Session K3: Focus Session: Tests of Lorentz Invariance

Studying Gravity and Gravitational Waves with Atom Interferometry

Local Lorentz Invariance (LLI) has been thoroughly tested for the Standard Model fields, but not for gravity.~ Using an atom interferometer, we have tested the LLI of gravity by searching for anomalous variations in gravity as the Earth revolves. Expressed within the Standard Model extension, this constrains violations of LLI in gravity to within parts per billion. Another pillar of gravitational theory is Local Position Invariance (LPI): the outcome of a nongravitational experiment is independent of where and when it is performed. One of LPI's central consequences is the gravitational redshift, which has so far been measured to an accuracy of 7$\times $10$^{-5}$. We show that atom interferometry confirms the predicted effect within an accuracy of 7$\times $10$^{-9}$, a 10,000 fold improvement. Finally, we show that breakthroughs in atom interferometry can enable the detection of gravitational waves in the Hz frequency range, where LIGO is insensitive. In particular, we will present Large Momentum Transfer in atom interferometers using Bragg diffraction and Bloch oscillations. We have already observed interference with transfer of 24 photon momenta and anticipate reaching 100, meeting the requirements for gravitational wave detection.   

New limits on spin-dependent Lorentz and CPT-violating interactions

Violation of Lorentz symmetry naturally arises in many extensions of the Standard Model aiming to include quantum gravity. One of the recurring features of such models is a coupling to particle spins violating local Lorentz invariance. I will describe new constraints placed on such coupling for neutrons using a K-$^3$He co-magnetometer. The co-magnetometer measures the difference between spin interactions of electrons and $^3$He nuclei, effectively eliminating the effects of ordinary magnetic fields. By rotating the co-magnetometer apparatus every 20 sec relative to a preferred frame we are also able to eliminate long term drifts and gyroscopic signal due to Earth rotation. We place limits on neutron interaction energy with a background Lorentz-violating field below 10$^{-32}$ GeV, which represents the most sensitive test of Lorentz and CPT symmetry for fermions, improving previous limits by more than an order of magnitude.   

Recent Results on Lorentz Violation in Atomic Experiments

Tests of Lorentz symmetry provide a potential means of detecting new physics originating at the Planck scale. The effects of hypothetical violations of Lorentz symmetry in experiments performed at presently accessible energies are described by the Standard-Model Extension (SME). In this talk, I will discuss recently proposed tests of Lorentz symmetry based on an investigation of gravitational couplings in the matter sector of the SME. Atom interferometers, torsion pendula, and falling antimatter are among the systems that can attain new sensitivities.   

Testing the Lorentz Invariance of Light with a Birefringent Cavity

We report on the progress of a novel experimental test of the isotropy of $c$, based on measuring the birefringence of a single optical cavity. Tests of the isotropy of $c$ typically compare the phase velocities of two orthogonally propagating optical modes. Using pairs of high-finesse optical cavities, such tests have constrained direction-dependent variations in the speed of light to the level of parts per $10^{17}$ [1-2]. The precision of these tests is presently limited by systematic stochastic fluctuations in the relative length of such cavities. We have developed an experiment which compares the phase velocities of two orthogonally polarized optical modes in a single high-finesse dielectric-filled optical cavity. Since anisotropies in $c$ can make otherwise isotropic materials optically birefringent [3-4], we anticipate that we will be able to place significantly tighter constraints on Lorentz violation for photons. \\[4pt] [1] S. Herrmann, A. Senger, K. M\"ohle, M. Nagel, E.V. Kovalchuk and A. Peters, PRD 80, 105011 (2009).\newline [2] Ch. Eisel, A. Yu. Nevsky, and S. Schiller, PRL 103, 090401 (2009).\newline [3] H. M\"uller, PRD 71, 045004 (2005).\newline [4] V.A. Kosteleck\'y and M. Mewes, PRD 80, 015020 (2009).   

Lorentz Symmetry Effects Connected with Cosmological Expansion

The possible extension of the laws of physics beyond the Standard Model and into deviations from Lorentz and Poincar\'e symmetries leads to a search for observable tests, both local and cosmological. I discuss the consequences for Lorentz symmetry of a hyperbolic cosmological geometry expanding in cosmic time. The high symmetry of the cosmic background radiation suggests that the expanding geometry approximates very closely to hyperbolic 3-space symmetry. The Lorentz symmetry under velocity boosts will then be supplemented by a second Lorentz-like symmetry in hyperbolic position space, with its own boost-like operator depending not on the ratio $\delta \bf{v}/c$ but on $\delta \bf{r}/ct_{\mbox{H}}$, where $t_{\mbox{H}}$ is the Hubble time. The spatial curvature entails new angular momentum effects. Lorentz symmetry is preserved and enhanced, but the spatial curvature brings in new operators permitting very weak transitions that would be totally forbidden under the zero curvature symmetry of the Poincar\'e group of Minkowski space-time. A coupling operator appears that depends on the product $(\delta \bf{v}/c) \cdot (\delta \bf{r}/ct_{\mbox{H}})$, suggesting more general operators $(\delta \bf{v}/c) \cdot (\delta \bf{r}/l_{\mbox{curv}}$, where $ l_{\mbox{curv}}$ is a local curvature length. The nature of the Poincar\'e symmetries that may be weakened will be explored. (See also a poster at this meeting, ``Group Theory of Lorentz Symmetry in the Cosmological Expansion.'')   

A Test of CPT and Lorentz Violation Using a Compact, Rotating Co-Magnetometer

The K-$^3$He co-magnetometer contains overlapping, coupled ensembles of high-density polarized K vapor and $^3$He nuclei that cancel external magnetic fields by a factor of $10^3-10^4$, but remain sensitive to anomalous electron and neutron spin couplings. A compact three-layer $\mu$-metal and inner ferrite shield further reduce magnetic interactions by a factor of $10^8$. The co-magnetometer, including lasers and a vibration isolation platform, are operated in a 1 Torr vacuum to achieve equivalent sensitivity of 2 fT/$\sqrt{\mbox{Hz}}$ at 0.02 Hz. We mount the vacuum bell jar and control electronics on a rotating platform allowing 180$^\circ$ reversals of the apparatus every 22 seconds. Since the co-magnetometer is also a sensitive gyroscope, Earth's rotation contributes significantly to our signal. We collect data in the North-South and East-West orientations, corresponding to the maximum and zero of the gyroscopic signal which are susceptible to different systematic effects. A sidereal, out-of-phase modulation in the two signals would provide evidence for a Lorentz violating field. We have automated the experiment to run 24 hours a day and achieved uninterrupted operation over several weeks. We have achieved more than an order of magnitude improvement in sensitivity to anomalous neutron coupling relative to existing limits.   

2010 Data Tables for Lorentz and CPT Violation

Recent bounds on coefficients for Lorentz violation include ones in the gravitational sector using AMO techniques. We discuss these and other tests of interest, as tabulated in arXiv:0801.0287v3.