matter axions.

Summary

The gist: This work presents a new class of electromagnetic resonators called “anyon cavity resonators” that exhibit bulk resonant modes with non-zero electromagnetic helicity in vacuo, which couple naturally to ultralight dark matter axions via amplitude modulations without needing an external magnetic field.

Novel Resonator Design

The paper introduces a new type of resonator through the formation of twisted hollow structures using equilateral triangular cross-sections, which leads to the realisation of a cavity with anyon rotational symmetry M¨obius-ring resonators stem from a well-studied and fascinating geometrical structure which features a one-sided topology; the M¨obius strip, and have been shown to exhibit fermion rotational symmetry with respect to a ring resonator with no twist (which exhibits boson rotational symmetry) Here, we present a new type of resonator through the formation of twisted hollow structures using equilateral triangular cross-sections, which leads to the realisation of a cavity with anyon rotational symmetry. Unlike all previous cavity resonators, the anyon resonator permits the existence of bulk resonant modes that exhibit non-zero electromagnetic helicity in vacuo, with non zero overlap of the electric and magnetic mode eigenvectors, R Ep · Bp dτ, integrated over the cavity volume.

Anyon Rotational Symmetry and Helicity

The anyon resonator permits the existence of bulk resonant modes that exhibit non-zero electromagnetic helicity in vacuo, with non zero overlap of the electric and magnetic mode eigenvectors, R Ep · Bp dτ, integrated over the cavity volume. The normalized helicity in (1) can range between ±1 and is tied to the conservation of Zilch [59], or photonic chirality [16] and is usually considered when photons interact with chiral molecules or materials [13, 15, 16]. The sign of the helicity depends on whether the modes E field and B field have net parallel alignment (+ve) or net anti-parallel alignment (−ve), and is given by, Hp = 2 Im[R Ep(⃗r) · B∗ p (⃗r) dτ] qR Ep(⃗r) · E∗ p (⃗r) dτ R Bp(⃗r) · B∗ p (⃗r) dτ, (1).

Axion Coupling Mechanism

In the upconversion limit, we show that these non-zero helical modes couple naturally to ultralight dark matter axions within the bandwidth of the resonator by adding amplitude modulated sidebands through the axion-photon chiral anomaly. This not only significantly reduces the complexity but also allows the possibility of utilising low-loss superconducting resonators [27–30] to search for ultra-light dark matter (ULDM) axions. The coupling is proportional to the normalized mode helicity of a monochromatic field mam = 1/2 √2 Qp ωa / ωp ⟨θ0Hp, which is proportional to the normalised mode helicity of a monochromatic field [51–58].

Linear and Ring Resonator Analysis

The investigation covers two twisted triangular cavity configurations: (a) a linear twisted resonator with electrically conducting boundary conditions at the ends, which allows arbitrary twist angle, ϕ, and (b) a twisted ring resonator similar to a M¨obius strip, with only discrete allowed ϕ values (ϕ = Zπ/3). The linear resonator geometry dictates the boundary conditions which are used to solve Maxwell’s equations for the resonant electromagnetic modes within this volume. For the linear case, the greatest impact of the twisting angle ϕ will be generated by the lowest order regular polygon.

Sensitivity Calculation

The sensitivity to axions is calculated using a complex Poynting theorem derived from the phasor form developed in the last section. The signal to noise ratio (SNR) is given by SNR = gaγγβpHp √2(1 + βp) q Qp 1 + 4Q2p (ωa/ωp) squared / 10 6 t ωa / 1 4 p ρac3 ωp √(Sam). This calculation assumes that the axion frequency is within the bandwidth of the resonant mode, which will be true in the ultra-light regime.

Experimental Feasibility

The paper demonstrates that three discrete ϕ valued linear resonators are 3D printed and show excellent agreement with predicted mode frequencies. If theoretically achievable Q-factors are attained, an ultra-stable oscillator based off one of these anyon cavity devices would permit the world’s most sensitive search for axion dark matter in the ultra-light mass range. The best way to configure such upconversion experiments is as a frequency stabilised oscillator locked tightly to the axion sensitive cavity as shown in Fig.6.

Quantum Electrodynamic Modifications

The coupling of axions to photons occurs due to the axion mixing with neutral pions and is thus couples to photons through the chiral anomaly. This “axionelectromagnetic chiral anomaly” may be described by the following interaction term, added to the Lagrangian of the photonic degrees of freedom [65]. The photon-axion coupling from Eq.(2) modifies parts of the electrodynamic equations of motion proportionally to the dynamic normalised coupling parameter, Θ(t) = gaγγa(t).

Conclusion

It has been demonstrated that an electromagnetic field with non zero helicity, Hp will be sensitive to ULDM axions. This unique property in an electromagnetic resonator is achievable using hollow, twisted triangular devices in either a linear or ring configuration. FEM has demonstrated that the eigenmodes of such systems do indeed produce Hp ∼ 1 for particular modes, and that these modes in fact tune in frequency as a function of twist angle ϕ. Three discrete ϕ valued linear resonators are 3D printed and demonstrate excellent agreement with predicted mode frequencies. If theoretically achievable Q-factors are attained, an ultra-stable oscillator based off one of these anyon cavity devices would permit the world’s most sensitive search for axion dark matter in the ultra-light mass range.

Acknowledgments

This work was funded by the Australian Research Council Centre of Excellence for Engineered Quantum Systems, CE170100009 and the Centre of Excellence for Dark Matter Particle Physics, CE200100058 This work was funded by the Australian Research Council Centre of Excellence for Engineered Quantum Systems, CE17.

References

[1] Douglas J. Ballon and Henning U. Voss. Classical m¨obius-ring resonators exhibit fermion-boson rotational symmetry Phys. Rev. Lett., 101:247701, Dec 2008

[59] Daniel M. Lipkin. Existence of a new conservation law in electromagnetic theory Journal of Mathematical Physics, 5(5):696–700, 2022/01/20 1964

[71] Michael E. Tobar, Catriona A. Thomson, Benjamin T. McAllister, Maxim Goryachev, Anton V. Sokolov, and Andreas Ringwald. Sensitivity of Resonant Axion Haloscopes to Quantum Electromagnetodynamics Annalen der Physik, 2200594, 2023

[78] E. Rubiola and R. Brendel. The am noise mechanism in oscillators IEEE IFCS Conf. Proc., pages 33–39, 2009

[81] Michael Edmund Tobar, Peter Wolf, Sebastien Bize, Giorgio Santarelli, and Victor Flambaum. Testing local lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser Physical Review D, 81(2), jan 2010

[82] Ben T. Mcallister, Stephen R. Parker, Eugene N. Ivanov, and Michael E. Tobar.

Improvements for AI systems

Ultra-Sensitive Axion Detection via Anyon Cavity Resonators: The improved AI system can perform searches for ultra-light dark matter axions in the mass range of 10−22 to 10−14 eV by implementing an ultra-stable oscillator configuration locked to the anyon cavity resonator. This allows for a sensitive ultra-light dark matter experiment by searching for signals in the Fourier spectrum of amplitude fluctuations, removing the typical requirement for an external magnetic field.
Non-Magnetic Field Axion Search Capability: The system can utilize superconducting materials to reduce surface losses and enhance sensitivity to axions because the anyon resonator's eigenmodes exhibit non-zero electromagnetic helicity, which couples low-mass axions to photons as an amplitude modulation of a single mode through a parametric interaction.
Enhanced Sensitivity via Helicity Maximization: The AI system can be optimized by designing cavity geometries (like the equilateral triangular cross-section) to maximize the mode helicity, as shown in Fig. 2(b), where helicity is maximised for the equilateral case and relates directly to the signal strength through Equation (22): mam = 1/sqrt(2)Qpωa/ωp⟨θ0Hp.
Direct Axion Coupling Search: The system can search for axions by analyzing the axion induced AM spectral density, SAam, given by Equation (24), which is proportional to the normalised mode helicity of a monochromatic field.
Unified Search Limit Determination: By incorporating quantum electromagnetodynamic modifications, the system can establish limits on gaγγ + gaMM (where gaEM and gaMM are extra axion-photon coupling terms) using only a single mode without the need for dual-mode excitation or a large volume magnet, effectively setting constraints on the axion coupling strength.

Abstract

Möbius-ring resonators stem from a well-studied geometrical structure with a one-sided topology, the Möbius strip, and have been shown to exhibit fermion rotational symmetry with respect to an untwisted ring resonator, which exhibits boson rotational symmetry [1]. Here, we present twisted hollow resonators with equilateral triangular cross-sections, leading to cavities with anyon rotational symmetry. Unlike conventional cavity resonators, these structures permit bulk resonant modes with a non-zero complex electromagnetic overlap C p= integral V E p times B p*,dτ. The real and imaginary parts of this overlap couple to different observable quadratures. Although the negative-frequency component of a real axion field is immaterial for haloscopes employing a static DC magnetic field, it must be retained for a pumped resonator because the complex forms of Maxwell's equations differ for positive and negative frequencies and produce distinct upper and lower mixing branches. Retaining both branches shows that the real overlap produces amplitude-modulated sidebands, whereas the imaginary helicity of the modes studied here produces phase-modulated sidebands through the axion-photon chiral anomaly. A sensitive ultra-light dark-matter experiment may therefore be realised with an ultra-stable oscillator and a phase-sensitive readout. The sensitivity curves calculated here require the assumed noise floor to be interpreted as phase-modulation noise rather than amplitude-modulation noise, and consequently require sufficiently low residual oscillator phase noise at the axion Fourier frequency. The scheme removes the usual requirement for an external magnetic field and permits superconducting resonators with reduced surface loss and enhanced axion sensitivity.