To test Lorentz symmetry we used a 3He/129Xe co-magnetometer. We will give a short summary of our experimental setup and the results of our latest measurements. We obtained preliminary results for the equatorial component of the background field interacting with the spin of the bound neutron: b_n < 3.72 x 10^(-32) GeV (95 C.L.).
We report on the search for Lorentz violating sidereal variations of the frequency difference of co-located spin-species while the Earth and hence the laboratory reference frame rotates with respect to a relic background field. The co-magnetometer used is based on the detection of freely precessing nuclear spins from polarized 3He and 129Xe gas samples using SQUIDs as low-noise magnetic flux detectors. As result we can determine the limit for the equatorial component of the background field interacting with the spin of the bound neutron to be bn < 3.7 x 10^{-32} GeV (95 C.L.).
Signals of CPT and Lorentz violation are possible in the context of spectroscopy using hydrogen and antihydrogen. We apply the Standard-Model Extension, a broad framework for Lorentz breaking in physics, to various transitions in the hydrogen and antihydrogen spectra. The results show an unsuppressed effect in the transition between the upper two hyperfine sublevels of the ground state of these systems. We also discuss related tests in Penning traps, and recent work on Lorentz violation in curved spacetime.
All evidence so far suggests that the absolute spatial orientation of an experiment never affects its outcome. This is reflected in the Standard Model of physics by requiring all particles and fields to be invariant under Lorentz transformations. The most well-known test of this important cornerstone of physics are Michelson-Morley-type experimentscite{MM, Herrmann2009,Eisele2009} verifying the isotropy of the speed of light. Lorentz symmetry also implies that the kinetic energy of an electron should be independent of the direction of its velocity, textit{i.e.,} its dispersion relation should be isotropic in space. In this work, we search for violation of Lorentz symmetry for electrons by performing an electronic analogue of a Michelson-Morley experiment. We split an electron-wavepacket bound inside a calcium ion into two parts with different orientations and recombine them after a time evolution of 95ms. As the Earth rotates, the absolute spatial orientation of the wavepackets changes and anisotropies in the electron dispersion would modify the phase of the interference signal. To remove noise, we prepare a pair of ions in a decoherence-free subspace, thereby rejecting magnetic field fluctuations common to both ionscite{Roos2006}. After a 23 hour measurement, we limit the energy variations to $htimes 11$ mHz ($h$ is Plancks constant), verifying that Lorentz symmetry is preserved at the level of $1times10^{-18}$. We improve on the Lorentz-violation limits for the electron by two orders of magnitudecite{Hohensee2013c}. We can also interpret our result as testing the rotational invariance of the Coloumb potential, improving limits on rotational anisotropies in the speed of light by a factor of fivecite{Herrmann2009,Eisele2009}. Our experiment demonstrates the potential of quantum information techniques in the search for physics beyond the Standard Model.
We propose using a Stark interference technique to directly measure the odd-parity c_{0j} components of the electron sector c_{mu u} tensor of the Standard-Model Extension. This technique has been shown to be a sensitive probe of parity violation in atomic dysprosium in a low-energy, tabletop experiment, and may also be straightforwardly applied to test Lorentz invariance. We estimate that such an experiment may be sensitive to c_{0j} coefficients as small as 10^{-18}.
We consider the possibility of the scenario in which the $P$, $T$ and Lorentz symmetry of the relativistic quantum vacuum are all the combined symmetries. These symmetries emerge as a result of the symmetry breaking of the more fundamental $P$, $T$ and Lorentz symmetries of the original vacuum, which is invariant under separate groups of the coordinate transformations and spin rotations. The condensed matter vacua (ground states) suggest two possible scenarios of the origin of the combined Lorentz symmetry, both are realized in the superfluid phases of liquid $^3$He: the $^3$He-A scenario and the $^3$He-B scenario. In these scenarios the gravitational tetrads are considered as the order parameter of the symmetry breaking in the quantum vacuum. The $^3$He-B scenarios applied to the Minkowski vacuum leads to the continuous degeneracy of the Minkowski vacuum with respect to the $O(3,1)$ spin rotations. The symmetry breaking leads to the corresponding topological objects, which appear due to the nontrivial topology of the manifold of the degenerate Minkowski vacua, such as torsion strings. The 4-fold degeneracy of the Minkowski vacuum with respect to discrete $P$ and $T$ symmetries suggests that the Weyl fermions are described by four different tetrad fields: the tetrad for the left-handed fermions, the tetrad for the right-handed fermions, and the tetrads for their antiparticles. This may lead to the gravity with several metric fields, so that the parity violation may lead to the breaking of equivalence principle. Finally we considered the application of the gravitational tetrads for the solution of the cosmological constant problem.