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Towards the Direct Detection of Composite Ultraheavy Dark Matter in Quantum Sensor Arrays

This paper investigates the sensitivity of quantum sensor arrays to composite ultraheavy dark matter interacting via gravity and a Yukawa force, demonstrating through Monte Carlo analysis that future accelerometer arrays can distinguish between different density profiles and characterize the mass and size of such extended dark matter objects.

Original authors: Dorian W. P. Amaral, Erqian Cai, Andrew J. Long, Juehang Qin, Christopher D. Tunnell

Published 2026-07-07

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CC BY 4.0

Original authors: Dorian W. P. Amaral, Erqian Cai, Andrew J. Long, Juehang Qin, Christopher D. Tunnell

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe is filled with invisible "ghosts" called Dark Matter. For decades, scientists have assumed these ghosts are tiny, point-like specks, like individual grains of sand. But what if, instead of tiny specks, the heaviest of these ghosts are actually giant, fluffy clouds?

This paper asks a simple question: If Dark Matter is a giant, fuzzy cloud rather than a tiny dot, how would we catch it?

Here is the story of their investigation, broken down into everyday concepts.

1. The Problem: The "Too Heavy" Paradox

Scientists know Dark Matter exists because it has gravity, but they can't see it. They are looking for "Ultraheavy Dark Matter" (UHDM)—particles so massive they weigh as much as a tiny grain of sand (about 22 micrograms).

Here is the catch: In physics, if something is that heavy but still a single, fundamental particle, it should collapse into a black hole. Since we don't see black holes floating around our labs, these heavy particles must be composite. They must be made of smaller parts stuck together, forming a "clump" with a real size and shape, like a fluffy marshmallow rather than a hard marble.

2. The Detector: A 3D Grid of "Quantum Microphones"

To find these heavy clumps, the authors propose using a Quantum Sensor Array.

The Setup: Imagine a giant cube (about 2 meters wide) filled with hundreds of tiny, ultra-sensitive sensors (like 8,000 tiny bells).
The Job: These sensors are so sensitive they can feel the tiniest tug of gravity or a mysterious new force.
The Event: When a Dark Matter clump flies through this cube, it doesn't just hit one sensor. It passes through, giving a little "push" (an impulse) to many sensors along the way, making them ring like bells.

3. The Mystery Force: The "Yukawa" Handshake

Gravity alone is too weak to be detected by these sensors for a single pass. So, the scientists assume these Dark Matter clumps also have a "secret handshake" with normal matter—a new, short-range force called a Yukawa force.

Think of this force like a magnet. If the magnet is close, it pulls hard. If it's far away, the pull disappears quickly.
The paper studies how this force behaves depending on how "fuzzy" the Dark Matter cloud is.

4. The Big Discovery: Size Matters

The paper compares two scenarios:

Scenario A (The Dot): The Dark Matter is a tiny, hard marble.
Scenario B (The Cloud): The Dark Matter is a large, fluffy cloud (a few centimeters wide).

The Surprising Result:
If the Dark Matter is a tiny dot, the sensors only feel a strong push if the "secret handshake" (the Yukawa force) reaches very far. If the force is short-range, the dot slips right through without being felt.

However, if the Dark Matter is a big, fluffy cloud:

The "Power Law" Effect: When the cloud is large, the sensors feel a different kind of push. Instead of the signal vanishing exponentially (like a light fading in the dark), it fades much more slowly (like a power law).
The Sweet Spot: The sensors work best when the size of the Dark Matter cloud matches the spacing between the sensors. It's like tuning a radio: if the cloud is the right size to brush against several sensors at once, the signal gets amplified.
The "Fuzzy" Advantage: For short-range forces, a big, fuzzy cloud is actually easier to detect than a tiny dot. The cloud's size allows it to "feel" the force over a larger area, whereas a dot might miss the force entirely if it's too short-range.

5. The Limits: When Things Get Too Big

There is a catch. If the Dark Matter cloud gets too huge (larger than the detector itself), the signal gets weak again.

Analogy: Imagine trying to feel a breeze. If the wind is a focused jet (the right size), you feel it strongly. If the wind is a massive, slow-moving ocean wave that covers the whole room, the air movement at any single point is very gentle. Similarly, if the Dark Matter cloud is huge, its mass is spread out so thin that the push on any single sensor is too weak to hear over the background noise.

6. The Conclusion

The paper concludes that if we build these quantum sensor arrays, we need to be ready for the possibility that Dark Matter isn't a tiny dot, but a fuzzy cloud.

If we see a signal that looks like it came from a big cloud, it tells us the Dark Matter has a specific size and shape.
This changes how we design our detectors. We shouldn't just look for tiny hits; we should look for patterns that suggest a large, fuzzy object passing through our grid of sensors.

In short: This paper tells us that if the heaviest Dark Matter particles are actually "fuzzy clouds," our future detectors might catch them much better than we thought—especially if those clouds are the right size to fit perfectly between our sensors.

Technical Summary: Towards the Direct Detection of Composite Ultraheavy Dark Matter in Quantum Sensor Arrays

Problem Statement
Ultraheavy dark matter (UHDM) candidates with masses at or above the Planck scale ( $M \gtrsim M_{\text{Pl}} \approx 22 \, \mu\text{g}$ ) cannot be elementary particles without collapsing into black holes; they must instead exist as composite objects with finite spatial extent. While previous proposals for direct detection using quantum sensor arrays (specifically 3D arrays of accelerometers) have focused on point-like UHDM, this assumption neglects the inevitable spatial extension of Planck-scale objects. Furthermore, purely gravitational interactions are insufficient for detection given current noise floors, necessitating the inclusion of a fifth force. This work addresses the gap in understanding how the finite size and specific density profiles of composite UHDM affect the detectability and signal phenomenology in quantum sensor arrays, particularly when interacting via gravity and a Yukawa-type fifth force.

Methodology
The authors develop a phenomenological framework to model composite UHDM clumps and simulate their interaction with a proposed quantum sensor array.

Modeling Composite UHDM:
- Mass and Scale: The clumps are characterized by mass $M \sim M_{\text{Pl}}$ and a characteristic radius $R$ .
- Density Profiles: Four radial density profiles are considered: Point-like ( $\delta$ -function), Tophat (constant density), Gaussian, and Exponential.
- Interactions: The clumps interact with sensor test masses via Newtonian gravity and a Yukawa fifth force. The potential includes a dimensionless strength parameter $\alpha$ and a screening length $\lambda$ . The force is calculated analytically for spherically symmetric profiles, noting that the Yukawa force violates Newton's shell theorem, allowing mass outside a given radius to contribute to the net force.
Detector Simulation:
- Array Configuration: A $20 \times 20 \times 20$ cubic array of sensors is modeled, with a total length $L \approx 1.9$ m and inter-sensor spacing $d = 10$ cm. Each sensor has a mass $m_s = 100$ g.
- Noise Model: The signal-to-noise ratio (SNR) accounts for thermal noise (scaling with $\sqrt{\tau}$ ) and quantum noise (scaling with $1/\sqrt{\tau}$ ). The optimal measurement time $\tau_{\text{opt}}$ is chosen to minimize total noise, with fiducial parameters including $T=15$ mK and a quantum squeezing factor $\xi = 15$ dB.
- Monte Carlo Analysis: The authors perform $10^3$ Monte Carlo simulations for various parameter sets. For each run, a clump trajectory is randomized (impact parameter, velocity drawn from a Maxwell-Boltzmann distribution). The impulse signal $S_i$ on each sensor is integrated over time, and the total array SNR is computed by summing individual sensor SNRs in quadrature.
- Sensitivity Criterion: A model is considered detectable if the expected number of encounters with SNR $\ge 10$ over a 5-year exposure is at least one ( $N_{\text{encounter}} P_{10} \ge 1$ ).

Key Contributions

Finite Extent Phenomenology: The paper establishes that the finite spatial extent of UHDM fundamentally alters the detection signal compared to the point-like limit. Specifically, for small screening lengths ( $\lambda \ll R$ ), the signal from extended clumps scales as $\lambda^2$ (power-law), whereas the point-like signal is exponentially suppressed ( $\propto e^{-b/\lambda}$ ).
Interplay of Scales: The study maps the complex interplay between the dark matter radius ( $R$ ), the inter-sensor spacing ( $d$ ), and the Yukawa screening length ( $\lambda$ ). It identifies regimes where the signal is enhanced or suppressed based on the relative magnitudes of these scales.
Density Profile Dependence: The work quantifies how different internal density structures (Tophat vs. Gaussian vs. Exponential) yield distinct sensitivity contours, particularly in the transition regions where the clump size is comparable to the detector geometry.

Results

Necessity of Fifth Force: Without a non-gravitational interaction ( $\alpha = 0$ ), the SNR never exceeds unity, confirming that purely gravitational detection of Planck-scale UHDM is currently infeasible with these arrays.
Small $\lambda$ Regime: When the Yukawa screening length is small ( $\lambda \ll R$ ), composite UHDM offers significantly better sensitivity than point-like UHDM. The signal scales as $\alpha \propto \lambda^{-2}$ for extended objects, compared to the exponential suppression for point-like objects. This suggests that extended models are easier to detect if the fifth force is short-ranged.
Large $\lambda$ Regime: When $\lambda \gg L$ (the array length), the force acts as a long-range coherent field. In this limit, point-like models generally yield higher sensitivity, and the signal becomes independent of $\lambda$ .
Optimal Clump Size: Sensitivity is maximized when the dark matter clump radius $R$ is comparable to the typical impact parameter of the array ( $R \approx \langle b \rangle \approx 1$ cm). If $R$ is too large ( $R \gg L$ ), the force is diluted across the array, and the signal is suppressed.
Mass and Flux Limits: Sensitivity degrades for very large masses ( $M \gtrsim 3 M_{\text{Pl}}$ ) due to the low flux of heavy particles (flux $\propto M^{-1}$ ). Conversely, for very small masses, sensitivity drops due to the weakening of the force ( $F \propto M$ ).

Significance and Claims
The authors claim this work provides the first systematic study of how the finite spatial extent of ultraheavy dark matter impacts direct detection prospects in quantum sensor arrays. They argue that assuming UHDM is point-like is theoretically inconsistent for masses at the Planck scale. The results suggest that future detector designs could be optimized by tuning the inter-sensor spacing to match the expected size of composite dark matter clumps. Furthermore, the distinct scaling behaviors (power-law vs. exponential) in different regimes offer a potential method to discriminate between theoretical models of UHDM (e.g., distinguishing between point-like and composite candidates, or different density profiles) should a detection occur. The paper concludes that future accelerometer arrays would provide valuable information regarding the mass and size of composite UHDM, characterizing signatures for various theoretical models.