Optical clocks show unprecedented accuracy, surpassing that of previously available clock systems by more than one order of magnitude. Precise intercomparisons will enable a variety of experiments, including tests of fundamental quantum physics and cosmology and applications in geodesy and navigation. Well-established, satellite-based techniques for microwave dissemination are not adequate to compare optical clocks. Here, we present phase-stabilized distribution of an optical frequency over 920 kilometers of telecommunication fiber. We used two antiparallel fiber links to determine their fractional frequency instability (modified Allan deviation) to 5 × 10(-15) in a 1-second integration time, reaching 10(-18) in less than 1000 seconds. For long integration times τ, the deviation from the expected frequency value has been constrained to within 4 × 10(-19). The link may serve as part of a Europe-wide optical frequency dissemination network.

Leveraging the unrivalled performance of optical clocks as key tools for geo-science, for astronomy and for fundamental physics beyond the standard model requires comparing the frequency of distant optical clocks faithfully. Here, we report on the comparison and agreement of two strontium optical clocks at an uncertainty of 5 × 10−17 via a newly established phase-coherent frequency link connecting Paris and Braunschweig using 1,415 km of telecom fibre. The remote comparison is limited only by the instability and uncertainty of the strontium lattice clocks themselves, with negligible contributions from the optical frequency transfer. A fractional precision of 3 × 10−17 is reached after only 1,000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than any previous long-distance clock comparison. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.

The comparison of different atomic transition frequencies over time can be used to determine the present value of the temporal derivative of the fine structure constant alpha in a model-independent way without assumptions on constancy or variability of other parameters, allowing tests of the consequences of unification theories. We have measured an optical transition frequency at 688 THz in 171Yb+ with a cesium atomic clock at 2 times separated by 2.8 yr and find a value for the fractional variation of the frequency ratio f(Yb)/f(Cs) of (-1.2+/-4.4)x10(-15) yr(-1), consistent with zero. Combined with recently published values for the constancy of other transition frequencies this measurement sets an upper limit on the present variability of alpha at the level of 2.0x10(-15) yr(-1) (1sigma), corresponding so far to the most stringent limit from laboratory experiments.

We have measured the frequency of the extremely narrow 1S-2S two-photon transition in atomic hydrogen using a remote cesium fountain clock with the help of a 920 km stabilized optical fiber. With an improved detection method we obtain f(1S-2S)=2466 061 413 187 018 (11)  Hz with a relative uncertainty of 4.5×10(-15), confirming our previous measurement obtained with a local cesium clock [C. G. Parthey et al., Phys. Rev. Lett. 107, 203001 (2011)]. Combining these results with older measurements, we constrain the linear combinations of Lorentz boost symmetry violation parameters c((TX))=(3.1±1.9)×10(-11) and 0.92c((TY))+0.40c((TZ))=(2.6±5.3)×10(-11) in the standard model extension framework [D. Colladay, V. A. Kostelecký, Phys. Rev. D. 58, 116002 (1998)].