Quantum dual-path interferometry scheme for axion dark matter searches

Cold dark matter is well supported, with the QCD axion a leading candidate motivated by the strong-CP problem and Peccei–Quinn symmetry breaking. Cosmological production suggests preferred axion mass windows in the μeV–neV range with very weak photon coupling. Haloscope resonant cavity experiments in a strong magnetic field convert axion dark matter into microwave photons, with enhancements from axion field coherence, magnetic field strength, and cavity quality factor. Modern cryogenics (≈20 mK) yields subunity thermal occupation at GHz frequencies, motivating a quantum description. The authors propose a dual-path Hanbury Brown–Twiss interferometry approach using a 50/50 beam splitter and linear amplifiers (or single-photon detectors) to measure cross-power and second-order correlations, aiming to overcome quantum fluctuation and added-noise limits that hinder single-path detection and long integration times.

Foundational axion theory addresses the strong-CP problem via PQ symmetry, predicting a light pseudo-Nambu–Goldstone boson that couples weakly to two photons. The haloscope concept (Sikivie) established resonant cavity searches. Classical calculations treat axion–photon conversion enhanced by cavity resonance and form factors, but their ability to capture single-quantum transition enhancements has been debated. Quantum optical techniques, notably HBT interferometry, have demonstrated noise reduction and correlation measurements in the microwave domain using linear detectors (e.g., HEMTs, JPAs, TWPAs). Prior dual-path microwave experiments achieved antibunching observation and effective noise reduction via cross-correlation, suggesting applicability to axion searches. Recent axion experiments have implemented near-quantum-limited amplifiers; however, insertion losses and amplifier degradation in magnetic fields remain issues. Cross-correlation processing has been explored for axion/WISP searches.

Quantum treatment of axion–photon conversion in a cavity with magnetic field B0: the axion–photon interaction is specified and the axion field is treated as a coherent, monochromatic, spatially homogeneous field over the cavity due to its long de Broglie wavelength and coherence time. The cavity electric field is quantized in modes. Using first-order time-dependent perturbation theory, the (0)→(1) photon transition probability and rate are derived, introducing a mode form factor Ck. In the long-time limit, the transition rate becomes R ∝ (Pa/(V m_a^2)) B0^2 ω_a Ck V Q with a quantum prefactor (showing an enhancement by cavity Q and a quantitative difference relative to the classical result by a factor π/2; overall larger than classical by 7π/2 as summarized). For typical haloscope parameters (V ~ 1 liter, Q ~ 10^6, B ~ 10 T), the single-photon conversion rate is O(1) s^-1 or up to ≤10 Hz depending on operating conditions. The axion behaves as a particle source emitting single photons, with multi-photon processes highly suppressed (higher-order or annihilation channels suppressed by coupling and operator dimension). The cavity thermal occupation at T ~ 20 mK for m_a ≥ 10^-6 eV is n < 1, so the cavity is usually in vacuum and functions as a single-photon emitter; re-conversion before readout is negligible within photon lifetime ~2Q/ω. Dual-path interferometry: the cavity output is split by a 50/50 microwave beam splitter (or implemented via a two-sided cavity with two symmetric ports), feeding two phase-preserving amplification chains. Complex envelopes S_i(t) are constructed from measured quadratures after amplification and downconversion, enabling calculation of instantaneous power and cross-power. The measurement model writes S_i(t) = G f(t) + G^-1 h_i(t) + v_i(t), where f(t) is the cavity field, h_i added amplifier noise, and v_i vacuum/weak thermal noise. Cross-correlation between channels isolates signal power while canceling uncorrelated amplifier noises. The second-order correlation function C^2(t, t+τ) is computed from four-point correlations of the split fields to test for nonclassical statistics (antibunching). Two hardware schemes are described: (a) single-sided cavity plus 50/50 splitter; (b) two-sided cavity producing two outputs directly, which mitigates insertion losses and can yield higher SNR. FPGA/GPU backends process time traces to compute cross-power and g^(2)(τ) in real time.

- Quantum single-photon transition rate: R = (π^2/2) (α0 Pa/(V m_a^2)) B0^2 ω_a Ck V Q, implying P_γ = ω_a R = m_a R and an explicit enhancement by cavity Q. The quantum result is larger than the classical by a numerical factor (stated as 7π/2 in the abstract; within the derivation a π/2 prefactor difference is noted). - Single-photon emitter behavior: For realistic haloscope parameters (V ~ 1 L, Q ~ 10^6, B ~ 10 T), the a→γ conversion rate is O(1) s^-1, and overall axion-converted emission behaves as a single-photon pulse train with rate R ≤ 10 Hz; multi-photon processes are negligible; probability of two conversions within a photon lifetime is R·(2πQ/ω) < 1. - Dual-path cross-power reduces effective noise: In realistic setups with insertion loss ~ -3 dB and JPAs, single-path effective noise temperature can be ~925 mK at 4.798 GHz versus SQL-limited ~240 mK. A dual-path scheme can approach ~120 mK effective noise (vacuum fluctuation limit) and demonstrated correlated noise ~80 mK with total ~180 mK at 7.2506 GHz using HEMTs, versus ~10 K noise per single chain. - SNR enhancement and scan speed: Cross-power cancels uncorrelated noise (N12 ≪ Ni), improving SNR compared to single-channel power. Even modest reductions in effective noise temperature near the quantum limit translate to large photon-number improvements; e.g., reducing from 925 mK to 120 mK corresponds to ~20× improvement in photon units. Consequently, integration time per frequency point is greatly reduced (SNR ∝ t^0.5), accelerating scans and improving sensitivity to g_aγγ. - Two-sided cavity scheme potentially yields up to an order-of-magnitude SNR improvement over single-path JPA-based amplification by avoiding insertion loss and minimizing channel sensitivity to losses. - Nonclassicality test via g^(2): The second-order correlation C^2(τ) exhibits antibunching (C^2(0) < C^2(τ)) for single-photon signals, enabling discrimination of axion-converted photons (C^2(0) ~ 0) from thermal backgrounds (C^2(0) ~ 1).

The quantum calculation confirms that cavity Q amplifies the single-quantum axion→photon transition, substantiating the interpretation of the haloscope as a single-photon source. Leveraging this, the dual-path HBT interferometry directly addresses the main experimental limitation: uncorrelated amplifier and insertion-loss-induced noise. Cross-power measurements cancel these uncorrelated contributions, lowering effective noise toward the quantum vacuum level and thereby boosting SNR and reducing required dwell time. The approach is robust to channel imbalance and can be implemented with existing microwave linear detector technology. The two-sided cavity variant further mitigates insertion losses. Moreover, g^(2) measurements provide a powerful orthogonal check on candidate signals, distinguishing nonclassical single-photon signatures expected from axion conversion from thermal noise, strengthening discovery claims and reducing false positives. Together these advances increase sensitivity to g_aγγ and can significantly speed up scans across wide frequency ranges, especially at higher frequencies where single-path chains are most noise-limited.

The authors develop a quantum-mechanical treatment of axion–photon conversion in a resonant cavity, showing Q-enhanced single-photon transition rates consistent with classical expectations but with a quantifiable prefactor difference. Recognizing the cavity as a single-photon emitter, they propose and analyze a quantum dual-path HBT interferometry readout that measures cross-power and second-order correlations. This scheme suppresses uncorrelated noise, reduces effective noise temperature toward the vacuum limit, and enhances SNR compared to single-path methods, enabling faster scans or improved sensitivity to the axion–photon coupling. They further show that g^(2)(τ) provides a nonclassicality test to validate axion-origin signals. Future work should integrate dual-path interferometry with quantum-limited preamplifiers (JPA/TWPA), squeezing, and emerging broadband high-efficiency microwave single-photon detectors, aiming to approach noise floors set by the cavity temperature and maximize search reach.

- Practical microwave single-photon detectors are not yet widely available; current detection relies on linear amplifiers with added noise. - Superconducting JPAs can degrade in strong magnetic fields; achieving >20 dB gain over ~1 GHz bandwidth near the SQL is challenging. - Insertion losses (~ -3 dB) between the cavity and amplifiers/circulators increase effective noise; although dual-path mitigates, residual correlated noise (e.g., leakage from 4 K HEMTs) can remain and must be measured and minimized. - Assumptions of balanced beam splitters and equal gains ease analysis; while not strictly required for noise cancellation, imperfections can reduce ideal performance gains. - The single-photon approximation assumes low thermal occupation (n < 1) and low conversion rates; at higher occupancies or rates, photon statistics and correlations may deviate from the idealized behavior. - Reported numerical gains depend on device- and frequency-specific parameters; generalization across the full axion mass range requires careful engineering.