A clock comparison experiment, analyzing the ratio of spin precession frequencies of stored ultracold neutrons and 199 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 ⊥ < 2 × 10 −20 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 |gn| < 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 |gn| < 3 × 10 −4 eV/c 2 m.PACS numbers: 14.20. Dh, 11.30.Er, 11.30.Cp, Lorentz symmetry is a fundamental hypothesis of our current understanding of physics and is central to the foundations of the Standard Model of particle physics (SM). However, the SM is widely believed to be only the low energy limit of some more fundamental theory, a theory which will probably violate more symmetries than the SM, in order to accomodate some features of the universe currently lacking in the SM, e.g., the baryon asymmetry. A SM extension including Lorentz and CPT violating terms has been presented in [1]. It provides a parametrisation of effects suitable to be tested by low energy precision experiments. In particular, clock comparison experiments [2, 3] have proven to be particularly sensitive to spin-dependent effects arising from a so-called cosmic spin anisotropy fieldb filling the whole universe. This Letter reports on a search for such an exotic field via its coupling to free neutrons.In the presence of a fieldb, the two spin states of the neutron will encounter an extra contribution to the energy splitting corresponding to the potential V = σ ·b where σ are the Pauli matrices. Thus, if a neutron is subjected to both a static magnetic field B and the new field b, its spin will precess at the modified Larmor frequency f n , which to first order inb is given byWe searched for a sidereal modulation (at a period of 23.934 hours) of the neutron Larmor frequency induced by b ⊥ , the component ofb orthogonal to the Earth's rotation axis. The experiment is also sensitive to a possible influence of the Sun on the spin precession dynamics, leading to a solar modulation (at a period of 24 h) of the Larmor frequency, as proposed in [4]. Such an effect could arise from a non-standard spin-dependent component of gravity [5,6] or from another long-range spindependent force [7,8]. In particular, a non-zero neutron gravitational dipole moment g n would induce a coupling through (see also [9])where G is Newton's constant, and for the mass M and
