NASDUCK': Laboratory Limits on Ultralight Dark-Photon Dark Matter with Null-Axis Magnetometry

Abstract

The dark photon is a well-motivated ultralight dark-matter candidate that may couple to the Standard Model through kinetic mixing. We search for dark-photon dark matter in the mass range $m_{A'}c^2 = 4\times10^{-12}$-$2\times10^{-9}\,\mathrm{eV}$ (1-500 kHz) using a three-axis magnetometer inside a large conductive shielded room. We set new laboratory limits on the kinetic-mixing parameter $ε$, improving upon previous laboratory bounds by up to three orders of magnitude. Our search exploits a geometry-defined null response along one axis as a noise reference; a subtraction procedure reduces the noise floor and improves sensitivity. These results establish the strongest laboratory constraints in this mass range and illustrate how null-axis magnetometry can broaden terrestrial searches for ultralight vector dark matter.

Figures (5)

• Figure 1: Detection concept and null-axis subtraction. (a) Conductive shielding suppresses external electromagnetic fields, while a dark-photon DM field effectively persists inside the shielded volume. The effect of the dark photon vector field $\vec{A}$ is equivalent to an effective current $\vec{J}_\mathrm{eff}= -\epsilon m_{A'}^2 \vec{A'}$, which generates a magnetic field inside the shield. (b)$\vec{J}_\mathrm{eff}$ generates a magnetic field $\vec{B}$ that is strongest near the faces parallel to it. A magnetic sensor is placed at the center of the floor (point $\vec{R}_1$), where magnetic fields will be excited by the $x$ and $y$ components of $\vec{J}_\mathrm{eff}$. (c) As the detector is moved from point $\vec{R}_1$ to point $\vec{R}_2$, the signal strength in the $x$ and $z$ directions changes. (d) We measure $\vec{B}$ at point $\vec{R}_1$, where the signal in the $z$ direction vanishes identically, regardless of the amplitude and direction of $\vec{J}_\mathrm{eff}$. In the $x$ direction, the dark photon produces a narrow-band signal in Fourier space, with frequency determined by the dark photon's rest mass. The $z$-direction measurement, serving as a pure noise channel, is subtracted from the measurement in the $x$ direction, yielding a lower noise version of it without affecting the signal. The same subtraction procedure is performed for $B_y$, not shown here.
• Figure 2: 95% C.L. upper limits on the kinetic-mixing parameter $\epsilon$ versus dark-photon mass $m_{A'}$ from this work. Limits are derived from the $B_x$ and $B_y$ channels, with sensitivity enhanced by null-axis subtraction using $B_z$ as a coherent noise reference (Fig. \ref{['fig:drawing']}). The light-blue region shows the point-by-point noise-subtracted limit ($>10^7$ scanned masses); the white curve is a 1% logarithmic-space average and the dark-blue band indicates the corresponding standard deviation. The black curve shows the averaged "direct" limit obtained without subtraction. Also shown are the Coulomb-law bound ( gray) Bartlett:1988yy, an illustrative projection for a $(50\,\mathrm{m})^3$ implementation with $0.1\,\mathrm{fT}/\sqrt{\mathrm{Hz}}$ sensitivity ( light-blue dashed) Gramolin:2020ict, and the corresponding Johnson-noise floor ($\sim10^{-2}\,\mathrm{fT}/\sqrt{\mathrm{Hz}}$, orange dashed). Astrophysical limits can be stronger at comparable masses Caputo:2021eaa but are subject to modeling uncertainties; see Ref. Hook:2025pbn.
• Figure 3: The diagonal elements of the dimensionless signal covariance matrix from Eq. \ref{['eq:cov_integral']}, illustrating the expected spectral shape of the dark photon signal. The parameters shown are for a signal at $f = m_{A'}c^2/h = 50kHz$ with an integration time of $T=7200s$. Orange points indicate the frequencies above half of the maximum, included in the analysis for this specific mass hypothesis.
• Figure 4: Magnitude of the Fourier-transformed magnetic field in the vicinity of the surviving point at $m_{A'}c^2/h = 1090.0303\,\mathrm{Hz}$. The scattered points show the absolute values of the Fourier coefficients in the $x$, $y$, and $z$ directions. The solid black line indicates the predicted signal amplitude in the $x$ direction for a dark photon with mixing parameter equal to the candidate’s maximum-likelihood value; the predicted $y$ amplitude has an identical shape but is lower by approximately $33\%$ and is not shown for visual clarity. Only a single frequency component in each of the $x$ and $y$ spectra lies noticeably above the surrounding noise.
• Figure 5: Measured conservative bound on the magnetic shielding factor in the frequency range 80--180 kHz, expressed as the ratio of magnetic field amplitude measured with the source outside the room to that measured with the source inside. Deviations below $\sim$100 kHz and narrow spectral features are caused by the limitation of the measured noise floor in the room.