Nuclear-Spin Comagnetometer Based on a Liquid of Identical Molecules

Atomic comagnetometers are used in searches for anomalous spin-dependent interactions. Magnetic field gradients are one of the major sources of systematic errors in such experiments. Here we describe a comagnetometer based on the nuclear spins within an ensemble of identical molecules. The dependence of the measured spin-precession frequency ratio on the first-order magnetic field gradient is suppressed by over an order of magnitude compared to a comagnetometer based on overlapping ensembles of different molecules. Our single-species comagnetometer is capable of measuring the hypothetical spin-dependent gravitational energy of nuclei at the ${10}^{-17}\mathrm{eV}$ level, comparable to the most stringent existing constraints. Combined with techniques for enhancing the signal such as parahydrogen-induced polarization, this method of comagnetometry offers the potential to improve constraints on spin-gravity coupling of nucleons by several orders of magnitude.

Figure 1

Experimentally measured $J$-coupling spectrum of acetonitrile-2-${}^{13}\mathrm{C}$ (${}^{13}{\mathrm{CH}}_3\mathrm{CN}$) in a 100 nT bias field along $z$. The top and bottom traces show the split spectrum at $J_{\mathrm{CH}}$ and $2J_{\mathrm{CH}}$, respectively. The related transitions used for comagnetometry are shown with solid red arrows.

Figure 2

Experimental demonstration of comagnetometry with an ensemble of identical molecules. (a) The measurements were taken while an oscillating magnetic field was applied along $z$ (see text). The red solid lines are the fitted curves. (b) The calculated $\mathrm{\Delta }{\nu }_2/\mathrm{\Delta }{\nu }_1$ based on (a) with a reduced ${\chi }^2$ of 1.09. The average value of $\mathrm{\Delta }{\nu }_2/\mathrm{\Delta }{\nu }_1$ (red dashed line) is 0.700 88(4). The inset shows the histogram of $\mathrm{\Delta }{\nu }_2/\mathrm{\Delta }{\nu }_1$ which follows a Gaussian distribution.

Figure 3

Comparison of the normalized frequency ratios between a single-species comagnetometer (red star, $\mathrm{\Delta }{\nu }_2/\mathrm{\Delta }{\nu }_1$) and two dual-species comagnetometers (black square, ${\nu }_h/\mathrm{\Delta }{\nu }_1$, black circle, ${\nu }_h/\mathrm{\Delta }{\nu }_2$, discussed in the text). All the data are taken with the same acetonitrile-2-${}^{13}\mathrm{C}$ (with $\sim 1\%$ water) and are normalized with the theoretical values at zero magnetic field gradient. (a) The normalized frequency ratio as a function of the gradient $d{B}_z/dy$, with constant bias magnetic field $B_z=100\mathrm{nT}$. The solid lines are the linearly fitted curves. (b) The normalized frequency ratios as a function of bias magnetic fields $B_z$, with constant gradient ${dB}_z/dy=-3\mathrm{nT}/\mathrm{cm}$. The solid line is the fitted curve based on $B_z^{-1}$. Each point is an average of eight measurements.