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.

https://science.sciencemag.org/content/sci/336/6080/441.full.pdf

A 920-Kilometer Optical Fiber Link for Frequency Metrology at the 19th Decimal Place

Three distinct techniques exist for distributing an ultrastable frequency reference over optical fibers. For the distribution of a microwave frequency reference, an amplitude-modulated continuous wave (cw) laser can be used. Over kilometer-scale lengths this approach provides an instability at 1 s of ∼3×10−14 without stabilization of the fiber-induced noise and ∼1×10−14 with active noise cancellation. An optical frequency reference can be transferred by directly transmitting a stabilized cw laser over fiber and then disseminated to other optical and microwave regions using an optical frequency comb. This provides an instability at 1 s of 2×10−14 without active noise cancellation and 3×10−15 with active noise cancellation [Recent results reduce the instability at 1 s to 6×10−18.] Finally, microwave and optical frequency references can be simultaneously transmitted using an optical frequency comb, and we expect the optical transfer to be similar in performance to the cw optical frequency transfer. The insta...

Remote transfer of ultrastable frequency references via fiber networks

We present theoretical predictions and experimental measurements for the achievable phase noise, timing jitter, and frequency stability in the coherent transport of an optical frequency over a fiber-optic link. Both technical and fundamental limitations to the coherent transfer are discussed. Measurements of the coherent transfer of an optical carrier over links ranging from 38 to 251 km demonstrate good agreement with theory. With appropriate experimental design and bidirectional transfer on a single optical fiber, the frequency instability at short times can reach the fundamental limit imposed by delay-unsuppressed phase noise from the fiber link, yielding a frequency instability that scales as link length to the 3/2 power. For two-way transfer on separate outgoing and return fibers, the instability is severely limited by differential fiber noise.

High-stability transfer of an optical frequency over long fiber-optic links

To compare the increasing number of optical frequency standards, highly stable optical signals have to be transferred over continental distances. We demonstrate optical-frequency transfer over a 1840-km underground optical fiber link using a single-span stabilization. The low inherent noise introduced by the fiber allows us to reach short term instabilities expressed as the modified Allan deviation of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ for a gate time $\ensuremath{\tau}$ of 1 s reaching $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ in just 100 s. We find no systematic offset between the sent and transferred frequencies within the statistical uncertainty of about $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$. The spectral noise distribution of our fiber link at low Fourier frequencies leads to a ${\ensuremath{\tau}}^{\ensuremath{-}2}$ slope in the modified Allan deviation, which is also derived theoretically.

Optical-Frequency Transfer over a Single-Span 1840 km Fiber Link

Using two-way exchange between coherent frequency combs, each phase-locked to the local optical oscillator, optical time–frequency transfer is demonstrated in free space across a 2-km-long link, with a timing deviation of 1 fs, a residual instability below 10−18 at 1,000 s and systematic offsets below 4 × 10−19.

Optical two-way time and frequency transfer over free space

Istituto Elettrotecnico Nazionale Galileo Ferraris (IEN), National Institute of Standards and Technology (NIST), National Physical Laboratory (NPL), Laboratoire National de Metrologie et d'Essais—Observatoire de Paris/Systemes de Reference Temps Espace (OP) and Physikalisch-Technische Bundesanstalt (PTB) operate cold-atom based primary frequency standards which are capable of realizing the SI second with a relative uncertainty of 1 × 10−15 or even below. These institutes performed an intense comparison campaign of selected frequency references maintained in their laboratories during about 25 days in October/November 2004. Active hydrogen maser reference standards served as frequency references for the institutes' fountain frequency standards. Three techniques of frequency (and time) comparisons were employed. Two-way satellite time and frequency transfer (TWSTFT) was performed in an intensified measurement schedule of 12 equally spaced measurements per day. The data of dual-frequency geodetic Global Positioning System (GPS) receivers were processed to yield an ionosphere-free linear combination of the code observations from both GPS frequencies, typically referred to as GPS TAI P3 analysis. Last but not least, the same GPS raw data were separately processed, allowing GPS carrier-phase (GPS CP) based frequency comparisons to be made. These showed the lowest relative frequency instability at short averaging times of all the methods. The instability was at the level of 1 part in 1015 at one-day averaging time using TWSTFT and GPS CP. The GPS TAI P3 analysis is capable of giving a similar quality of data after averaging over two days or longer. All techniques provided the same mean frequency difference between the standards involved within the 1σ measurement uncertainty of a few parts in 1016. The frequency differences between the three fountains of IEN (IEN-CsF1), NPL (NPL-CsF1) and OP (OP-FO2) were evaluated. Differences lower than the 1σ measurement uncertainty were observed between NPL and OP, whereas the IEN fountain deviated by about 2σ from the other two fountains.

https://iopscience.iop.org/article/10.1088/0026-1394/43/1/016/pdf

Comparison between frequency standards in Europe and the USA at the 10-15 uncertainty level

Istituto Elettrotecnico Nazionale Galileo Ferraris (IEN), National Institute of Standards and Technology (NIST), National Physical Laboratory (NPL), Laboratoire National de Metrologie et d’Essais – Observatoire de Paris / Systemes de Reference Temps Espace (OP), and Physikalisch-Technische Bundesanstalt (PTB) performed an intense comparison campaign of selected frequency references maintained in their laboratories during about 25 days in October/November 2004. The active hydrogen maser reference standards used at all laboratories served at the same time as frequency references for the institutes’ fountain frequency standards. The fountains of IEN, NPL, and OP were operated for most of the time during the same period, and results of the fountain comparisons are given in an accompanying paper. Three techniques of frequency (and time) comparisons were employed. Going beyond the standard procedures, two-way satellite time and frequency transfer was performed in an intensified measurement schedule of 12 equally spaced measurements per day. The data of dual frequency geodetic GPS receivers were processed to yield an ionosphere-free linear combination of the code observations from both GPS frequencies, typically referred to as TAI P3 analysis. Last but not least, the same GPS raw data were separately processed allowing GPS carrier-phase based frequency comparisons to be made. These showed the lowest instability at short averaging times of all of the methods. The instability was at the level of 1 part in 10 15 at one-day averaging time, similar to what was achieved with TWSTFT. The GPS TAI P3 analysis is capable of giving a similar quality of data provided that averaging over two days or longer is acceptable. The analysis presented here shows that all techniques provide the same mean frequency difference between the standards involved within the measurement uncertainty of a few parts in 10.

/pdf/time-and-frequency-comparisons-between-four-european-timing-1db6qd5t8s.pdf

Time and Frequency Comparisons Between Four European Timing Institutes and NIST Using Multiple Techniques

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Comparison between frequency standards in Europe and the USA at the 10-15 uncertainty level

Time and Frequency Comparisons Between Four European Timing Institutes and NIST Using Multiple Techniques