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 ${}^{199}$Hg atoms is reported. %57 No daily variation of this ratio could be found, from which is set an upper limit on the Lorentz invariance violating cosmic anisotropy field $b_{\bot} < 2 \times 10^{-20} {\rm eV}$ (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 $\mathrm{\mid }{g}_n\mathrm{\mid }<0.3$eV/$c^2$ 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} $eV\mathrm{/}$c^2 $m.