Axion-mediated photon-to-photon transitions in high finesse dielectric resonators

TL;DR

This work analyzes axion-mediated photon-to-photon transitions within a high‑finesse dielectric spherical resonator to enhance the weak axion–photon coupling. It combines fully analytical first‑order perturbation theory with Mie theory to derive a symmetry‑based selection rule, showing allowed transitions between TE$_{\ell}$ and TM$_{\ell}$ modes under parity change and conserved angular momentum $\ell$, provided the mode frequency difference matches the axion frequency $\Omega_{\alpha}$. Using a coherent galactic axion field and a Born‑approximation treatment, the authors calculate the transition matrix element $G$ and the rate $R_{\alpha\gamma\gamma}$, then assess realistic enhancement via photon number in mm‑scale resonators in the microwave regime, with explicit numbers for $m_{\alpha}=1\,\mu$eV and $S=62.5$ mm. They project experimental reach, discuss materials and quality factors needed to reach axion parameter spaces (KSVZ/DFSZ), and introduce DARK‑ROSE as a scalable search strategy that can probe axion masses in the $0.2\,\mu$eV to 1 meV range without an external magnetic field, while noting extensions to solid-state axion‑like quasiparticles in metamaterials. Overall, the paper provides a concrete, analytically tractable pathway to resonant axion–photon detection using dielectric resonators and outlines practical sensing limits and scanning protocols.

Abstract

Axions are hypothetical particles that could address both the strong charge-parity problem in quantum chromodynamics and the enigmatic nature of dark matter. However, if axions exist, their mass remains unknown, and they are expected to interact very weakly with the electromagnetic field, which explains why they have not been detected yet. This study proposes a way to substantially augment the axion-photon interaction by confining the photons within high-quality-factor dielectric resonators, increasing their intensity and lifetime, and thus the possibility of interacting with axions in the background. In view of this, we study resonant axion-mediated photonic transitions in millimeter-sized spherical dielectric resonators, based on fully analytical calculations to the first order in perturbation theory. Such resonators exhibit high lifetime Mie resonances in the microwave part of the spectrum, with a separation that can be tailored with the radius of the sphere to match the expected axion frequency, allowing axion-mediated photonic transitions when particular selection rules are fulfilled. We predict experimentally accessible axion mass regimes where such triply resonant transitions can be realized with standard dielectric resonators. We propose an experiment for probing such interactions named DARK-ROSE.

Figures (4)

• Figure 1: Discrete photonic Mie resonance frequencies for a spherical dielectric resonator of radius $S$ corresponding to fundamental ($\nu=1$) TE (blue) and TM (red) modes of angular momentum $\ell$. The dots indicate the presence of additional modes beyond the displayed range.
• Figure 2: Schematic representation of axion-induced photonic transitions between electromagnetic modes in a spherical resonator. Left: An axion is absorbed, enabling a transition from a transverse electric (TE) mode to a transverse magnetic (TM) mode with the same angular momentum $\ell$. Right: The reverse process, where a transition from TM to TE mode is accompanied by the emission of an axion. The initial and final photonic states are marked with open and solid circles, respectively, while axions are represented by dashed arrows.
• Figure 3: (a) Scaled resonance frequencies $( fS/c )$ for transverse electric (TE) and transverse magnetic (TM) modes of the spherical dielectric resonator under consideration as a function of the angular momentum index $\ell$. The data highlights the splitting between TE$_{\ell}$ and TM$_{\ell}$ modes at each $\ell$. (b) The corresponding frequency difference $\Delta fS/c = (f_{\mathrm{TM}_{\ell}} - f_{\mathrm{TE}_{\ell}})S/c$, quantifying the frequency difference as a function of $\ell$.
• Figure 4: Constraints and projected sensitivities on the axion--photon--photon coupling $|\tilde{g}_{a\gamma\gamma}|$ versus the axion mass $m_a$. The rose-shaded wedge denotes the projected sensitivity of the DARK-ROSE concept. Shaded regions indicate published exclusions from RBF+UF, ADMX, ORGAN and CAST. While the transparent grayscale overlays show the HAYSTAC, TOORAD, MADMAX and IAXO projected reaches (datasets digitized from the IAXOmass repository). Dashed lines mark the KSVZ and DFSZ respective model bands. Both axes are logarithmic; the plotting range is $2\times10^{-7}\le m_a\le 5\times10^{-3}\,\mathrm{eV}/c^2$ and $10^{-18}\le|\tilde{g}_{a\gamma\gamma}|\le10^{-9}\,\mathrm{GeV}^{-1}$.