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A new test of Lorentz invariance in the weak interactions has been made by searching for variations in the decay rate of spin-polarized 20 Na nuclei. This test is unique to Gamow-Teller transitions, as was shown in the framework of a recently developed theory that assumes a Lorentz symmetry breaking background field of tensor nature. The nuclear spins were polarized in the up and down direction, putting a limit on the amplitude of sidereal variations of the form jðÀ up À À down Þj=ðÀ up þ À down Þ < 3  10 À3 . This measurement shows a possible route toward a more detailed testing of Lorentz symmetry in weak interactions.Lorentz invariance means that physical laws are independent of boosts and rotations. It is at the basis of all known interactions. In the weak sector relatively few tests of Lorentz invariance have been made, even though the understanding of the weak interactions has been crucial in developing the standard model. In this work we consider a new test that exploits the spin degrees of freedom in decay, searching for a dependence of the nuclear lifetime on the orientation of the nucleus. Recent theoretical work [1] enables relating the present test to other possible Lorentz symmetry tests in the weak interactions and put them in the overall framework developed by Kostelecký and coworkers [2]. Tests whether in neutral-meson [3] or neutrino [4] oscillations the combination of charge conjugation, parity and time reversal is conserved and tests of relativity exploiting the beta-decay endpoint spectrum [5] also concern the weak domain, however, they differ in nature.We write the relative variation in the -decay rate À asHere, À 0 is the standard model decay rate, with the velocity vector of the particle in units of the speed of light. The nuclear polarization of the parent nucleus is hĨi=I. A is the -asymmetry parameter in the standard model that violates parity. Other parameters in the decay of spin-polarized nuclei [1] are not relevant for this work. Lorentz invariance violation (LIV) appears in Eq. (1) with magnitudes 1

A single trapped Ra + (Z = 88) ion provides a very promising route towards a most precise measurement of Atomic Parity Violation (APV), since APV effects grow faster than Z 3 . This experiment promises the best determination of the electroweak coupling constant at the lowest accessible energies. Such a measurement provides a sensitive test of the Standard Model in particle physics. At the present stage of the experiment, we focus on trapping and laser cooling stable Ba + ions as a precursor for radioactive Ra + . Online laser spectroscopy of the isotopes 209−214 Ra + in a linear Paul trap has provided information on transition wavelengths, fine and hyperfine structures and excited state lifetimes as test of atomic structure calculations. Additionaly, a single trapped Ra + ion could function as a very stable clock.

Lorentz invariance has been tested rather poorly on the weak interaction in comparison to the electromagnetic interaction. This work discusses which tests on the weak interaction may be relevant. In particular, it considers exploiting the spin degrees of freedom in β decay for testing rotational invariance. The relation between the various phenomenological tests of Lorentz invariance is shown using a new theoretical framework.

Results of optical frequency transfer over a carrier-grade dense-wavelength-division-multiplexing (DWDM) optical fibre network are presented. The relation between soil temperature changes on a buried optical fibre and frequency changes of an optical carrier through the fibre is modelled. Soil temperatures, measured at various depths by the Royal Netherlands Meteorology Institute (KNMI) are compared with observed frequency variations through this model. A comparison of a nine-day record of optical frequency measurements through the 2 × 298 km fibre link with soil temperature data shows qualitative agreement. A soil temperature model is used to predict the link stability over longer periods (days-months-years). We show that one-way optical frequency dissemination is sufficiently stable to distribute and compare e.g. rubidium frequency standards over standard DWDM optical fibre networks.