Axion-Photon Oscillations

Updated 20 December 2025

Axion-photon oscillations are a quantum phenomenon where photons and axions interconvert via magnetic field-induced mixing governed by a coupling constant.
The process produces resonant conversion effects that impact laboratory measurements, astrophysical spectra, and cosmic microwave background polarization.
Experimental strategies like light-shining-through-walls and polarimetric surveys exploit spectral modulations to constrain axion-like particle properties.

Axion-photon oscillations are a quantum phenomenon resulting from the coupling between photons and (pseudo-)scalar axion or axion-like particle (ALP) fields, typically in the presence of an external magnetic field or time-dependent axion background. This mixing leads to interconversion between photon and axion states, with rich implications for laboratory searches, astrophysical propagation, cosmic microwave background polarization, and more. The phenomenon is governed by the axion-photon interaction Lagrangian, $\mathcal{L}_{a\gamma} = -\frac{1}{4}g_{a\gamma}\,a\,F_{\mu\nu}\tilde F^{\mu\nu} = g_{a\gamma} a\,\mathbf{E}\cdot\mathbf{B}$ , where $g_{a\gamma}$ is a model-dependent coupling constant, $a$ the axion field, $F_{\mu\nu}$ the electromagnetic field tensor, and $\tilde F^{\mu\nu}$ its dual. In various physical and cosmological settings, axion-photon oscillations manifest as energy- and polarization-dependent spectral features, altered cosmic-ray propagation, cosmic birefringence, and highly model-dependent bounds on axion or ALP properties.

1. Theoretical Framework and Formalism

The axion-photon coupling modifies Maxwell's equations and introduces off-diagonal terms in the photon-axion Hamiltonian, resulting in oscillation between photon and axion states. For a beam of energy $E$ propagating along the $z$ -direction through a transverse magnetic field $B_\perp$ , the evolution is governed by the Schrödinger-like equation

$i\,\frac{d}{dz} \begin{pmatrix}A_\|(z)\ a(z)\end{pmatrix} = \left(\begin{pmatrix} \Delta_\gamma & \Delta_{a\gamma} \ \Delta_{a\gamma} & \Delta_a \end{pmatrix}\right) \begin{pmatrix}A_\|(z)\ a(z)\end{pmatrix},$

where $\Delta_{a\gamma} = \frac{1}{2}g_{a\gamma} B_\perp$ , $\Delta_a = -m_a^2/(2E)$ (with $m_a$ the axion mass), and $\Delta_\gamma$ includes plasma, vacuum birefringence, and other dispersive effects. Diagonalization yields a mixing angle

$\tan(2\theta) = \frac{2\Delta_{a\gamma}}{\Delta_\gamma - \Delta_a},$

with resonance ( $\theta = \pi/4$ ) occurring when the photon and axion effective masses cross. The probability of conversion over distance $L$ is

$P_{\gamma\to a}(E;L) = \sin^2(2\theta)\,\sin^2\left(\frac{\Delta_{\mathrm{osc}} L}{2}\right),$

with $\Delta_{\mathrm{osc}} = \sqrt{(\Delta_\gamma - \Delta_a)^2 + 4\Delta_{a\gamma}^2}$ (Wang et al., 2015, Meyer et al., 2021, Galanti, 2022).

2. Propagation Scenarios: Homogeneous, Multidomain, and Stochastic Fields

Axion-photon oscillations are highly sensitive to environmental conditions. In laboratory or compact astrophysical settings (e.g., light-shining-through-walls experiments, magnetospheres of white dwarfs), fields can be treated as homogeneous, and the above two-level formula applies directly.

In astrophysical or cosmological contexts, especially for photon propagation over extragalactic distances, the magnetic field is typically structured in coherent domains of length $\ell$ with random orientation (the "discrete- $\varphi$ " domain model). In this setting, after $N$ domains the average photon-to-axion conversion probability is (Wang et al., 2015)

$\langle P_{\gamma\to a}\rangle = \frac{1}{3}[1 - \exp(-3N P_{\mathrm{ad}}/2)],$

where $P_{\mathrm{ad}}$ is the single-domain probability.

In more realistic continuous or turbulent field models, the direction and magnitude of $B_\perp$ varies smoothly, leading to conversion probabilities that depend sensitively on the spectral statistics of the field. In the "continuous- $\varphi$ " regime, energy- and mass-dependent resonant peaks and enhanced conversion (up to $\mathcal{O}(1)$ ) can occur, drastically modifying transfer functions compared to the discrete model (Wang et al., 2015, Kachelriess et al., 2021, Li, 2022). Monte Carlo techniques or transfer-matrix methods are required for accurate predictions in these scenarios.

3. Experimental and Observational Signatures

Axion-photon oscillations have broad experimental implications across low-energy laboratory searches, high-energy astrophysics, and cosmology.

Laboratory and Resonant Enhancement

Experiments such as ALPS II (light-shining-through-walls) and dielectric haloscopes rely on coherent photon-axion-photon oscillations in strong static magnetic fields. Oscillation probabilities are severely suppressed for $m_a^2/(2E)\gg g_{a\gamma} B$ , but spatially or temporally modulated magnetic fields can cancel this momentum mismatch, enabling "axion magnetic resonance" (AMR). At resonance, the conversion probability grows quadratically with system length, providing order-of-magnitude gains in sensitivity (Seong et al., 2023, Almpanis, 5 Jun 2025). High-finesse dielectric resonators can exploit sharp angular momentum and parity selection rules, achieving enhancements by $Q/V$ factors more than ten orders of magnitude compared to free space (Almpanis, 5 Jun 2025).

Astrophysical Photon Transparency

In the presence of intergalactic magnetic fields ( $B\sim$ nG, domain size $\sim$ Mpc), photon-ALP oscillations can harden gamma-ray spectra from distant blazars by enhancing the effective transparency beyond the exponential attenuation due to pair production on the extragalactic background light. The resulting survival probabilities can exhibit "spectral wiggles," energy-dependent oscillatory modulations, and non-exponential tails at energies up to $\sim 1000$ TeV (Wang et al., 2015, Galanti et al., 2018, Kachelriess et al., 2021). These features are robust to details of the field model and can be diagnosed via the discrete power spectrum of photon events (Kachelriess et al., 2021).

Cosmic Microwave Background Polarization

A coherently oscillating axion dark-matter field at mass scale $10^{-23}$ – $10^{-18}$ eV induces a global, temporally sinusoidal rotation of the CMB polarization, observable as "AC cosmic birefringence" (Collaboration et al., 2020, Collaboration et al., 2021). The rotation angle is

$\alpha(t) = \frac{1}{2}g_{\phi\gamma}\phi_0\sin(mt+\delta),$

where $\phi_0=\sqrt{2\rho_{\text{DM}}}/m$ for local dark-matter density. CMB polarimeters place world-leading bounds on $g_{\phi\gamma}$ in the ultralight regime, ruling out large classes of axion dark-matter models using time-domain analyses of the Stokes $Q$ , $U$ parameters.

4. Polarization Effects and Diagnostic Theorems

Axion-photon oscillations induce not only intensity modulations but also characteristic alterations in photon polarization, even if the source is unpolarized. The evolution of Stokes parameters $(I, Q, U, V)$ is governed by the underlying beam density matrix, with the degree of linear polarization $\Pi_L$ given by

$\Pi_L = \frac{\sqrt{Q^2+U^2}}{I}.$

Generic predictions include the appearance of nonzero $\Pi_L$ in X-ray and $\gamma$ -ray bands and almost complete polarization ( $\Pi_L\rightarrow 1$ ) in the very-high-energy regime after propagation through the Galaxy (Galanti, 2022). The amplitude of conversion and the maximal polarization that can be induced are bounded by tight theorems relating polarization to axion-photon conversion probabilities; specifically, for an initially unpolarized beam, $P_{\gamma\to a} \leq 1/2$ at any energy or propagation distance (Galanti, 2022).

Astrophysical polarimetry (e.g., of SGRs, blazars, or white dwarfs (Gill et al., 2011)) thus becomes a probe of $g_{a\gamma}$ , with non-observation of polarization enhancements placing model-independent bounds.

5. Resonances and Nonlinear Effects in Astrophysical Environments

Resonant conversion maximally enhances axion-photon interconversion when the effective photon mass (e.g., plasma frequency) matches $m_a$ . In cold plasmas, as in the Earth's mantle or magnetospheres of neutron stars, $m_\gamma^2 = \omega_p^2 = 4\pi \alpha n_e/m_e$ tunes the resonance, enabling scenarios such as "axion tomography" of the Earth (Nicolaidis, 2020), explanations of anomalous events (e.g., ANITA), and electromagnetic bursts from axion-star collisions with neutron stars or magnetars (Amin et al., 2021).

At large values of the dimensionless coupling parameter $\kappa = g_{a\gamma}a_0\omega R$ (with $a_0$ axion field amplitude, $R$ radius), nonlinear and parametric-resonance effects can dominate, leading to exponential growth of photon occupancy and possible "explosive" conversions in dense axion clumps. Plasma-induced resonances can further enhance output for astrophysical sources—and, conversely, destroy or deplete axion condensates in the early universe (Amin et al., 2021).

6. Extensions: Hidden Sectors and Multiparticle Oscillations

In models where the dark sector includes both axion-like particles and hidden photons, the mixing matrix generalizes to three (or more) states with multiple oscillation frequencies and mixing angles. The phenomenology includes additional resonant regimes, distinctive "gaps" in sensitivity depending on the baseline and field conditions, and strategies involving the tuning of external parameters (magnetic field, length, refractive index) for optimal detection (Alvarez et al., 2017). In cosmological settings, axion-photon-dark photon oscillations in the presence of a dark photon field can produce strong frequency-selective conversion, with notable implications for the cosmic 21 cm signal without affecting the global CMB spectrum (Choi et al., 2019).

Table: Oscillation Regimes and Observational Contexts

Physical Setting	Key Regime	Experimental Observable
Laboratory (LSTW, haloscope)	Homogeneous, static $B$	Regeneration, power excess
CMB polarization	Ultralight axion DM, $\phi(t)$	AC cosmic birefringence, rotation
Blazar $\gamma$ -rays	Extragalactic, turbulent $B$	Spectral "wiggles", hardening
Polarization surveys	Jet/host/IGM/MW propagation	Degree of linear polarization
Earth/NS magnetospheres	Resonant, plasma-matching	Upward air-shower (ANITA), radio

7. Current Bounds and Future Prospects

Direct-detection experiments constrain $g_{a\gamma}$ in the laboratory regime, typically $g_{a\gamma}\lesssim 10^{-10}~\mathrm{GeV}^{-1}$ for $m_a\sim10^{-5}$ – $10^{-3}~\mathrm{eV}$ (e.g., CAST, ALPS-II). Astrophysical observations, including CMB polarization rotation ( $g_{a\gamma}\lesssim 4.5 \times 10^{-12}~\mathrm{GeV}^{-1}~(m/10^{-21}~\mathrm{eV})$ (Collaboration et al., 2021)) and continuum polarization limits from magnetic white dwarfs (Gill et al., 2011), probe complementary regions in the parameter space.

Future high-sensitivity CMB polarimeters, laboratory resonator arrays with AMR, gamma-ray telescopes with wide energy coverage, and X-ray/MeV polarimetry missions (IXPE, eXTP, COSI, AMEGO) are expected to improve reach by factors of several to orders of magnitude, exploring unconstrained ALP parameter space and potentially revealing signals in forthcoming datasets (Collaboration et al., 2020, Collaboration et al., 2021, Almpanis, 5 Jun 2025).