We report on two ultrastable lasers each stabilized to independent silicon Fabry-Pérot cavities operated at 124 K. The fractional frequency instability of each laser is completely determined by the fundamental thermal Brownian noise of the mirror coatings with a flicker noise floor of $4\times {10}^{-17}$ for integration times between 0.8 s and a few tens of seconds. We rigorously treat the notorious divergences encountered with the associated flicker frequency noise and derive methods to relate this noise to observable and practically relevant linewidths and coherence times. The individual laser linewidth obtained from the phase noise spectrum or the direct beat note between the two lasers can be as small as 5 mHz at 194 THz. From the measured phase evolution between the two laser fields we derive usable phase coherence times for different applications of 11 to 55 s.

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.

We present a laser system based on a 48 cm long optical glass resonator. The large size requires a sophisticated thermal control and optimized mounting design. A self-balancing mounting was essential to reliably reach sensitivities to acceleration of below $\mathrm{\Delta }\nu /\nu <2\times {10}^{-10}/\mathrm{g}$ in all directions. Furthermore, fiber noise cancellations from a common reference point near the laser diode to the cavity mirror and to additional user points (Sr clock and frequency comb) are implemented. Through comparison with other cavity-stabilized lasers and with a strontium lattice clock, instability of below $1\times {10}^{-16}$ at averaging times from 1 to 1000 s is revealed.

We present a transportable optical clock (TOC) with ${}^{87}\mathrm{Sr}$. Its complete characterization against a stationary lattice clock resulted in a systematic uncertainty of $7.4\times {10}^{-17}$, which is currently limited by the statistics of the determination of the residual lattice light shift, and an instability of $1.3\times {10}^{-15}/\sqrt{\tau }$ with an averaging time $\tau$ in seconds. Measurements confirm that the systematic uncertainty can be reduced to below the design goal of $1\times {10}^{-17}$. To our knowledge, these are the best uncertainties and instabilities reported for any transportable clock to date. For autonomous operation, the TOC has been installed in an air-conditioned car trailer. It is suitable for chronometric leveling with submeter resolution as well as for intercontinental cross-linking of optical clocks, which is essential for a redefinition of the International System of Units (SI) second. In addition, the TOC will be used for high precision experiments for fundamental science that are commonly tied to precise frequency measurements and its development is an important step to space-borne optical clocks.