Search for Axionlike Dark Matter Using Solid-State Nuclear Magnetic Resonance

We report the results of an experimental search for ultralight axionlike dark matter in the mass range 162–166 neV. The detection scheme of our Cosmic Axion Spin Precession Experiment is based on a precision measurement of ${}^{207}\mathrm{Pb}$ solid-state nuclear magnetic resonance in a polarized ferroelectric crystal. Axionlike dark matter can exert an oscillating torque on ${}^{207}\mathrm{Pb}$ nuclear spins via the electric dipole moment coupling $g_d$ or via the gradient coupling $g_{aNN}$. We calibrate the detector and characterize the excitation spectrum and relaxation parameters of the nuclear spin ensemble with pulsed magnetic resonance measurements in a 4.4 T magnetic field. We sweep the magnetic field near this value and search for axionlike dark matter with Compton frequency within a 1 MHz band centered at 39.65 MHz. Our measurements place the upper bounds $|g_d|<9.5\times {10}^{-4}{\mathrm{GeV}}^{-2}$ and $|g_{aNN}|<2.8\times {10}^{-1}{\mathrm{GeV}}^{-1}$ (95% confidence level) in this frequency range. The constraint on $g_d$ corresponds to an upper bound of $1.0\times {10}^{-21}e\mathrm{cm}$ on the amplitude of oscillations of the neutron electric dipole moment and $4.3\times {10}^{-6}$ on the amplitude of oscillations of $CP$-violating $\theta$ parameter of quantum chromodynamics. Our results demonstrate the feasibility of using solid-state nuclear magnetic resonance to search for axionlike dark matter in the neV mass range.

Figure 1

Experimental setup. (a) The sample was a cylindrical ferroelectric PMN-PT crystal with diameter 0.46 cm and thickness 0.50 cm. It was electrically polarized along the cylinder axis, indicated with the black arrow. The pickup coil and the cancellation coil were coaxial with the crystal, and the axis of the Helmholtz excitation coil was orthogonal. The vertical leading magnetic field $B_0$ set the direction of the equilibrium spin polarization. Coils were supported by G-10 fiberglass cylinders shown in gray and pink. (b) Electrical schematic, showing the excitation and pickup circuits. Excitation pulses generated with the digital-to-analog converter (DAC) were amplified ($A_e$) and coupled to the excitation coil via a tuned tank circuit that included matching and tuning capacitors, as well as a resistor to set the circuit quality factor. The pickup probe was also designed as a tuned tank circuit, coupling the voltage induced in the pickup coil to a low-noise cryogenic amplifier ($A_1$), whose output was filtered, further amplified, and digitized with an analog-to-digital converter (ADC). (c) Pulsed NMR sequence used for FID measurements. The spin-ensemble equilibrium magnetization, initially parallel to $B_0$, was tilted into the transverse plane by the excitation pulse. The FID signal was recorded after the excitation pulse, as the magnetization precessed and its transverse component decayed.

Figure 2

Sensitivity calibration. (a) Measurements of ${}^{207}\mathrm{Pb}$ FID following a spin excitation pulse of length $t_p=20\mathrm{ms}$. The excitation carrier frequency was set to 39.71 MHz, and the Rabi frequency was ${\mathrm{\Omega }}_e=0.88\mathrm{rad}/\mathrm{ms}$. The data points show the in-phase (blue circles) and the out-of-phase (orange squares) quadratures of the Fourier transform of the detected voltage, referred to the input of the pickup probe amplifier $A_1$. Data points were binned and averaged, the error bars show one standard deviation for each bin. The lines show the best-fit simulation of the spin response, with the light-colored narrow bands indicating the range of simulation results if parameters are varied by one standard deviation away from their best-fit values. We performed the fitting simultaneously to three FID datasets, with excitation-pulse lengths $t_p=0.2,2,20\mathrm{ms}$, with free parameters including the spin coherence time $T_2$ and pickup-circuit transfer coefficient $\alpha$ (see Supplemental Material [53]). (b) Measurement of the normalized ${}^{207}\mathrm{Pb}$ NMR excitation spectrum near Larmor frequency 39.71 MHz. Excitation pulses of length 1.6 ms and Rabi frequency ${\mathrm{\Omega }}_e=0.88\mathrm{rad}/\mathrm{ms}$ were delivered at the carrier frequencies shown on the $x$ axis. Data points show the amplitude of the spin FID response, normalized so that the integral of the spectrum is unity. The error bars indicate one standard deviation uncertainties of the FID spectrum fits. We model the excitation spectrum as a super-Gaussian of order 2 (red line) [53]. (c) Detector calibration for varying drive Rabi frequency. Data points show the amplitude of the spin FID response after an excitation pulse of length 20 ms, delivered at the carrier frequency 39.71 MHz, with Rabi frequency ${\mathrm{\Omega }}_e$ plotted on the $x$ axis. The error bars indicate one standard deviation uncertainties, obtained by grouping 100 consecutive FID measurements taken at each ${\mathrm{\Omega }}_e$ into five sets and independently analyzing each set [53]. The orange line shows the spin response simulated using the Bloch equations with parameters extracted from data in (a). (d) Measurement of ferroelectric hysteresis in the PMN-PT single crystal. The remanent polarization $P_r$ persists after the applied voltage has been ramped down to zero.

Figure 3

Results of the search for spin interactions with axionlike dark matter. (a) The axionlike dark matter EDM coupling (left $y$ axis) and nucleon gradient coupling (right $y$ axis) limits in the mass range 162–166 neV shown with a blue line. The shaded region above the line is excluded at 95% confidence level. The green region is excluded by analysis of cooling of the supernova SN1987A; the color gradient indicates theoretical uncertainty [16]. Existing bounds at other masses, as well as CASPEr sensitivity projections, are shown in Fig. S9 of the Supplemental Material [53]. (b) The histogram of the optimally filtered power spectral density of transverse sample magnetization within the frequency window centered at 39.16 MHz. The red line shows the Gaussian distribution model, and the vertical black dashed line shows the $3.355\sigma$ candidate threshold at $17{\mathrm{fT}}^2$.