First Search for Ultralight Dark Matter Using a Magnetically Levitated Particle

Abstract

We perform the first search for ultralight dark matter using a magnetically levitated particle. A sub-millimeter permanent magnet is levitated in a superconducting trap with a measured force sensitivity of $0.2\,\mathrm{fN/\sqrt{Hz}}$. We find no evidence of a signal and derive limits on dark matter coupled to the difference between baryon and lepton number, $B - L$, in the mass range $(1.10360 \text{ - } 1.10485) \times 10^{-13}\,\mathrm{eV} / c^2$. Our most stringent limit on the coupling strength is $g_{B - L} \lesssim 2.98 \times 10^{-21}$. We propose the POLONAISE (Probing Oscillations using Levitated Objects for Novel Accelerometry in Searches of Exotic physics) experiment, featuring short-, medium-, and long-term upgrades that will give us leading sensitivity in a wide mass range and demonstrating the promise of this novel quantum sensing technology in the hunt for dark matter.

Figures (7)

• Figure 1: Schematic of the experimental setup inside the dilution refrigerator. Shown are the plates of the cryostat, the multi-stage mass-spring system used to shield against external vibrations, and the holder for the trap and magnet. The inset shows the superconducting trap containing the magnet. The effect of the $\boldsymbol{B}$-field can be modelled by an image dipole. The oscillatory force imparted by the ULDM field, $F_\mathrm{DM}^p(t)$, is also indicated. The black arrows illustrate the coupling of the flux of the moving particle to the pick-up coil. Further details and photographs of the setup can be found in Ref. Fuchs:2023ajk.
• Figure 2: The force-power spectral density, $S_{FF}$, with frequency $f$ measured by our experiment. The fit to the force noise background via \ref{['eq:force-noise-bkg']} is shown. The vertical line highlights the resonance frequency $f_0 \approx 26.699\,\mathrm{Hz}$ relevant for motions parallel to the zenith. Data initially reported in Ref. Fuchs:2023ajk.
• Figure 3: The $90\%$ confidence level limits on the gauge coupling strength $g_{B - L}$ with dark matter mass $m_\mathrm{DM}$ (bottom axis) and Compton frequency $f_\mathrm{DM}$ (top axis). Shown is the data-driven limit derived from the measurements presented in \ref{['fig:exp-data']}, as well as the median limit and $1\sigma$/$2\sigma$ bands derived from our Monte Carlo analysis supp_mat. Also shown are the existing limits from the Eöt-Wash Wagner:2012uiAxionLimits and MICROSCOPE MICROSCOPE:2022doyAmaral:2024tjg experiments.
• Figure 4: Projected $90\%$ confidence level limits on the gauge coupling strength $g_{B - L}$ with dark matter mass $m_\mathrm{DM}$ (bottom axis) and Compton frequency $f_\mathrm{DM}$ (top axis) for POLONAISE. Projections are based on the short-, medium-, and long-term configurations detailed in \ref{['tab:configs']}. Also shown is our current best limit from \ref{['fig:present-lims']} (red star), as well as the existing limits from the MICROSCOPE (MS) MICROSCOPE:2022doyAmaral:2024tjg, Eöt-Wash (EW) Wagner:2012uiAxionLimits, and LIGO/Virgo (LV) LIGOScientific:2021ffgAxionLimits experiments.
• Figure 5: Distribution of the measured excess power $p$ in the coherent regime for $\kappa = 5$ (see \ref{['eq:kappa_app']}). Data was simulated from $10^6$ Monte Carlo runs beginning from \ref{['eq:force-short-noise']}. The solid line shows the analytical result of \ref{['eq:lik-coh']} and is in excellent agreement with simulations.