Axion-Photon Conversion

• Axion-photon conversion is the process where axion-like particles transform into photons under external magnetic fields, serving as a key mechanism in dark matter detection.
• This phenomenon exhibits resonant conversion when plasma frequency matches the axion mass, and nonresonant conversion otherwise, with probabilities governed by magnetic field strength and plasma conditions.
• Experimental and observational approaches, including laboratory setups and astrophysical searches in solar and neutron star environments, address challenges posed by low conversion rates and detection sensitivity.

Axion-photon conversion refers to the interconversion of axion-like particles and photons in the presence of a background electromagnetic field, typically a magnetic field. This phenomenon arises because of the pseudo-scalar axion coupling to the electromagnetic field, which enables an axion to oscillate into a photon (and vice versa) under suitable conditions. The conversion process is foundational to experimental searches for axions and axion-like particles and is invoked in multiple astrophysical and laboratory contexts. Axion-photon conversion underlies methods for dark matter detection, the interpretation of high-energy astrophysical observations, and the modeling of radiative processes in strong-field environments.

1. Fundamental Theory and Mixing Mechanism

The theoretical underpinning of axion-photon conversion is encapsulated by the interaction Lagrangian

$$L_{a\gamma\gamma} = -\frac{g_{a\gamma\gamma}}{4}\, a\, F^{\mu\nu}\tilde F_{\mu\nu} = g_{a\gamma\gamma}\, a\, \mathbf{E} \cdot \mathbf{B},$$

where $a$ is the axion field, $g_{a\gamma\gamma}$ the axion-photon coupling constant, $\mathbf{E}$ the electric field, and $\mathbf{B}$ the magnetic field (Laming, 2013). This term is only nonzero when the photon's electric field component is aligned with an external magnetic field, hence only the photon polarization parallel to $\mathbf{B}$ ("ordinary mode") mixes with the axion.

The dynamics of the photon-axion system in a plasma are described by coupled equations (derivable from an effective Lagrangian) with a mixing mass matrix: $$M = \begin{pmatrix} \frac{m^2-\omega_p^2}{2\omega} & g_{a\gamma\gamma}\, B \ g_{a\gamma\gamma}\, B & -\frac{m^2-\omega_p^2}{2\omega} \end{pmatrix},$$ where $m$ is the axion mass and $\omega_p$ the plasma frequency. Diagonalizing this matrix yields mixed eigenstates and a mixing angle

$$\tan 2\theta = \frac{2\,g_{a\gamma\gamma}\, B\,\omega}{\omega_p^2 - m^2}.$$

The time evolution of states and the resulting conversion probability follow standard two-level system dynamics, with ℙ(a → γ) exhibiting oscillatory behavior and being enhanced when $\omega_p^2 \approx m^2$, i.e., at resonance.

2. Resonant and Nonresonant Conversion Regimes

The conversion probability depends strongly on the relation between the axion mass and the photon plasma frequency $\omega_p$:

• Resonant Conversion: For axion masses $m > 10^{-4}$ eV (for solar parameters), efficient conversion occurs at layers where $\omega_p \simeq m$, leading to maximal mixing. The transition probability across the resonance is

$$P_{\text{conv}} \approx \pi \frac{g_{a\gamma\gamma}^2 B^2 k h}{\omega_p^2},$$

with $k$ as the photon wavenumber and $h$ as the density scale height (Laming, 2013). This is a Landau-Zener-type result. Resonance must occur at sufficiently optically thin layers to escape subsequent Compton broadening.

• Nonresonant Conversion: For $m < 10^{-4}$ eV, or if resonance is not reached within the medium, conversion is nonresonant, adhering to

$$P(a\to\gamma) \simeq \frac{s^2}{4}\,g_{a\gamma\gamma}^2 B^2,$$

with $s$ as the path length in the magnetic field (Laming, 2013). Nonresonant conversion is intrinsically small due to suppressed mixing.

Both regimes are controlled by the electron density, magnetic field strength, axion mass/coupling, and local plasma conditions. In astrophysical plasmas, the resonance condition defines a specific conversion surface, critically affecting the detectability of axion-induced photons.

3. Experimental and Observational Manifestations

Laboratory Experiments

In "light-shining-through-a-wall" and haloscope experiments, conversion is driven by a strong magnetic field in a controlled environment. The conversion probability is quadratic in both path length and field strength. Dielectric haloscopes employ stacked dielectric layers to engineer “Garibian wave functions” that overcome momentum mismatch between nearly at-rest axion dark matter and the outgoing photon by breaking translational invariance, leading to nontrivial transition rates measurable via microwave photon detection (Ioannisian et al., 2017).

Astrophysical Contexts

• Solar Axion Searches: The M1 decay of $^{57}$Fe at 14.4 keV in the solar core can emit axions that are converted into X-rays in the solar envelope (Laming, 2013). Detectability is severely limited by the conversion region's depth (too deep incurs Compton broadening prior to escape) and small conversion probability (typical values $\sim 10^{-33}$ per photon for nonresonant scenarios).
• Neutron Star Magnetospheres: Resonant conversion of dark matter axions to radio photons is predicted where the local plasma frequency matches the axion mass. The conversion probability is enhanced, but the practical interpretation of the observable signal is affected by plasma inhomogeneity, refraction, dephasing, and geometric factors (Witte et al., 2021, McDonald et al., 2023).
• Cosmological/Intergalactic Applications: In the early universe or intergalactic medium, ALPs can resonantly convert to photons, modifying the Cosmic Microwave Background (CMB) radio tail and the global 21-cm absorption trough ("EDGES anomaly") (Moroi et al., 2018, Addazi et al., 13 Nov 2024, Setabuddin et al., 11 Sep 2025).

Energetic Photon Propagation

In the context of ultra-high-energy cosmic photons (e.g., TeV–PeV photons from GRBs or AGNs), axion-photon conversion permits photons to “hide” as axions, crossing cosmological distances unattenuated, and reconvert in the galactic magnetic field to be observable, explaining apparent transparency of the universe to such photons (Zhang et al., 2022, Wang et al., 2023).

4. Limitations and Model Dependence

Conversion rates are typically extremely low for parameters relevant to standard axion dark matter models:

• Mass-Coupling Relations: In many models (DFSZ, KSVZ), higher axion mass implies higher coupling, but for large masses, resonant conversion occurs at optically thick regions, suppressing escape of observable photons. For masses below the resonance threshold, conversion is negligible.
• Astrophysical Uncertainties: Calculations rely on precise modeling of magnetic field strengths, plasma gradients, and geometric configuration (e.g., orientation of magnetic fields, plasma density gradients), leading to uncertainties of several orders of magnitude in expected flux or signal strength (Laming, 2013, McDonald et al., 2023).
• Instrumental Sensitivity: Even for resonant conversion, the predicted photon count rates are well below the detection thresholds of current X-ray and radio instruments for Solar and astrophysical axion searches in standard parameter ranges.

In special cases where coupling constants are decoupled from axion mass (as for “arion” models), non-standard parameter regions may be probed, allowing potentially larger signals in solar or astrophysical contexts.

5. Quantum, Plasma, and Geometric Effects

• Quantum Enhancements: Recent work explores the photon-axion conversion in nonclassical quantum states (e.g., squeezed or photon-added coherent states), demonstrating conversion probability enhancements scaling as |β|^2(N+1) e^2(N+1r) for such engineered photon states. This suggests substantial sensitivity improvements for laboratory experiments employing quantum sensing techniques (Ikeda et al., 17 Jun 2025).
• Plasma Effects: Plasma-induced effective photon mass is central to the resonant condition. Plasma inhomogeneity, turbulence, and anisotropy affect both the resonance profile and the escape probability of converted photons, particularly in neutron star and solar contexts (Witte et al., 2021, Millar et al., 2021, McDonald et al., 2023).
• Geometric Considerations: In strongly curved spacetime (e.g., near neutron stars or black holes), general relativistic corrections to the magnetosphere model and coordinate system are essential for correct flux and conversion predictions (Satherley et al., 3 Sep 2024). Anisotropic or multipole magnetic field structures further affect the conversion efficiency and angular distribution of converted photons (Sakurai et al., 2023).

6. Contemporary Applications and Constraints

Axion-photon conversion features prominently in the interpretation of anomalies in radio, X-ray, and gamma-ray astronomy:

• ARCADE2/EDGES anomalies: Resonant conversion of axion-like dark radiation into photons can account for both excess radio background and enhanced 21-cm absorption trough, providing astrophysical constraints on ALP masses (~10⁻¹⁴–10⁻¹² eV), couplings, and primordial magnetic fields (Addazi et al., 13 Nov 2024, Setabuddin et al., 11 Sep 2025).
• Gamma-Ray Transparency: Detection of multi-TeV/PeV photons from distant extragalactic sources constrains or supports axion-photon scenarios, with implications for ultralight ALP search windows (Zhang et al., 2022, Wang et al., 2023).
• Indirect DM Searches: Resonant axion-photon conversion in neutron star magnetospheres is a primary target for next-generation radio telescopes (e.g., SKA), requiring detailed theoretical modeling accounting for magnetospheric plasma, general relativity, and axion phase-space (Witte et al., 2021, McDonald et al., 2023, Satherley et al., 3 Sep 2024).

Continuous development in quantum sensing, detector technology, and numerical modeling is required to further test the full span of parameter space allowed by astrophysical and laboratory constraints.

7. Summary Table: Key Regimes for Axion-Photon Conversion

Regime	Conversion Enhancement	Limitation or Bottleneck
Resonant (ω_p ≈ m_a)	Maximal (Landau-Zener)	Location of resonance must be optically thin
Nonresonant	Suppressed	Weak coupling, small path integral
Dielectric interface	Momentum mismatch bridged	Engineering of dielectric stack geometry
Quantum (squeezed states)	Exponential/proportional enhancement	Demanding state preparation in lab
Strong curvature (GR)	Surface shape, inclination, & plasma affected	Requires full GR treatment of magnetosphere

• Solar and laboratory theory: (Laming, 2013, Ioannisian et al., 2017)
• Astrophysical and cosmological applications: (Moroi et al., 2018, Addazi et al., 13 Nov 2024, Setabuddin et al., 11 Sep 2025)
• Neutron stars and GR corrections: (Witte et al., 2021, McDonald et al., 2023, Satherley et al., 3 Sep 2024)
• Quantum effects: (Ikeda et al., 17 Jun 2025)
• Observational anomalies: (Zhang et al., 2022, Wang et al., 2023, Sakurai et al., 2023)
• Fundamental quantum kinetics: (McDonald et al., 2023)

The theory and phenomenology of axion-photon conversion remain an essential crossroad between particle physics, quantum optics, plasma physics, and observational astrophysics, serving as a cornerstone in the ongoing search for physics beyond the Standard Model.