Searching for Ultralight Scalar Dark Matter with Clocks in Low Earth Orbit

TL;DR

This work develops a clock-based probe of ultralight scalar dark matter with quadratic couplings to the SM, focusing on how DM density near Earth is reshaped by matter and how this yields a monopole plus dipole field profile detectable by clocks in Low Earth Orbit. By solving the Klein–Gordon equation with Earth as a dense boundary, the authors quantify the field profile $\phi^2$ and its angular structure through Legendre coefficients $a_l$, enabling both space–ground and space–space clock comparisons to constrain the couplings $d_X^{(2)}$. They derive phase and frequency measurement strategies, including SNR-based sensitivities, and show that LEO clocks—especially optical and nuclear ones—can explore parameter space inaccessible to ground experiments, with dipole modulation providing a robust cross-check. The results indicate that missions like ACES, as well as future optical/nuclear clocks in ISS-like orbits, could deliver world-leading constraints on certain photon, electron, gluon, and light-quark couplings, contingent on integration time and clock stability. Overall, the work highlights a concrete, executable path to leverage space-based quantum clocks to probe quadratically coupled ultralight DM and extract potential DM properties from monopole-dipole signatures.

Abstract

The density of ultralight dark matter can be modified in the vicinity of macroscopic bodies when the dark matter possesses quadratic couplings to the Standard Model. If these couplings are sufficiently strong, Earth's atmosphere acts to shield the dark matter, thereby limiting the effectiveness of laboratory-based experiments. Experiments performed at altitudes exceeding the dark matter de Broglie wavelength experience the same orbit-averaged field amplitude as in the absence of scattering. Quantum clocks are capable of detecting variations in fundamental parameters due to the dark matter background. If based on the International Space Station, they are therefore well-suited to probe dark matter masses $m_{\rm DM}\gtrsim 10^{-9} \text{\, eV}$. Moreover, when the dark matter de Broglie wavelength is smaller than Earth's radius ($m_{\rm DM} \gtrsim 10^{-10}$ eV), the dark matter profile around Earth exhibits a dipole feature. In Low Earth Orbits this dipole temporally modulates potential dark matter signals. This provides a powerful cross-check of the orbit-averaged effect and can enhance the sensitivity of these experiments. We find optical clocks could give rise to world-leading constraints in some cases. Orbiting nuclear clocks could probe even more of the parameter space inaccessible to ground-based experiments.

Figures (9)

• Figure 1: Example field profile due to scattering of dark matter from the Earth's surface for dark matter mass $m_{\rm DM} \approx 10^{-9} \, \rm eV$ and coupling $d_e \approx 2 \times 10^{17}$ (or $d_{m_e} \approx 1 \times 10^{18}$ or $d_{g} \approx 4 \times 10^{14}$ or $d_{\hat{m}} \approx 3 \times 10^{16}$). The $x-$ and $y-$ axes are plotted in units of Earth radii $R_{\oplus}$. The color bar indicates the square of the field value $\phi^2(r,\theta)$ in units of the (field value)$^2$ at infinity $\phi_0^2$. The dark matter wind is incident from the bottom of the figure; the induced shadow is visible above the Earth.
• Figure 2: Legendre coefficients $a_l(h,m_{\rm DM})$ for the field profile (see Eq. (\ref{['eq: phi^2 legendre']})) at $h = 0.06\, R_\oplus$, the height of the ISS orbit, as a function of the dark matter mass $m_{\rm DM}$. The upper axis gives the corresponding value of the average momentum of the DM wind $k_0$ in units of inverse Earth radii.
• Figure 3: Legendre coefficients $a_l(h,m_{\rm DM})$ for the field profile (see Eq. (\ref{['eq: phi^2 legendre']})) evaluated at $m_{\rm DM} = 10^{-9}\, \rm eV$ as a function of height $h$ measured in Earth radii $R_\oplus$. The ISS orbit is at $h= 0.06 R_\oplus$, while the MICROSCOPE experiment orbit corresponds to $h=0.1 R_\oplus$.
• Figure 4: Schematic representation of coordinates in the Earth-centered inertial frame at an instant when $\alpha_{\rm test}(t) = \alpha_{\rm DM} + \pi$. The dark matter wind is shown as incident from the upper-left with momentum vector $\Vec{k_0}$. The Earth rotates about its axis with frequency $\Omega_{\oplus}$. The declination of the incident wind and the experiment are given by $\delta_{\rm DM}$ and $\delta_{\rm test}$, respectively.
• Figure 5: Example time-dependence of $\cos \theta_r$, see Eq. (\ref{['eq: costheta']}), with $\delta_0 = 52 ^{\circ}$. and $\omega/\Omega=72$. For the case of a space-ground comparison, the red (orange) dots represent the $\cos \theta_r$ values sampled over the course of a single day when the satellite is descending (ascending). The Earth-based clock is located at $45^{\circ}$ N.