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A new method of probing Lorentz invariance in the neutron sector is described. The method is baed on stable quartz bulk acoustic wave oscillators compared on a rotating table. Due to Lorentz-invariance violation, the resonance frequencies of acoustic wave resonators depend on the direction in space via a corresponding dependence of masses of the constituent elements of solids. This dependence is measured via observation of oscillator phase noise built around such devices. The first such experiment now shows sensitivity to violation down to the limit $\tilde{c}^n_Q=(-1.8\pm2.2)\times 10^{-14}$ GeV. Methods to improve the sensitivity are described together with some other applications of the technology in tests of fundamental physics.

We demonstrate that experiments measuring the transition energies of rare-earth ions doped in crystalline lattices are sensitive to violations of Local Lorentz Invariance and Einstein's Equivalence Principle. Using the crystal field of LaCl$_{3}$ as an example, we calculate the frame-dependent energy shifts of the transition frequencies between low-lying states of Ce$^{3+}$, Nd$^{3+}$, and Er$^{3+}$ dopants in the context of the Standard Model Extension, and show that they have high sensitivity to electron anomalies that break rotational invariance.

We consider the role of the internal kinetic energy of bound systems of matter in tests of the Einstein equivalence principle. Using the gravitational sector of the standard model extension, we show that stringent limits on equivalence principle violations in antimatter can be indirectly obtained from tests using bound systems of normal matter. We estimate the bound kinetic energy of nucleons in a range of light atomic species using Green's function Monte Carlo calculations, and for heavier species using a Woods-Saxon model. We survey the sensitivities of existing and planned experimental tests of the equivalence principle, and report new constraints at the level of between a few parts in $10^{6}$ and parts in $10^{8}$ on violations of the equivalence principle for matter and antimatter.

We propose using a Stark interference technique to directly measure the odd-parity c_0j components of the electron sector c_\mu\nu 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 report a joint test of local Lorentz invariance and the Einstein equivalence principle for electrons, using long-term measurements of the transition frequency between two nearly degenerate states of atomic dysprosium. We present many-body calculations which demonstrate that the energy splitting of these states is particularly sensitive to violations of both special and general relativity. We limit Lorentz violation for electrons at the level of $10^{-17}$, matching or improving the best laboratory and astrophysical limits by up to a factor of 10, and improve bounds on gravitational redshift anomalies for electrons by 2 orders of magnitude, to $10^{-8}$. With some enhancements, our experiment may be sensitive to Lorentz violation at the level of $9\times 10^{-20}$.

We present a consistent, generally covariant quantization of light for non-vacuum birefringent, Lorentz-symmetry breaking electrodynamics in the context of the Standard Model Extension. We find that the number of light quanta in the field is not frame independent, and that the interaction of the quantized field with matter is necessarily birefringent. We also show that the conventional Lorenz gauge condition used to restrict the photon-mode basis to solutions of the Maxwell equations must be weakened to consistently describe Lorentz symmetry violation.

The recent realization that atom interferometers (AIs) can be used to test the gravitational redshift tests has proven to be controversial in some quarters. Here, we address the issues raised against the interpretation of AIs as redshift tests, reaffirming the fact that Mueller et al. [Nature 463, 926 (2010)] indeed report a gravitational redshift test.

We review the physics of atoms and clocks in weakly curved spacetime, and how each may be used to test the Einstein Equivalence Principle (EEP) in the context of the minimal Standard Model Extension (mSME). We find that conventional clocks and matter-wave interferometers are sensitive to the same kinds of EEP-violating physics. We show that the analogy between matter-waves and clocks remains true for systems beyond the semiclassical limit. We quantitatively compare the experimentally observable signals for EEP violation in matter-wave experiments. We find that comparisons of $^{6}$Li and $^{7}$Li are particularly sensitive to such anomalies. Tests involving unstable isotopes, for which matter-wave interferometers are well suited, may further improve the sensitivity of EEP tests.

For most theories which parametrize modifications of General Relativity, including those which violate the equivalence principle, gravitational redshift tests typically offer weaker constraints on such test parameters than do precision measurements of the universality of free fall (UFF) and local Lorentz invariance (LLI). Although redshift anomalies are often linked with violations of UFF or LLI, they do not have to be. We offer a simple model in which particle masses anomalously vary with the gravitational potential. This generates gravitational redshift anomalies unconstrained by existing tests of UFF or LLI. We propose new experiments to limit such effects.

A recent measurement of the gravitational redshift was based on interference of matter waves. Operation in microgravity can improve it by a factor of $10^5$ and, in some models, even $10^{10}$.

We demonstrate that Michelson-Morley tests, which detect direction-dependent anisotropies in the speed of light, can also be used to place limits upon isotropic deviations of the vacuum speed of light from $c$, as described by the photon sector Standard Model Extension (SME) parameter $\tilde{\kappa}_{tr}$. A shift in the speed of light that is isotropic in one inertial frame implies anisotropic shifts in others. Using observer Lorentz covariance, we derive the time-dependent variations in the relative resonance frequencies of a pair of electromagnetic resonators that would be generated by such a shift in the rest frame of the Sun. A new analysis of a recent experimental test of relativity using this result constrains $\tilde{\kappa}_{tr}$ with a precision of $7.4\times10^{-9}$. This represents the first constraint on $\tilde{\kappa}_{tr}$ by a Michelson-Morley experiment and the first analysis of a single experiment to simultaneously set limits on all nine non-birefringent terms in the photon sector of the SME.

The absence of vacuum Cherenkov radiation for 104.5 GeV electrons and positrons at LEP combined with the observed stability of 300 GeV photons at the Tevatron constrains deviations of the speed of light relative to the maximal attainable speed of electrons. Within the Standard-Model Extension (SME), the limit $-5.8\times10^{-12} \leq \tilde{\kappa}_{\rm tr}-{4/3}c_e^{00} \leq 1.2\times10^{-11}$ is extracted, which sharpens previous bounds by more than 3 orders of magnitude. The potential for further refinements of this limit with terrestrial experiments and astrophysical observations is discussed.

We consider the possibility that Lorentz violation can generate differences between the limiting velocities of light and charged matter. Such effects would lead to efficient vacuum Cherenkov radiation or rapid photon decay. The absence of such effects for 104.5 GeV electrons at the Large Electron Positron collider and for 300 GeV photons at the Tevatron therefore constrains this type of Lorentz breakdown. Within the context of the standard-model extension, these ideas imply an experimental bound at the level of -5.8 x 10^-12 <= \tilde\kappa_tr-(4/3)c_e^00 <= 1.2 x 10^-11 tightening existing laboratory measurements by 3-4 orders of magnitude. Prospects for further improvements with terrestrial and astrophysical methods are discussed.

In an earlier paper [1] (hep-ph/0408006), the bound on the Standard Model Extension photon-sector parameter $\tilde{\kappa}_{tr}$ [2] (hep-ph/0205211) set by the heavy-ion storage-ring experiment of Saathoff et al. [3] was incorrectly reported. We show that the correct bound on $\tilde{\kappa}_{tr}$ which resulted from this experiment is in fact $2.2\times 10^{-7}$.