Search for Axionlike Dark Matter with a Liquid-State Nuclear Spin Comagnetometer

We report the results of a search for axionlike dark matter using nuclear magnetic resonance (NMR) techniques. This search is part of the multifaceted Cosmic Axion Spin Precession Experiment program. In order to distinguish axionlike dark matter from magnetic fields, we employ a comagnetometry scheme measuring ultralow-field NMR signals involving two different nuclei (${}^{13}\mathrm{C}$ and ${}^1\mathrm{H}$) in a liquid-state sample of acetonitrile-2-${}^{13}\mathrm{C}$ (${}^{13}\mathrm{C}{\mathrm{H}}_3\mathrm{CN}$). No axionlike dark matter signal was detected above the background. This result constrains the parameter space describing the coupling of the gradient of the axionlike dark matter field to nucleons to be $g_{aNN}<6\times {10}^{-5}{\mathrm{GeV}}^{-1}$ (95% confidence level) for particle masses ranging from ${10}^{-22}\mathrm{eV}$ to $1.3\times {10}^{-17}\mathrm{eV}$, improving over previous laboratory limits for masses below ${10}^{-21}\mathrm{eV}$. The result also constrains the coupling of nuclear spins to the gradient of the square of the axionlike dark matter field, improving over astrophysical limits by orders of magnitude over the entire range of particle masses probed.

Figure 1

(a) The energy level diagram and the ZULF-NMR spectrum of acetonitrile-2-${}^{13}\mathrm{C}$. $F$ is the quantum number of the total nuclear angular momentum. The spectrum has features at frequencies corresponding to $J_{\mathrm{CH}}$ ($\sim 140\mathrm{Hz}$, red) and $2J_{\mathrm{CH}}$ ($\sim 280\mathrm{Hz}$, green). $\mathrm{\Delta }{\nu }_{1,2}$ are the frequency splittings used to realize the comagnetometer. (b) The direction of the expected average axion wind velocity. In galactic coordinates, the Sun is moving towards the Cygnus constellation (90° longitude and 0° latitude). The direction of the expected axion wind velocity is 270° longitude and 0° latitude. The celestial coordinates are shown in black, and the lab coordinates are shown in purple. For celestial coordinates, the $Z$ direction is the Earth’s rotating axis. For lab coordinates, the $z$ axis is the direction of the applied magnetic field. $\chi$ is the angle between $z$ and $Z$ [38].

Figure 2

The amplitude spectrum of the measured $\mathrm{\Delta }\mathcal{R}$ (black line). Under the hypothesis assuming no axion, the mean of the amplitude spectrum of the collection of Monte Carlo–generated datasets is shown in the green line. The blue and orange lines depict the false-alarm thresholds corresponding to the amplitude necessary to reach the global $p$ values at $5\sigma$ level and 95% confidence level at each frequency, respectively.

Figure 3

Limits on the coupling of nucleons with the gradient of the axion field (a) and with the gradient of the square of the axion field (b). The red region shows the parameter space excluded by this Letter (CASPEr ZULF comagnetometer) at the 95% confidence level. The region excluded by the PSI neutron EDM experiment is shown in light blue and is surrounded by black dashed line [32]. The improved region obtained with this work is depicted with black slash lines. The dashed red line shows the projected sensitivity of our system using PHIP (parahydrogen-induced polarization, with a projected ${10}^5$ enhancement factor in the signal to noise ratio) [59]. The orange region shows the limits given by the CASPEr ZULF sideband experiment [37], including the projected sensitivity (dashed orange line). Other shaded regions depict constraints from supernova energy-loss bounds (SN1987A, green) [56, 57], and laboratory searches for new spin-dependent forces (yellow, 95% confidence level) [58].