Quantum interferometric probe of neutron--hidden neutron oscillations

This paper proposes using macroscopic quantum interferometry with very cold neutrons in a Mach–Zehnder setup to directly probe neutron–hidden neutron oscillations, demonstrating that existing facilities can access previously unexplored parameter space relevant to baryonic dark matter by detecting phase-dependent intensity modulations.

The Gist

The Big Picture: Hunting for a "Ghost" Neighbor

Imagine the universe is a crowded party. We can see and touch most of the guests (the "visible" matter), but we know there are invisible guests (dark matter) because we can feel their presence through gravity. One theory suggests that among these invisible guests is a "ghost neutron"—a particle that looks exactly like a regular neutron but belongs to a hidden, dark sector.

The big question is: Can a regular neutron turn into this ghost neutron? If it can, it would vanish from our world and reappear in the hidden one. This paper proposes a new, highly sensitive way to catch this transformation happening.

The Problem with Previous Searches

So far, scientists have tried to find these ghost neutrons by building "neutron prisons" (using ultracold neutrons) and watching to see if neutrons simply disappear.

• The Analogy: Imagine trying to prove a magician is turning water into wine by watching a bucket of water. If the water level drops, you might guess it turned into wine. But what if the bucket has a tiny leak? Or what if the water evaporated? It's hard to tell if the water actually transformed or just leaked away.
• The Limitation: Current methods rely on counting how many neutrons are missing. They can't distinguish between a neutron turning into a ghost and a neutron just getting lost or absorbed by the walls.

The New Solution: The Neutron Interferometer

The authors propose using a Mach-Zehnder Interferometer. Think of this not as a prison, but as a splitting race track.

1. The Split: A beam of very cold neutrons is split into two paths (Path I and Path II), like a runner splitting into two lanes.
2. The Journey:
   • Path I: The neutrons travel through a quiet zone with no special magnetic tricks.
   • Path II: The neutrons travel through a "magnetic playground." Here, scientists can tune a magnetic field to act like a radio tuner.
3. The Resonance (The Tuning): The paper suggests that if you tune the magnetic field to a very specific frequency, it creates a "bridge" that makes it much easier for a regular neutron to jump into the ghost state. This is called resonance.
4. The Reunion: The two paths merge back together at the end.

How It Detects the Ghost

This is where the magic happens. In quantum physics, particles act like waves. When the two paths merge, the waves usually interfere with each other, creating a pattern of bright and dark spots (like ripples in a pond meeting).

• The "Ghost" Effect: If a neutron turns into a ghost neutron while traveling through the magnetic playground (Path II), it effectively "leaves the race." It doesn't come back to the finish line to merge with the other path.
• The Signal: Because some neutrons vanished into the hidden world, the final "wave pattern" changes in two specific ways:
  1. The Pattern Shifts: The interference pattern gets messed up because the waves from Path II are weaker.
  2. The Volume Drops: The total number of neutrons hitting the detector drops significantly only when the magnetic field is tuned to the right "ghost frequency."

The Analogy: Imagine two identical speakers playing the same song. If you turn off one speaker (because the sound turned into a ghost), the music doesn't just get quieter; the specific harmonics change, and you hear a distinct "hole" in the sound. The paper argues that by listening for this specific "hole" in the neutron signal, they can prove the ghost exists, rather than just guessing because neutrons went missing.

The Results and Sensitivity

The authors ran the numbers on this setup using existing technology (specifically, very cold neutrons at facilities like the ILL in France).

• The Sensitivity: They claim this setup is incredibly sensitive. It can detect mixing amplitudes as small as $10^{-14}$ eV.
• The Comparison: This is like being able to hear a whisper in a hurricane. It allows them to probe a region of "dark matter" parameters that previous experiments couldn't reach, specifically for very small differences in mass between the real neutron and the ghost neutron.
• The "Lock-in" Trick: To make sure they aren't fooled by the equipment breaking or the neutrons just hitting the walls, they plan to rapidly switch the magnetic field on and off.
  • On Resonance: If ghosts exist, neutrons vanish.
  • Off Resonance: Neutrons stay put.
  • By comparing the two, they can subtract out all the "noise" (like leaks or absorption) and isolate the "ghost" signal.

Conclusion

In short, this paper proposes a new, high-precision "quantum microscope." Instead of just counting missing neutrons, it uses the wave nature of neutrons and magnetic tuning to create a specific, undeniable signature of a neutron turning into a hidden dark matter particle. If successful, this would open a new window into the "hidden sector" of the universe using a tabletop experiment.

Technical Summary

Technical Summary: Quantum Interferometric Probe of Neutron–Hidden Neutron Oscillations

Problem Statement
The nature of dark matter remains a central unresolved issue in particle physics and cosmology. Hidden-sector extensions of the Standard Model (SM) predict the existence of a neutral partner to the neutron ($n'$), often referred to as a "hidden neutron." Weak mixing between ordinary neutrons ($n$) and these hidden states induces oscillations between visible and dark baryonic sectors. While experimental searches have historically relied on ultracold-neutron (UCN) storage and beam disappearance measurements, a substantial region of the parameter space remains inaccessible. Specifically, existing techniques struggle to probe small mass splittings ($\delta m \lesssim$ neV) and weak mixing amplitudes ($\epsilon_{nn'} \lesssim 10^{-14}$ eV). These limitations arise from intrinsic constraints such as finite neutron lifetimes, material losses, and the absence of phase-sensitive observables capable of distinguishing genuine conversion processes from systematic effects.

Methodology
The authors propose a macroscopic quantum interferometric approach using a Mach–Zehnder interferometer operating with very cold neutrons (VCNs). The setup is designed to convert neutron–hidden neutron oscillations into measurable phase-dependent intensity modulations.

• Theoretical Framework: The mixing is modeled analogously to two-flavor neutrino oscillations. The system is described by an effective mass Hamiltonian where the mixing angle and energy eigenvalues depend on the mass splitting ($\delta m$), the mixing amplitude ($\epsilon_{nn'}$), and external potentials (magnetic fields $B$ and material potentials $V$). A key feature is the resonance condition $\delta m \simeq \Delta E = \mu_n B + V$, where mixing is maximized.
• Experimental Configuration: The proposed device utilizes a VCN beam with a wavelength centered at $\lambda = 40$ Å (velocity $v \approx 100$ m/s) to maximize the time of flight. The interferometer employs half-transparent Ni-mirrors for beam splitting and recombination, and high-reflectivity Ni-mirrors for path reflection.
  • Path I: The beam travels through guide fields and an active magnetic region where the field $B_I$ is kept at zero in the baseline configuration.
  • Path II: The beam passes through a tunable active magnetic field $B_{II}$ and a silicon phase shifter ($D = 200$ µm).
  • Detection: Beams recombine at a second mirror and are detected at two output ports (O and H).
• Signal Extraction: The experiment employs a "magnetic lock-in" technique. By periodically switching the active magnetic field between an on-resonance configuration ($B_{ON}$) and a detuned off-resonance setting ($B_{OFF}$), the setup extracts a differential signal. This method suppresses static optical losses and systematic effects (which are insensitive to the magnetic field), isolating the modulation caused by $n \to n'$ conversion.

Key Contributions

1. Novel Observable: The paper identifies a distinct signature of hidden-sector mixing: a correlated modulation of the interference pattern accompanied by a resonant suppression of the total detected intensity. Unlike conventional disappearance experiments that measure only neutron loss, this interferometric approach provides a differential measurement based on controlled phase manipulation.
2. Resonant Enhancement: The setup exploits the resonance condition to scan the hidden-sector parameter space with high mass selectivity. By tuning the magnetic field, the experiment can target specific mass splittings.
3. Optimization for VCNs: The design is specifically optimized for Very Cold Neutrons to maximize the interaction time in the active magnetic region ($L \approx 600$ mm), thereby enhancing the transition probability ($P_{n \to n'} \propto t^2$).

Results
Numerical analysis based on the proposed geometry and parameters (including a monochromatic beam and Gaussian wave packets with 10–20% bandwidth) yields the following findings:

• Sensitivity: Existing cold-neutron facilities (e.g., ILL PF2) are estimated to achieve sensitivity to mixing amplitudes as small as $\epsilon_{nn'} \sim 10^{-14}$ eV for mass splittings $\delta m \sim 10^{-9}$ eV. This corresponds to oscillation times $\tau_{nn'} \sim 0.1$ s.
• Signal Characteristics: At resonance (e.g., $B \approx 16.58$ mT for $\delta m = 1$ neV), the total intensity ($I_{tot} = I_H + I_O$) shows a clear suppression compared to the no-mixing case. The interference fringes in the transmitted intensity ($I_H$) also exhibit a distinct deviation from the standard pattern.
• Robustness: The signal drop is preserved even with broadband VCN beams, despite the reduction in interference contrast due to the short longitudinal coherence length of the packet.
• Statistical Feasibility: With an estimated count rate of $\sim 20$ s$^{-1}$, the apparatus can accumulate $\sim 1.7 \times 10^6$ events per day. For mixing parameters leading to percent-level conversion probabilities, the expected deficit ($\sim 10^4$ events/day) is well above Poisson statistical fluctuations.

Significance
The paper establishes neutron interferometry as a new precision frontier for laboratory searches of hidden baryonic sectors. The proposed method offers a complementary and, in the regime of small mass splittings, superior reach compared to current UCN storage and beam-based experiments. By harnessing quantum coherence, the approach provides a scalable, table-top pathway to test dark-sector physics, potentially accessing regions of parameter space relevant to baryonic dark matter scenarios that are currently experimentally inaccessible. Future implementations at next-generation pulsed facilities, such as the European Spallation Source (ESS), are projected to further extend this reach to oscillation times of $\tau_{nn'} \sim 1$ s.