Precision Microwave Oscillators and Interferometers to Test Lorentz Invariance in Electrodynamics (an Update)

We present latest results from two complementary tests of Lorentz invariance in electrodynamics. The first test of is an even parity test, which compares two orthogonal cryogenic sapphire microwave oscillators rotating in the lab. We have now acquired over 1 year of data, allowing us to avoid the short data set approximation (less than 1 year) that assumes no cancelation occurs between the k_e_ and k₀₊ parameters from the photon sector of the standard model extension. Thus, we are able to place independent limits on all eight k_e_ and k₀₊ parameters. Our results represents up to a factor of 10 improvement over previous non rotating measurements (which independently constrained 7 parameters), and is a slight improvement (except for k^zz _e_₎ over results from previous rotating experiments that assumed the short data set approximation. Also, an analysis in the Robertson-Mansouri-Sexl framework allows us to place a new limit on the isotropy parameter P_MM = delta - beta + 1#2 of 9.4(8.1) x 10^-11, an improvement of a factor of 2. The second test is a rotating odd parity test, which compares the phase shift of two oneway propagating waves that experience different permeability over the length of propagation. A sensitive carrier suppression microwave interferometer is used to obtain highly sensitive phase comparison using a Mach-Zedner configuration. This experiment is sensitive to the isotropic Lorentz violating parameter k_tr, and is the first rotating experiment of this type. We show here that the first operation of this experiment should set a limit of order 10^-7.