Comparing ultrastable lasers at 7 × 10-17 fractional frequency instability through a 2220 km optical fibre network

Ultrastable lasers are essential tools in optical frequency metrology enabling unprecedented measurement precision that impacts on fields such as atomic timekeeping, tests of fundamental physics, and geodesy. To characterise an ultrastable laser it needs to be compared with a laser of similar performance, but a suitable system may not be available locally. Here, we report a comparison of two geographically separated lasers, over the longest ever reported metrological optical fibre link network, measuring 2220 km in length, at a state-of-the-art fractional-frequency instability of 7 × 10-17 for averaging times between 30 s and 200 s. The measurements also allow the short-term instability of the complete optical fibre link network to be directly observed without using a loop-back fibre. Based on the characterisation of the noise in the lasers and optical fibre link network over different timescales, we investigate the potential for disseminating ultrastable light to improve the performance of remote optical clocks.

First industrial-grade coherent fiber link for optical frequency standard dissemination

We report on a fully bidirectional 680 km fiber link connecting two cities for which the equipment, the setup, and the characterization are managed for the first time by an industrial consortium. The link uses an active telecommunication fiber network with parallel data traffic and is equipped with three repeater laser stations and four remote double bidirectional erbium-doped fiber amplifiers. We report a short-term stability at 1 s integration time of 5.4×10^-16 in 0.5 Hz bandwidth and a long-term stability of 1.7×10^-20 at 65,000 s of integration time. The accuracy of the frequency transfer is evaluated as 3×10^-20. No shift is observed within the statistical uncertainty. We show a continuous operation over five days with an uptime of 99.93%. This performance is comparable with the state-of-the-art coherent links established by National Metrology Institutes in Europe. It is a first step in the construction of an optical fiber network for metrology in France, which will give access to an ultrahigh performance frequency standard to a wide community of scientific users.

A clock network for geodesy and fundamental science

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.

Comparing the frequency of two distant optical clocks will enable sensitive tests of fundamental physics. Here, the authors compare two strontium optical-lattice clocks 690 kilometres apart to a degree of accuracy that is limited only by the uncertainty of the individual clocks themselves.

Stability of the proton-to-electron mass ratio

We report a limit on the fractional temporal variation of the proton-to-electron mass ratio as 1/(m(P)/m(e)) partial differential/partial differential(t)(m(P)/m(e))=(-3.8+/-5.6) x 10(-14) yr(-1), obtained by comparing the frequency of a rovibrational transition in SF6 with the fundamental hyperfine transition in Cs. The SF6 transition was accessed using a CO2 laser to interrogate spatial 2-photon Ramsey fringes. The atomic transition was accessed using a primary standard controlled with a Cs fountain. This result is direct and model-free.

Direct determination of the Boltzmann constant by an optical method

We have recorded the Doppler profile of a well-isolated rovibrational line in the nu(2) band of (14)NH(3). Ammonia gas was placed in an absorption cell thermalized by a water-ice bath. By extrapolating to zero pressure, we have deduced the Doppler width which gives a first measurement of the Boltzmann constant k(B) by laser spectroscopy. A relative uncertainty of 2 x 10(-4) has been obtained. The present determination should be significantly improved in the near future and contribute to a new definition of the kelvin.

Long-distance frequency dissemination with a resolution of 10(-17)

We use a new technique to disseminate microwave reference signals along ordinary optical fiber. The fractional frequency resolution of a link of 86 km in length is 10(-17) for a one day integration time, a resolution higher than the stability of the best microwave or optical clocks. We use the link to compare the microwave reference and a CO2/OsO4 frequency standard that stabilizes a femtosecond laser frequency comb. This demonstrates a resolution of 3 x 10(-14) at 1 s. An upper value of the instability introduced by the femtosecond laser-based synthesizer is estimated as 1 x 10(-14) at 1 s.

Slow molecule detection or Ramsey fringes in two-photon spectroscopy: which is better for high resolution spectroscopy and metrology ?

The CO2 laser locked onto a saturated absorption resonance of OsO4 provides a secondary frequency standard in the 10 mm region, with an accuracy of 50 Hz to 1 kHz. For averaging times less than 100 s its stability performance is better than the Hydrogen maser. This paper deals with the present attempt to increase this performance by using a two-photon molecular resonance as a reference. We begin with some preliminary and promising results on a two-photon line of SF6 leading to characteristics similar to those obtained with a saturation line of OsO4 . Then two alternative methods to increase the resolution are presented : optical detection of slow molecules and a new development of the well-known Ramsey fringes. Metrological features are analyzed for both methods.