Searching for axions with quantum interferometry

This paper proposes a novel axion search framework using quantum interferometry to detect axion-photon interactions via induced Aharonov-Bohm and Berry phases in superconducting circuits and interferometers, offering projected sensitivities that could significantly improve upon current limits for specific axion mass ranges.

The Gist

Imagine the universe is filled with an invisible, ghostly fog called Dark Matter. For decades, scientists have been trying to catch a glimpse of this fog, suspecting it's made of tiny, wobbly particles called axions. These axions are so light and so shy that they barely interact with anything, making them incredibly hard to find.

This paper proposes a new way to catch these ghosts. Instead of trying to "catch" them like a fish in a net (which is how most current experiments work), the authors suggest we listen for the echoes they leave behind in the quantum world. They propose using two different "listening devices" based on the strange rules of quantum mechanics.

Here is a simple breakdown of their two main ideas:

1. The "Quantum Compass" (The rf-SQUID)

The Concept:
Imagine you have a tiny, super-conducting loop of wire (like a perfect hula hoop for electricity) with a tiny break in it, bridged by a "Josephson Junction." This setup is called an rf-SQUID. It's incredibly sensitive to magnetic fields.

The Analogy:
Think of the axion dark matter as a gentle, rhythmic wind blowing through the universe. Usually, this wind is invisible. But, according to the paper, when this "axion wind" blows past a strong magnetic field, it creates a tiny, invisible electric current.

How it works:

• The Setup: You place your super-conducting loop (the SQUID) in a strong magnetic field.
• The Interaction: As the axion "wind" blows, it generates a tiny, oscillating current in the loop.
• The Signal: This current changes the magnetic flux (the amount of magnetic "stuff") passing through the loop. In the quantum world, changing the magnetic flux changes the phase (the timing or "beat") of the electrons flowing in the loop.
• The Result: This shift in timing creates a tiny, measurable voltage spike. It's like the axion wind tapping a drum, and the SQUID is the drumhead that vibrates in response.

Why it's exciting:
The authors calculate that this method could be 10 to 100 times more sensitive than current experiments for finding very light axions. It's like upgrading from a paper cup telephone to a high-definition fiber-optic cable.

2. The "Quantum Dance Floor" (The Mach-Zehnder Interferometer)

The Concept:
This idea uses a laser beam split into two paths, like a race track with two lanes. One lane is the "control," and the other is the "test" lane where a magnetic field is slowly rotated.

The Analogy:
Imagine two dancers (photons) starting a race side-by-side.

• Dancer A runs on a flat, empty track.
• Dancer B runs on a track where the floor is slowly rotating (the magnetic field).
• If axions exist, they act like a subtle, invisible partner that Dancer B interacts with. This interaction doesn't change how fast Dancer B runs, but it changes their style or orientation (this is called a "Berry Phase").

How it works:

• When the two dancers meet back at the finish line, they try to dance in sync.
• Because Dancer B picked up a subtle "style shift" (the geometric phase) from the axions, they are slightly out of step with Dancer A.
• This mismatch creates a pattern of light and dark (interference fringes) that scientists can measure.

The Catch:
While this is a beautiful idea that proves the concept works, the authors admit that for this specific setup, the "style shift" caused by axions is currently too small to see with our best equipment. It's like trying to hear a whisper in a hurricane. However, it opens the door for future, more advanced quantum sensors.

3. The "Three-Act Play" (Axions + Quasiparticles)

The paper also looks at a more complex scenario involving Topological Insulators (special materials that conduct electricity on their surface but not inside).

• In these materials, axions can mix with "quasiparticles" (collective vibrations of electrons).
• The authors found that while you can measure a phase shift here, the signal is mostly dominated by the material itself, not the axions. It's like trying to hear a violin solo, but the orchestra is playing so loudly that you can barely hear the violin.
• The Value: Even though it's hard to see the axion here, proving that the math works in such a complex system validates the whole theory.

The Big Picture

The main takeaway of this paper is a shift in strategy:

• Old Way: Look for axions by seeing if they turn into photons (like a light bulb turning on).
• New Way: Look for axions by seeing how they change the quantum rhythm (phase) of light or electricity.

The Verdict:
The "Quantum Compass" (rf-SQUID) is the star of the show. It's a practical, near-future experiment that could revolutionize our search for dark matter. The "Quantum Dance Floor" is a brilliant proof-of-concept that might become powerful once our technology gets better at measuring tiny quantum shifts.

In short, the authors are saying: "Stop trying to catch the ghost; instead, listen for the creaking floorboards it leaves behind."

Technical Summary

1. Problem Statement

Axions and Axion-Like Particles (ALPs) are compelling candidates for dark matter (DM) and solutions to the Strong CP problem. However, their extremely weak coupling to photons ($g_{a\gamma\gamma}$) makes detection challenging.

• Current Limitations: Traditional detection methods (e.g., cavity haloscopes like ADMX) rely on resonant conversion of axions to photons in strong magnetic fields. These are effective for specific mass ranges but struggle with ultralight axions (where resonant enhancement is absent) or require complex tuning.
• The Gap: There is a need for complementary search strategies that do not rely solely on power/conversion measurements but instead exploit quantum phase observables (Aharonov-Bohm and Berry phases) to detect axion-photon interactions.

2. Methodology

The authors propose three distinct experimental setups utilizing quantum phase measurements to detect axion-induced effects:

A. Aharonov-Bohm (AB) Phase in rf-SQUIDs

• Concept: In a Radio Frequency Superconducting Quantum Interference Device (rf-SQUID), a Josephson junction (JJ) in a superconducting loop is sensitive to magnetic flux.
• Mechanism: A coherently oscillating axion DM background ($a(t)$) interacting with a static background magnetic field ($B_0$) generates an effective current density ($J_{eff} \propto g_{a\gamma\gamma} \dot{a} B_0$).
• Detection: This current induces a time-dependent magnetic flux ($\delta\Phi_a$) threading the SQUID loop. This flux alters the gauge-invariant phase difference across the Josephson junction, generating a measurable oscillating voltage signal ($V \propto d\Phi/dt$) at the axion frequency ($\omega_a \approx m_a$).

B. Berry Phase in Mach-Zehnder Interferometry (Two-Level System)

• Concept: A Mach-Zehnder Interferometer (MZI) splits a laser beam. One arm passes through a region with an adiabatically rotating transverse magnetic field, while the other serves as a reference.
• Mechanism: The rotation of the magnetic field direction induces a geometric (Berry) phase in the axion-photon mixing system. The mixing Hamiltonian acquires a complex phase factor, causing the eigenstates to trace a closed loop on the Bloch sphere.
• Detection: The accumulated Berry phase manifests as a shift in the interference fringe pattern. This phase is purely geometric (dependent on the path in parameter space, not time) and does not require the axion to constitute DM.

C. Berry Phase in Three-Level Systems (Photon-AQP-Axion)

• Concept: Extending the analysis to topological magnetic insulators hosting Axion Quasiparticles (AQPs).
• Mechanism: In materials like antiferromagnetic topological insulators (e.g., MnBi$_2$Te$_4$), AQPs hybridize with photons and axions. The system is modeled as a three-level coupled system (Photon-AQP-Axion).
• Detection: The authors analyze the Berry phase in the Terahertz (THz) regime, investigating whether the axion contribution can be distinguished from the dominant AQP effects.

3. Key Contributions & Results

rf-SQUID (AB Phase) Results

• Sensitivity: For benchmark parameters (inductance $M_{eff} = 50$ nH, $B_0 = 5$ T, integration time $T_{eff} = 6$ s), the projected sensitivity reaches:
  $$g_{a\gamma\gamma}^{min} \sim 7.8 \times 10^{-14} \, \text{GeV}^{-1}$$
  at an axion mass $m_a \sim 10^{-10}$ eV.
• Improvement: This represents an improvement of one to two orders of magnitude over existing limits in this specific parameter space.
• Scalability: The setup acts as a broadband sensor. Sensitivity degrades for masses where the axion coherence time is shorter than the integration time ($m_a \gtrsim 7 \times 10^{-10}$ eV) or due to low-frequency $1/f$ noise ($m_a \lesssim 4 \times 10^{-15}$ eV).

MZI (Berry Phase) Results

• Sensitivity: For conservative tabletop benchmarks (laser $\lambda=1064$ nm, $B=10$ T, $T=2.7$ h), the sensitivity is:
  $$g_{a\gamma\gamma}^{min} \sim 6.8 \times 10^{-4} \, \text{GeV}^{-1}$$
  at $m_a \sim 2$ meV.
• Comparison: This is currently weaker than existing astrophysical bounds ($g_{a\gamma\gamma} \lesssim 5 \times 10^{-11}$ GeV$^{-1}$).
• Potential: The authors note that using quantum-enhanced metrology (e.g., entangled $N$-photon states reaching the Heisenberg limit) could improve sensitivity to $\sim 3 \times 10^{-12}$ GeV$^{-1}$, potentially surpassing current bounds.
• Significance: This serves as a proof-of-principle for phase-based axion searches that do not rely on axions being DM.

Three-Level System (AQP) Results

• Finding: In the THz regime with topological materials, a measurable Berry phase of order $\sim 0.15\pi$ is predicted.
• Limitation: The observable phase is dominated by the AQP sector (material properties), while the genuine axion-induced correction is negligible ($\sim 10^{-34}\pi$) for the considered parameters.
• Conclusion: While not a competitive axion search channel itself, this validates the formalism in a complex coupled system and identifies a measurable "standard physics" signal in topological media.

Graviton-Photon System

• The authors briefly analyzed the Berry phase for graviton-photon mixing. They found the effect is suppressed by the Planck scale and violates adiabaticity conditions in realistic lab settings, rendering it unobservable compared to axion scenarios.

4. Significance and Outlook

• New Framework: The paper establishes quantum phase observables as a viable and complementary framework for axion searches, distinct from traditional power-based haloscopes.
• Immediate Impact: The rf-SQUID AB phase proposal is the most phenomenologically promising result, offering immediate potential to probe ultralight axion DM with significantly improved sensitivity.
• Long-term Potential: The Berry phase interferometry proposals highlight a path forward for quantum-enhanced axion searches. While current tabletop sensitivities are limited by technical noise, future advancements in phase stability, squeezed states, and cryogenic operation could make these geometric phase probes competitive.
• Validation: The analysis of the three-level AQP system demonstrates the robustness of the geometric phase formalism in rich, coupled quantum systems, providing a theoretical bridge between condensed matter physics and axion phenomenology.

In summary, the paper argues that while traditional methods search for axions via energy conversion, quantum interferometry offers a powerful alternative by detecting the subtle phase shifts imprinted by axion-photon interactions, with the rf-SQUID approach currently standing out as a highly competitive near-term experimental avenue.