State-of-the-art optical oscillators based on lasers frequency stabilized to high finesse optical cavities are limited by thermal noise that causes fluctuations of the cavity length. Thermal noise represents a fundamental limit to the stability of an optical interferometer and plays a key role in modern optical metrology. We demonstrate a novel design to reduce the thermal noise limit for optical cavities by an order of magnitude and present an experimental realization of this new cavity system, demonstrating the most stable oscillator of any kind to date. The cavity spacer and the mirror substrates are both constructed from single crystal silicon and operated at 124 K where the silicon thermal expansion coefficient is zero and the silicon mechanical loss is small. The cavity is supported in a vibration-insensitive configuration, which, together with the superior stiffness of silicon crystal, reduces the vibration related noise. With rigorous analysis of heterodyne beat signals among three independent stable lasers, the silicon system demonstrates a fractional frequency stability of 1 × 10 −16 at short time scales and supports a laser linewidth of <40 mHz at 1.5 µm, representing an optical quality factor of 4 × 10 15 .

The advent of novel measurement instrumentation can lead to paradigm shifts in scientific research. Optical atomic clocks, due to their unprecedented stability 1,2,3 and uncertainty, 4,5,6,7 are already being used to test physical theories 8,9 and herald a revision of the International System of units (SI). 10,11 However, to unlock their potential for cross-disciplinary applications such as relativistic geodesy, 12 a major challenge remains. This is their transformation from highly specialized instruments restricted to national metrology laboratories into flexible devices deployable in different locations. 13,14,15 Here we report the first field measurement campaign performed with a ubiquitously applicable 87 Sr optical lattice clock. 13 We use it to determine the gravity potential difference between the middle of a mountain and a location 90 km apart, exploiting both local and remote clock comparisons to eliminate potential clock errors. A local comparison with a 171 Yb lattice clock 16 also serves as an important check on the international consistency of independently developed optical clocks. This campaign demonstrates the exciting prospects for transportable optical clocks.The application of clocks in geodesy fulfils long-standing proposals to interpret a measurement of the fractional relativistic redshift Δνrel/ν0 to determine the gravity potential difference ΔU = c 2 Δνrel/ν0 between clocks at two sites (c being the speed of light). 12 National geodetic height systems based on classical terrestrial and satellite-based measurements exhibit discrepancies at the decimetre level. 17 Optical clocks, combined with high performance frequency dissemination techniques 18,19 offer an attractive way to resolve these discrepancies, as they combine the advantage of high spectral resolution with small error accumulation over long distances. 18,20 However, to achieve competitive capability requires high clock performance: a fractional frequency accuracy of 1×10 17 corresponds to a resolution of about 10 cm in height. Furthermore, it is important to realize that the sideby-side frequency ratio has to be known to determine the remote frequency shift Δνrel. Taking the uncertainty budgets of optical clocks for granted, harbours the possibility of errors, because very few have been verified experimentally to the low 10 17 region or beyond. 5,7,18,21 A transportable optical clock not only increases the flexibility in measurement sites but mitigates the risk of undetected errors by enabling local calibrations to be performed.The test site chosen for our demonstration of chronometric levelling 12 with optical clocks was the Laboratoire Souterrain de Modane (LSM) in France, with the Italian metrology institute INRIM in Torino serving as the reference site. The height difference between the two sites is approximately 1000 m, corresponding to a fractional redshift of about 10 -13 . From a geodetic point of view, LSM is a challenging and interesting location in which to perform such measurements: firstly, it is located in the middl...

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.

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