Rotating optical cavity experiment testing Lorentz invariance at the ${10}^{-17}$ level

We present an improved laboratory test of Lorentz invariance in electrodynamics by testing the isotropy of the speed of light. Our measurement compares the resonance frequencies of two orthogonal optical resonators that are implemented in a single block of fused silica and are rotated continuously on a precision air bearing turntable. An analysis of data recorded over the course of one year sets a limit on an anisotropy of the speed of light of $\Delta c/c\sim 1\times {10}^{-17}$. This constitutes the most accurate laboratory test of the isotropy of $c$ to date and allows to constrain parameters of a Lorentz violating extension of the standard model of particle physics down to a level of ${10}^{-17}$.

Figure 1

Left: High-finesse fused silica resonators used in this experiment. Right: Basic principle of the experiment. The frequencies of two lasers, each stabilized to one of two orthogonal cavities, are compared during active rotation of the setup. (Photograph by E. Fesseler).

Figure 2

Allan deviation calculated from a comparison of the two stabilized laser frequencies (a) while the setup is rotating and (b) with a stationary non rotating setup.

Figure 3

Schematic of the complete rotating setup (top) and the custom-made vacuum chamber (bottom). $\mathrm{TS}=\mathrm{\text{Tilt Sensor}}$, $\mathrm{PDH}=\mathrm{\text{Pound-Drever-Hall}}$ laser stabilization electronics.

Figure 4

Results I. a): Cosine amplitudes $C$ (left) and Sine amplitudes $S$ (right) of a systematic beat frequency modulation at $2{\omega }_{\mathrm{tt}}$ for all $n=13384$ measurement subsets (10 rotations each). $t_0^{\prime }$ is set to an instant when one of the resonators is oriented along the North-South axis. b) $+$ c): Amplitudes of a superimposed $2{\omega }_{\oplus }$ (11.96 h) (b), respectively ${\omega }_{\oplus }$ (23.93 h) (c) modulation of $C$ and $S$, respectively, as expected for an anisotropy of $c$ fixed within a sidereal frame. Each point represents the amplitudes determined from a 23.93 h set of data. 64 such data sets are included. $t_0$ is set to an instant when the East-West axis of the laboratory coincides with the $Y$ axis of the adopted SCCEF reference frame. Error bars are omitted for the purpose of clarity except for one representative data point. d): Amplitudes $C_0$ and $S_0$ as modeled in Eqs. (6, 7), which are most prone to constant systematic effects (note the different scale). The mean values and standard errors [shown in red in (b), (c), and (d)] of the modulation amplitudes as modeled in Eqs. (6, 7) are $C_0=-0.2\pm 11.7$, $C_{s1}=15.5\pm 6.0$, $C_{c1}=-9$, $9\pm 7.2$, $C_{s2}=-1.5\pm 6.6$, $C_{c2}=4.0\pm 6.6$ and $S_0=-10.2\pm 14.4$, $S_{s1}=-3.1\pm 6.4$, $S_{c1}=-2$, $7\pm 8.1$, $S_{s2}=-5.0\pm 6.2$, $S_{c2}=-5.5\pm 6.7$ ($\mathrm{\text{all values}}\times {10}^{-18}$).

Figure 5

Results II. Data of Fig. 4 plotted vs time. As in Fig. 4 each point represents the amplitude determined from a 23.93 h set of data. See caption of Fig. 4 for more details.