Fig. 1: Visualization of the spin-based interferometer.
From: Searching for dark matter with a spin-based interferometer
a The two devices comprising the interferometer are indicated in their respective locations in Mainz and Kraków. The small red arrows at the Earth’s surface point in the directions of the sensor sensitivity axes. In our model, Earth is moving in the galactic rest frame at velocity vE through the ALP DM field, characterized by its de Broglie wavelength λDB, that is more than a thousand times larger than the Earth’s radius. Besides its translational motion, Earth rotates around its axis, giving rise to sidereal modulation of the signal at the frequency ωE. Base image: Google Earth. Image ©2025 Google, Image Landsat / Copernicus, Data SIO, NOAA, U.S. Navy, NGA, GEBCO, IBCAO. 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 ωa, while the latter results in (generally asymmetric) sidebands separated from the carrier by the sidereal frequency ωE. 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). The frequency points are intended for illustration purposes and do not correspond to experimental data. 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 AK only in the Kraków data, and sideband signatures of different amplitudes and phases in both Kraków (\({A}_{\pm }^{{{\rm{K}}}}\)) and Mainz (\({A}_{\pm }^{{{\rm{M}}}}\)) data. The phase difference between the signals arises due to the different orientation of the sensitive axes (π/2), as well as the different locations (ϕ) of the sensors. Appropriate phasing allows to coherently add the ALP signals, while the noise adds incoherently.
