Test of Lorentz Invariance with Spin Precession of Ultracold Neutrons

A clock comparison experiment, analyzing the ratio of spin precession frequencies of stored ultracold neutrons and ${}^{199}\mathrm{Hg}$ atoms, is reported. No daily variation of this ratio could be found, from which is set an upper limit on the Lorentz invariance violating cosmic anisotropy field $b_{\perp }<2\times {10}^{-20}\mathrm{eV}$ (95% C.L.). This is the first limit for the free neutron. This result is also interpreted as a direct limit on the gravitational dipole moment of the neutron $|g_n|<0.3\mathrm{eV}/c^2\mathrm{m}$ from a spin-dependent interaction with the Sun. Analyzing the gravitational interaction with the Earth, based on previous data, yields a more stringent limit $|g_n|<3\times {10}^{-4}\mathrm{eV}/c^2\mathrm{m}$.

Figure 1

Vertical cut through the cylindrical precession chamber for UCN and ${}^{199}\mathrm{Hg}$. Schematically indicated are the $\approx 70\mathrm{mm}$ diameter Cs vapor filled bulbs and their mounts. The scalar Cs magnetometer measures the magnitude of $B$ found at the center of the spherical bulb.

Figure 2

The upper figure shows the variation of the ratio $R$ around its average. For clarity, the data are folded modulo 24 hours and binned every half hour. The lower figure shows modulus of the discrete Fourier Transform of the same data set. The line would be evidence that this frequency is too much represented as compared with a white noise.