Earth Matter Enhanced Axion Dark Matter Search

Abstract

Laboratory searches for ultralight axion dark matter (DM) have traditionally assumed the terrestrial density of axions is equal to the average density of DM in the solar system. However, quadratic couplings to matter introduce a non-trivial field profile near the Earth. In this work, we present the first dedicated experimental implementation of this environment-aware axion DM wind search framework. Leveraging the extreme sensitivity of a K--Rb--$^{21}$Ne comagnetometer to pseudo-magnetic fields induced by axion DM, we analyzed our data in the context of the massively enhanced local gradient of axions due to interactions with matter, though no signal candidates were found. Consequently, we have set the most stringent limits on axion-neutron derivative interactions for masses $m_a \in [0.041, ~28.9]~\rm feV$, improving from previous experiments that ignore terrestrial matter effects by as much as three orders of magnitude for certain masses. Our work highlights the necessity of accounting for environmental modifications in precision frontier experiments and demonstrates how geophysical variations can be harnessed to act as a natural amplifier for DM possibly enabling future detection in parts of the parameter space that were previously beyond reach.

Figures (10)

• Figure 1: The Earth-effected axion DM and its detection principle. (a) Due to the quadratic coupling of axions and fermions, Earth's dense matter changes the effective mass of the axion inside it. For a generic quadratic coupling, the effect can be analogous to light traveling between two media with vastly different refractive indices. The presence of the Earth introduces a new small length scale with its radius, and at the surface of the Earth, the radial direction gradient of the axion field will be greatly enhanced, providing an excellent opportunity for a highly sensitive comagnetometer whose sensitive axis is pointing along the radial direction. Operating in the self-compensation regime, our coupled alkali-noble-gas comagnetometer is specifically configured with the sensitive axis perpendicular to the ground to benefit from the enhancement. For transverse magnetic-field noise, the noble-gas nuclear spins adiabatically follow the perturbation and generate an opposing effective field: it largely cancels the noise experienced by the alkali-metal spins, leaving their orientation nearly unchanged. In contrast, an axion-gradient-induced anomalous field couples primarily to the nuclear spins, driving transverse precession that is read out by the alkali-metal spins acting as an in-situ ultrahigh-sensitivity magnetometer. (b) Radial profiles of the axion field amplitude (blue) and gradient (green), normalized to their unenhanced values with angular dependence averaged. We choose a Compton frequency $m_a/2\pi = 1~\mathrm{Hz}$ and a decay constant $f_a = 10^{13.5}~\mathrm{GeV}$ (corresponding to the regime $k R_{\mathrm{E}} < q R_{\mathrm{E}} \lesssim \hbar$ for demonstration. The enhancement of the radial gradient at the surface scales approximately as $1/(k R_{\mathrm{E}})\times \left((f_a)^c/f_a\right)^2$(see the definition of $(f_a)^c$ in main text.), while the field amplitude remains nearly unchanged. (c) Spatial distribution of the axion gradient enhancement ratio for the same parameter. A pronounced enhancement of the gradient is visible near the Earth’s surface, while the effect rapidly attenuates both inside the Earth and far outside it.
• Figure 2: Comparison of responses to classical magnetic fields and non-magnetic inputs. (a) Simulated ratio between the comagnetometer responses to the anomalous field $b_y^n$ (i.e., axion DM field) and to the classical magnetic field $B_x$, showing relative enhanced sensitivity to low-frequency anomalous axion DM field at the compensation point. (b) Frequency-dependent response measured by physically rotating the sensor along the sensitive axis using a custom rotation platform near the compensation point. Deviating from the compensation point reduces the low-frequency response to rotations, while increasing the response to magnetic fields. (c) The compensation-point data from (b), shown separately for clarity. At 0.1 Hz, the equivalent magnetic response to rotation is approximately one order of magnitude larger than that to an applied magnetic field. The error bars denoting one standard deviation are too small to be visually resolved. The response to axion DM field from simulation is also shown and is nearly identical to the response to rotations, due to the (relative to magnetic fields) larger coupling of rotations to nuclear spins compared to electron-based spins. (d) As a demonstration of the accuracy of the sensor, a measurement is made with the sensitive axis reoriented to lie parallel to the ground (unlike in the DM search), and a rotation platform is used to rotate the sensitive axis within the horizontal plane. The measured data over one full revolution follows the sinusoidal projection of the Earth's rotation onto the sensitive axis. The error bars denote one standard deviation, but are too small to be visually resolved.
• Figure 3: Constraints from the search on the axion-neutron coupling from the data, as well as future projections. The purple solid line show our $95\%$ C.L. exclusion limit of this experiment, with the averaged of the bound plotted in solid dark purple line calculated in a log space at binning resolution of 5% of the mass. The purple dashed and dotted lines show the future projections and the sensitivity of the theoretically optimal comagnetometer, respectively. By aligning the sensitive axis radially, we maximize the coupling to the Earth-induced axion field gradient, achieving a significant sensitivity enhancement. Existing laboratory constraints on axion-neutron coupling, which ignored the enhanced gradient (light-yellow) include comagnetometers Lee:2022vvbGavilan-Martin:2024nloBloch:2019lcy, ChangE wei2025darkxu2024constraining, Mainz-Kraków Gavilan-Martin:2024nlo, with other constraints beyond the bounds of the plot and are not shown Bloch:2021vnnBloch:2022kjmAbel:2022vfgGarcon:2019inhWu:2019exd. The gray regions are from constraints placed directly on $f_a$ and arise from EDM measurements Abel:2017rtmRoussy:2020ilyJEDI:2022hxa, atomic clocks Madge:2024aotZhang:2022ewz and the MICROSCOPE experiment Gue:2025nxq and are also relevant (see text for further discussion). The bounds on $f_a$ from similar type of experiments Schulthess:2022pbpRoussy:2020ilyZhang:2022ewzFan:2024pxs are not shown. The blue shaded region ("Earth Bound") is excluded to prevent the Earth from sourcing an axion-field new minimum. Astrophysical bounds from white-dwarfs (cyan dashed) Balkin:2022qer and neutron-star cooling (green shaded) Buschmann:2021juvSpringmann:2024mjp are provided for context, however, these astrophysical bounds rely heavily on complex modeling of stellar equations of state; thus, they suffer from significant systematic uncertainties, emphasizing the importance of the more controlled terrestrial searches. Our results surpass previous laboratory limits by 2-3 orders of magnitude and probe the parameter space beyond the Earth-sourced bound. In this plot we set $c_n=10$ ($g_{an}= c_n/f_a$); see Fig. \ref{['fig:scalingcn']} for other $c_n$ values.
• Figure 4: left panel: The solid blue line is the global $p$-value $p_{\rm global}$ as a function of the $q_{\rm th}$ obtained from a null Monte Carlo test for axion mass region centered around $0.05~{\rm Hz}$, with the dashed orange line showing its fit. right panel: The blue dots represent the Monte Carlo experiments of the corresponding particle frequency. The orange line shows the interpolating function for the $\alpha(\nu)$ using the blue dots. The notations and Monte Carlo method are adapted from ref. Lee:2022vvb.
• Figure 5: The final limits and the corresponding Earth bounds shown in purple ($c_n=10$), brown ($c_n=50$), blue ($c_n=100$). The Earth bounds directly depends on decay constant $f_a$, thus scales linearly with $c_n$, while the experimental constraints scale as $c_n^{-3/2}$ in this regime.