Dark matter remains one of the central puzzles of physics: its existence is confirmed by gravitational and cosmological observations, but its non-gravitational properties are unknown. Ultralight dark matter is especially interesting because its wave nature opens up new detection strategies. Unlike conventional experiments based on exciting particles, ultralight dark matter can scatter coherently off all the nucleons of a macroscopic target, greatly enhancing the cross section. Existing proposals use single macroscopic targets, such as torsion balances, but the MICROSCOPE satellite, with its nested multilayer structure, is qualitatively different. When the sizes of and distances between the components are comparable to the dark matter wavelength, the standard description of scattering off a single object breaks down, and interference effects arise, similar to those in two-slit optics. This work sits alongside studies that use torsion balances and atomic interferometers to search for dark matter, but it is the first to consider interference between several macroscopic targets in a space experiment.
The authors developed a theoretical formalism for the scattering of dark matter waves off several macroscopic targets, generalizing the first Born approximation. They calculated the force acting on each cylinder through the scattering amplitudes, using the Lippmann-Schwinger equation and Ehrenfest's theorem. For the specific case of MICROSCOPE, two coaxial hollow cylinders with a radial gap of about 1 cm were considered. The signal depends on the angle of incidence of the dark matter wave relative to the sensitive axis, which changes because of the satellite's rotation. The data analysis was performed in the frequency domain: the differential acceleration at the rotation frequency was fitted by a sum of a cubic polynomial for the drift and a dark matter signal template with an unknown cross section. Statistical uncertainties were estimated by least squares with weights based on the noise power spectral density, while systematic errors were taken from the equivalence analysis at the same frequency.
The calculations showed that for dark matter wavelengths much larger than the radial gap between the cylinders, interference completely suppresses the differential acceleration, whereas without interference it would tend toward a constant value. For session 218, the signal was modulated by the satellite's rotation with an amplitude depending on the dark matter mass. Analysis of all MICROSCOPE sessions gave constraints on the dark matter-nucleon scattering cross section: for a mass of 5×10⁻³ eV the cross section was (−5.5±1.6stat±4.2syst)×10⁻⁵³ cm² for SUREF and (14.9±5.3stat±4.5syst)×10⁻⁵³ cm² for SUEP. No significant signal was found, so upper limits were set at the 2σ level. The tightest constraints, on the order of 10⁻⁵² cm², were achieved at a mass of 5×10⁻³ eV, where the coherence length is comparable to the size of the cylinders. Including the outer shell as a third scatterer strengthens the signal and improves the constraints.
This work is the first to demonstrate that quantum interference in the scattering of dark matter waves off several macroscopic objects produces observable signals in precision accelerometers. Unlike neighboring studies that use single targets or torsion balances, it exploits the nested structure of MICROSCOPE, which makes it possible to probe a regime where the wavelength is comparable to the sizes of and distances between the bodies. The resulting constraints on the quadratic coupling of dark matter to nucleons in the mass range 10⁻³–10⁻² eV are two orders of magnitude stronger than previous ones. This establishes multicomponent precision accelerometers as a new class of detectors for dark matter wave interference.
The topic could develop toward the design of dedicated dark matter interferometers with optimized body geometry. Accounting for interference with the outer shell has already shown a signal enhancement, which opens a path to greater sensitivity by adding more scatterers. Future space missions with more precise accelerometers and controlled orientation could use this effect to search for dark matter over a broader mass range.
The results will influence the design of future experiments searching for ultralight dark matter, especially space-based tests of the equivalence principle and precision gravimetry. They will also stimulate theoretical studies of interference effects in dark matter wave scattering off complex structures.
The next step could be to analyze data from other space missions, such as LISA Pathfinder, taking into account interference between the test masses. It is also important to develop more accurate models of systematic errors at the rotation frequency in order to improve the constraints.
The work is connected to the unsolved problem of the nature of dark matter, especially the question of its non-gravitational interactions. It also touches on the fundamental problem of quantum interference of macroscopic objects, which has not yet been observed for masses as large as the MICROSCOPE test masses.
The two MICROSCOPE cylinders are separated by a gap of just 1 centimeter, but for dark matter waves with a mass of 5×10⁻³ eV the coherence length is about 10 centimeters, which allows them to interfere like light in Young's experiment.