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

TL;DR

This work addresses the direct detection of composite ultraheavy dark matter with masses around the Planck scale using a three-dimensional quantum sensor array. It develops a phenomenological framework for spatially extended UHDM with multiple density profiles and a Yukawa fifth force, and it employs Monte Carlo simulations to project detector sensitivities across the parameters $M$, $R$, $\alpha$, and $\lambda$. The results reveal nontrivial interplay between the DM scale radius, sensor spacing, and screening length, showing regimes where extended DM signals can exceed point-like expectations and guiding future detector design. The findings provide a path to infer the mass and size of UHDM and to distinguish between candidate theoretical models of ultraheavy dark matter.

Abstract

Quantum sensor arrays have recently been proposed as a promising platform for the direct detection of ultraheavy dark matter, which is typically assumed to behave as a point-like particle. However, particles with masses at or above the Planck scale cannot be elementary; instead, they must exist as composite objects with finite spatial extent. Such spatially extended dark matter models lead to distinctive phenomenology in these detectors, particularly when the dark matter also interacts through long-range forces with their own characteristic length scales. In this work, we study the sensitivity of quantum sensor arrays to composite, ultraheavy dark matter interacting via both gravity and a novel Yukawa force. We consider three phenomenologically motivated density profiles -- a tophat, a Gaussian, and an exponential -- and contrast their signals with the point-like limit. Using a Monte Carlo analysis based on the predicted impulse signals and estimates of thermal and quantum noise, we obtain sensitivity projections for a future realization of a quantum sensor array. We find a non-trivial interplay between the dark-matter scale radius, the inter-sensor spacing, and the Yukawa screening length. Future accelerometer arrays would provide valuable information about the mass and size of composite ultraheavy dark matter, and our work will help to characterize the signatures of different theoretical models of ultraheavy dark matter.

Figures (8)

• Figure 1: The normalized mass density profiles of the dark matter clump $\rho(r)/\rho_0$ with radial distance $r$ as a fraction of the clump's characteristic radius $R$. The considered spatially extended profiles are the tophat, Gaussian, and exponential profiles, as given in \ref{['eq:rho_profs']}. Schematically shown is also a dark matter clump, considered to have a mass $M \sim M_\mathrm{Pl}$ and radius $R \lesssim 10\,\mathrm{m}$.
• Figure 2: A cross section of the $3$D quantum sensor array in the rest frame of the dark matter clump. The clump is placed at the origin $\mathcal{O}$ of the $xz$--coordinate plane and has a mass $M$. Its mass density profile is governed by the function $\rho(r')$, which also depends on an assumed characteristic length scale $R$ for the DM clump. The sensor array is placed at an initial central displacement $\boldsymbol{r}_0 \equiv X\,\hat{\boldsymbol{x}} + Z\, \hat{\boldsymbol{z}}$, where $X$ and $Z$ are random variables, with a random orientation $\hat{\boldsymbol{n}}$. In this frame, the array moves at a velocity $\boldsymbol{v}_\mathrm{DM} = - v\,\hat{\boldsymbol{z}}$, with $v$ a random variable distributed according to a 3D Maxwell-Boltzmann distribution with a scale parameter $v_0 / \sqrt{2}$ and $v_0 \approx 238\,\mathrm{km\,s^{-1}}$ the dark matter virial velocity. The sensor array consists of a total of $N \times N \times N$ sensors of mass $m_s$, where $N$ is the number of sensors along any one dimension. The array has a total length $L = (N-1)d \sim 1\,\mathrm{m}$, where $d \sim 10\,\mathrm{cm}$ is the inter-sensor spacing. Each sensor experiences a force $\boldsymbol{F}\textbf{(}\boldsymbol{r}(t)\textbf{)}$ due to the dark matter clump. Also shown are the positions of a single sensor at times $t = -t_\mathrm{imp}/2$, $t = 0$, and $t = t_\mathrm{imp}/2$, where $t_\mathrm{imp}$ is the typical duration of an impulse.
• Figure 3: The single sensor signal $\mathcal{S}_i$, defined as the impulse delivered to a sensor by a passing DM clump, with varying Yukawa screening length $\lambda$. The signal is calculated via \ref{['eq:sig']}, taking the Yukawa interaction strength to be $\alpha = 10^{7}$ and assuming that a sensor of mass $m_s = 100\,\mathrm{g}$ passes by a DM clump of mass $M = M_\mathrm{Pl}$ with impact parameter $b = 1\,\mathrm{cm}$. Left: The signal for the point-like ($\mathrm{P}$), tophat ($\mathrm{T}$), Gaussian ($\mathrm{G}$), and exponential ($\mathrm{E}$) dark matter mass profiles (cf. \ref{['eq:rho_profs']}) for a clump radius of $R = 10\,\mathrm{cm}$. For $\lambda \lesssim b$, the point-like signal decays exponentially, while that for any one of the extended profiles scales as $\mathcal{S}_i \propto \lambda^2$. Right: The signal for the exponential profile with varying clump radius. As $R \rightarrow 0$, we retrieve the point-like result.
• Figure 4: The summed signal (cf. \ref{['eq:sig']}) with characteristic dark matter clump radius $R$ for the different dark matter density profiles $\rho$ we consider in this work (cf. \ref{['eq:rho_profs']}). The vertical lines indicate the geometrical scales of the detector array, including the sensor spacing $d = 10\,\mathrm{cm}$ and the array length $L = 1.9\,\mathrm{m}$, as well as the expected value of the impact parameter $\langle b \rangle = d / (2 \sqrt{N}) \approx 1\,\mathrm{cm}$, with $N = 20$ the number of sensors along a single array dimension. Results are computed for dark matter mass $M = M_\mathrm{Pl}$ and strength parameter $\alpha = 10^7$. The signal scales as $\mathcal{S}_\mathrm{tot} \propto \alpha M$ if the Yukawa force dominates over the gravitational force. Left: The result for $\lambda = 1\,\mathrm{cm}$. For radii $\lambda \lesssim R \lesssim L$, the signal goes as $R^{-1}$. Right: The result for the screening length $\lambda = 10\,\mathrm{m}$. For radii $d \lesssim R \lesssim \lambda$, the signal goes as $R^{-2}$. For both choices of $\lambda$, the relationship of the signal to $R$ depends on the assumed density profile at large DM radii.
• Figure 5: Projected sensitivities to the Yukawa screening length $\lambda$ with characteristic dark matter clump radius $R$ for the dark matter density profiles we consider in this work (cf. \ref{['eq:rho_profs']}). Sensitivities are drawn for strength parameters $\alpha \in \{10^{5}, 10^{6}, 10^{8}\}$. The vertical lines indicate the geometrical scales of the detector array, including the sensor spacing $d = 10\,\mathrm{cm}$ and the array length $L = 1.9\,\mathrm{m}$, as well as the expected value of the impact parameter $\langle b \rangle = d / (2 \sqrt{N}) \approx 1\,\mathrm{cm}$, with $N = 20$ the number of sensors along a single array dimension. Results are computed for dark matter mass $M = M_\mathrm{Pl}$.