Improved test of Lorentz Invariance in Electrodynamics using Rotating Cryogenic Sapphire Oscillators

We present new results from our test of Lorentz invariance, 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 ${\tilde{\kappa }}_{e-}$ and ${\tilde{\kappa }}_{o+}$ parameters from the photon sector of the standard model extension. Thus, we are able to place independent limits on all eight ${\tilde{\kappa }}_{e-}$ and ${\tilde{\kappa }}_{o+}$ 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 ${\tilde{\kappa }}_{e-}^{ZZ}$) 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 $P_{MM}=\delta -\beta +1\mathrm{/}2$ of $9.4(8.1)\times {10}^{-11}$, an improvement of a factor of 2.