Tests of Lorentz Invariance using a Microwave Resonator

The frequencies of a cryogenic sapphire oscillator and a hydrogen maser are compared to set new constraints on a possible violation of Lorentz invariance. We determine the variation of the oscillator frequency as a function of its orientation (Michelson-Morley test) and of its velocity (Kennedy-Thorndike test) with respect to a preferred frame candidate. We constrain the corresponding parameters of the Mansouri and Sexl test theory to $\delta -\beta +1/2=(1.5\pm 4.2)\times {10}^{-9}$ and $\beta -\alpha -1=(-3.1\pm 6.9)\times {10}^{-7}$ which is of the same order as the best previous result for the former and represents a 30-fold improvement for the latter.

Figure 1

Typical relative frequency stability of the CSO H-maser difference after removal of a linear frequency drift. The inset is a schematic drawing of the cylindrical sapphire oscillator with the Poynting vector $\mathbf{P}$ in the whispering gallery (WG) mode, the velocity $\mathbf{v}(t)$ of the cylinder with respect to the CMB, and the relevant angles for a photon in the WG mode.

Figure 2

Measured relative frequency difference between the CSO and the hydrogen maser after removal of the adjusted offsets and rates, and best fit model (3) of Lorentz invariance violation (solid line). The inset shows a subset of the data (days 283 to 293) after premultiplication of the data and the model by the weighting matrix of the WLS adjustment (for presentation purposes data points were averaged by a factor of 2). The error bar is the maximum signal amplitude within the final $1\sigma$ uncertainties of the parameters.