Searching for dark matter with a 1000 km baseline interferometer

TL;DR

This work targets ultralight axion-like particle (ALP) dark matter by modeling it as a classical, coherently oscillating field whose gradient couples to neutron, proton, and electron spins. A two-station interferometric network of K-Rb-$^3$He comagnetometers separated by ~1000 km leverages sidereal modulation and cross-site coherence to search for ALP-gradient signals across nine orders of magnitude in mass, from $m_a\approx10^{-22}$ to $4\times10^{-14}$ eV. No ALP signal is observed; the analysis places new laboratory upper limits on $g_{aNN}$, $g_{aPP}$, and $g_{aee}$, improving previous neutron and proton constraints by up to three orders of magnitude and extending sensitivity to electron couplings. The results demonstrate the potential of a distributed, baseline-spanning DM detector network for probing ultralight bosonic DM and set the stage for expanded networks and future runs within the CASPEr/GNOME ecosystem.

Abstract

Axion-like particles (ALPs) arise from well-motivated extensions to the Standard Model and could account for dark matter. ALP dark matter would manifest as a field oscillating at an (as of yet) unknown frequency. The frequency depends linearly on the ALP mass and plausibly ranges from $10^{-22}$ to $10$ eV/$c^2$. This motivates broadband search approaches. We report on a direct search for ALP dark matter with an interferometer composed of two atomic K-Rb-$^3$He comagnetometers, one situated in Mainz, Germany, and the other in Kraków, Poland. We leverage the anticipated spatio-temporal coherence properties of the ALP field and probe all ALP-gradient-spin interactions covering a mass range of nine orders of magnitude. No significant evidence of an ALP signal is found. We thus place new upper limits on the ALP-neutron, ALP-proton and ALP-electron couplings reaching below $g_{aNN}<10^{-9}$ GeV$^{-1}$, $g_{aPP}<10^{-7}$ GeV$^{-1}$ and $g_{aee}<10^{-6}$ GeV$^{-1}$, respectively. These limits improve upon previous laboratory constraints for neutron and proton couplings by up to three orders of magnitude.

Figures (10)

• Figure 1: (a) Schematics of the comagnetometric interferometer. The two devices comprising the interferometer are indicated in their respective locations in Mainz and Kraków. The small red arrows at the Earth surface point in the directions of the sensor sensitivity axes. In our model, Earth is moving in the galactic rest frame at velocity $v_{\text{E}}$ through the ALP DM field, characterized by its de Broglie wavelength $\lambda_{\text{DB}}$, that is more than a thousand times larger than the Earth radius. Besides its translational motion, Earth rotates around its axis giving rise to sidereal modulation of the signal at the frequency $\omega_{\text{E}}$. (b) Orientation of the sensitive axes of the comagnetometers with respect to Earth's rotation axis. The sensitive axes of the comagnetometers can be decomposed into components along and perpendicular to the Earth's rotation axis. The former results in an ALP signal component (carrier) arising at the ALP Compton frequency $\omega_a$, while the latter results in (generally asymmetric) sidebands separated from the carrier by the sidereal frequency $\omega_\text{E}$. (c) Signal interferometry in the data analysis (illustration). The points in the three subfigures correspond to the complex Fourier amplitudes of all probed frequency bins of the Mainz (left), Kraków (middle) datasets and their combination (right). We assume normal noise distributions. The circles indicate the standard deviation. The points marked with red, blue, and orange represent injected ALP signatures observable in both comagnetometers and how they appear in the combined signal. Due to the directional sensitivity of the comagnetometers, the injected ALP signal manifests as a carrier of amplitude $A^\text{K}$ only in the Kraków data, and sideband signatures of different amplitudes and phases in both Kraków ($A_\pm^\text{K}$) and Mainz ($A_\pm^\text{M}$) data. The phase difference between the signals arises due to the different orientation of the sensitive axes ($\pi/2$), as well as the different locations ($\phi$) of the sensors. Appropriate phasing allows to coherently add the ALP signals, while the noise adds incoherently.
• Figure 2: Signal estimator $S(\omega)$, obtained by interfering the Mainz and Kraków comagnetometer data, for frequencies above $\omega_{\text{E}}$. The results are shown as a function of frequency in the upper figure. The data shows a $1/f$ scaling behaviour up to $10^{-1}$ Hz consistent with technical noise of the apparatus. The peak sensitivity of the estimator reaches $10^{-17}$ T. No ALP candidate is found beyond the global 95% significance threshold in p-value, as shown in the lower plot.
• Figure 3: Histogram of the measured-noise distribution and the combined amplitude value at $\omega_{\text{E}}$ as a function of the measured Fourier amplitude. For an ALP field oscillating below $\omega_{\text{E}}$, the sidebands are not resolved and an ALP signature is present at $\omega_{\text{E}}$. However, $A^{M+K}(\omega_{\text{E}})$ is compatible with the expected noise distribution and thus no ALP candidates with frequencies $\omega_a<\omega_{\text{E}}$ are reported. The blue arrow indicates the frequency bin at $\omega_{\text{E}}$, the dashed red line indicates the 95% confidence detection threshold and the orange distribution is the measured noise for the the frequency bins between $\omega_{\text{E}}$ and 0.01 Hz. The amplitude is normalized by the standard deviation $\Delta A^{M+K}(\omega)$ to whiten the noise.
• Figure 4: Exclusion plot for the neutron coupling (mean limits). Other laboratory (solid lines) and astrophysical (dashed lines) constraints are shown for reference and extracted from AxionLimits: CASPEr-ZULF wu_search_2019garcon_constraints_2019, K-$^3$He lee_improved_2018lee_laboratory_2023, nEDM abel_search_2017, PSI HgM abel_search_2023, SNO bhusal_searching_2021, NASDUCK bloch_nasduck_2022, Hefei $^{129}$Xe jiang_search_2021, ChangE wei_dark_2023, and neutron-star cooling buschmann_upper_2022.
• Figure 5: Exclusion plot for the proton coupling (mean limits). Other laboratory (solid lines) and astrophysical (dashed lines) constraints are shown for reference and extracted from AxionLimits: CASPEr-ZULF wu_search_2019garcon_constraints_2019, ChangE wei_dark_2023, and neutron-star cooling buschmann_upper_2022.