Test of Special Relativity Using a Fiber Network of Optical Clocks

Phase compensated optical fiber links enable high accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution. By searching for a daily variation of the frequency difference between four strontium optical lattice clocks in different locations throughout Europe connected by such links, we improve upon previous tests of time dilation predicted by special relativity. We obtain a constraint on the Robertson-Mansouri-Sexl parameter $|\alpha |\lesssim 1.1\times {10}^{-8}$, quantifying a violation of time dilation, thus improving by a factor of around 2 the best known constraint obtained with Ives-Stilwell type experiments, and by 2 orders of magnitude the best constraint obtained by comparing atomic clocks. This work is the first of a new generation of tests of fundamental physics using optical clocks and fiber links. As clocks improve, and as fiber links are routinely operated, we expect that the tests initiated in this Letter will improve by orders of magnitude in the near future.

Figure 1

Allan deviation of the fractional frequency difference between SYRTE’s clocks Sr2 and SrB and NPL’s Sr clock. After less than one day, the instability of the fractional frequency difference averages down to a few ${10}^{-17}$. This frequency instability is solely limited by the performances of the clocks, as the fiber link between SYRTE and NPL shows a fractional frequency instability of $1\times {10}^{-18}$ at 1000 s.

Figure 2

Correlations and histograms of the parameters of model (7) in fit $C$ of Table 1, corresponding to the NPL-SYRTE comparison data from Sr2 and SrB combined, using the MCMC fitting method with $10^5$ points.

Figure 3

Correlations and histograms of the parameters of fit $D$ of Table 1, corresponding to the fit of the PTB-SYRTE comparison data, using the MCMC fitting method with $10^5$ points.