Search for Spin-Dependent Gravitational Interactions at Earth Range

Among the four fundamental forces, only gravity does not couple to particle spins according to the general theory of relativity. We test this principle by searching for an anomalous scalar coupling between the neutron spin and the Earth’s gravity on the ground. We develop an atomic gas comagnetometer to measure the ratio of nuclear spin-precession frequencies between ${}^{129}\mathrm{Xe}$ and ${}^{131}\mathrm{Xe}$, and search for a change of this ratio to the precision of ${10}^{-9}$ as the sensor is flipped in Earth’s gravitational field. The null results of this search set an upper limit on the coupling energy between the neutron spin and the gravity on the ground at $5.3\times {10}^{-22}\mathrm{eV}$ (95% confidence level), resulting in a 17-fold improvement over the previous limit. The results can also be used to constrain several other anomalous interactions. In particular, the limit on the coupling strength of axion-mediated monopole-dipole interactions at the range of Earth’s radius is improved by a factor of 17.

Figure 1

(a) Illustration of the experimental setup. The comagnetometer is mounted on a system of a horizontally placed rotation table (No. 1), a tilt table, and a tilted rotation table (No. 2). (b) Coordinate systems of the setup. The $x\text{−}y\text{−}z$ system is defined by the geographical orientations, and corresponds to table No. 1; similarly, the $x^{\prime }\text{−}{y}^{\prime }\text{−}{z}^{\prime }$ system corresponds to table No. 2. ${\mathbf{\Omega }}_E$ is contained in the $y\text{−}z$ plane by definition, and tilted by ${\theta }_L=31.82°$ above the $z$ axis. ${\mathbf{B}}_0$ forms a small angle $\beta$ with the $x^{\prime }\text{−}{z}^{\prime }$ plane, and its projection on $x^{\prime }\text{−}{z}^{\prime }$ forms an angle $\alpha$ with $z^{\prime }$.

Figure 2

(a) Frequency-ratio amplitude $R_{\mathrm{amp}}$ as a function of $\phi$. For each data point, in order to determine the amplitude, $R$ is measured at 13 positions of $\alpha$, costing a measurement time of 26 h. (b) Frequency ratio $R$ as a function of $\alpha$ with $\phi =0$ and $\beta +\psi ={\theta }_L$. $R$ is shown as $\delta R(\alpha )=R(\alpha )-\overline{R(\alpha )}$. Each data point takes 2 h to collect. The red lines in both plots are fitting results. ${\phi }_0$ and ${\alpha }_0$ are offset angles. The data in both plots are taken with $B_0=2.32\mathrm{\mu }\mathrm{T}$ and $T=110°\mathrm{C}$.

Figure 3

(a) All the data collected in the search for anomalous couplings. Each data point represents an average result from 16 experiment cycles taken in over 60 min. The weighted average of all data is ${\mathrm{\Omega }}_m/2\pi =11605.2\pm 2.5$ (stat) nHz, with the reduced ${\chi }^2$ as 1.2. (b) Studies of systematic effects by varying the bias field, cell temperature, pump beam powers, etc. The weighted average of all data is given in the window “All.” In both (a) and (b), the red lines mark the recommended value of Earth’s rotation frequency.

Figure 4

The upper limits (95% CL) on the monopole-dipole coupling constants $|g_s^N{g}_p^n|/\hslash c$. Line 1 is based on a ${}^3\mathrm{He}\text{−}{}^{129}\mathrm{Xe}$ comagnetometer [38]; line 2 uses a self-compensating ${}^3\mathrm{He}\text{−}\mathrm{K}$ comagnetometer [20]; line 3 is from the analysis of astronomical observation [21, 39]; line 4 is from the spectroscopy of trapped ${\mathrm{Be}}^{+}$ ions [14]; line 5 is from a ${}^{199}\mathrm{Hg}\text{−}{}^{201}\mathrm{Hg}$ comagnetometer [17]; and line 6 is from this Letter.