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.

Non-reciprocity in optical fiber links: experimental evidence

Fundamental limits of fiber link are set by non-reciprocal effects that violate the hypothesis of equality between forward and backward path. Non-reciprocal noise arises technically from the set-up asymmetry, and fundamentally by the Sagnac effect when the fiber link encloses a non-zero area. As a pre-requisite for observation of Sagnac effect in fiber links, we present a study on phase noise and frequency stability contributions affecting coherent optical frequency transfer in bi-directional fiber links. Both technical and fundamental limitations of Two-Way optical frequency transfer are discussed. Our model predicts and our experiments substantially verify that the dominant noise mechanism at low Fourier frequencies is the polarization asymmetry induced by the temperature and relative humidity variations impacted on fiber links. The flicker noise floor due to the non-reciprocal noise arising from polarization mode dispersion is evidenced for the first time. We perform a post-processing approach which enables us to remove this polarization noise, improve the long-term stability and remove a frequency bias. We evaluate the uncertainty contributions of all the effects discussed for our 50 km spooled fiber link, dominated by its non-reciprocal noise induced by polarization mode dispersion with uncertainty of 1.9( ± 0.8)( ± 1.2) × 10^-20. After correction, the linear drift of the residual phase is as low as 27 yoctosecond/s, leading to an uncertainty of the frequency transfer of 2.6 ( ± 39) × 10^-22, confirming its potential for searching for more fundamental effects such as Sagnac effect or transient frequency variation due to dark matter.

Unidirectional two-way optical frequency comparison and its fundamental limitations

High-quality frequency transfer based on existing telecommunication fiber links allows state-of-the-art microwave and optical clocks to be compared on a continental and potentially even intercontinental scale. We present a half-a-year-long data set of unidirectional optical frequency transfer over a 2×43km urban fiber link. We observe a relative frequency instability of 8.0×10^-16 at 1 s and at best 6.0×10^-18 at 10⁶s integration time. Our results show that the unidirectional two-way method gives the possibility to perform comparisons of international primary standards over fiber links faster than over satellite links. Moreover, we investigate the major limiting factors of such a unidirectional setup.

Reciprocity of propagation in optical fiber links demonstrated to 10-21

We present a study of the fundamental limit of fiber links using dedicated link architecture. We use an experimental arrangement that enables us to detect the forward and backward propagation noise independently and simultaneously in optical fiber and where the optical phase evolution is expected to be driven by the only contribution of the reference arms of the Michelson interferometer ensemble. In this article, we demonstrate indeed the high correlation between the optical phase evolution and the temperature variation of the interferometer ensemble, leading to a frequency offset of (4.4±2.3)×10^-21. Using a simple temperature model and a Bayesian analysis to evaluate the model parameters, we show that the temperature effect can be compensated with post-processing, removing the frequency offset down to (0.5±2.0)×10^-21. The residual slope of the optical phase evolution over 33 days is 350 yoctosecond/s. Using a global temperature parameter, we divide these 33 days dataset in four subsets and analyse their uncertainties. We show that they are self-consistent when the temperature is taken into account. This provides an alternative method to evaluate the accuracy of a fiber link, especially when the dataset includes large dead times. The result is finally interpreted as a test of the reciprocity of the propagation delay in an optical fiber. This unprecedented transfer capability could enable the comparisons of future optical clocks with expected performance at 10^-20 level and open new possibilities for stringent tests of special and general relativity.

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.

Studying the fundamental limit of optical fiber links to the 10-21 level

We present a hybrid fiber link combining effective optical frequency transfer and evaluation of performances with a self-synchronized two-way comparison. It enables us to detect the round-trip fiber noise and each of the forward and backward one-way fiber noises simultaneously. The various signals acquired with this setup allow us to study quantitatively several properties of optical fiber links. We check the reciprocity of the accumulated noise forth and back over a bi-directional fiber to the level of 3.1(±3.9) × 10^-20 based on a 160000s continuous data. We also analyze the noise correlation between two adjacent fibers and show the first experimental evidence of interferometric noise at very low Fourier frequency. We estimate redundantly and consistently the stability and accuracy of the transferred optical frequency over 43 km at 4 × 10^-21 level after 16 days of integration and demonstrate that a frequency comparison with instability as low as 8 × 10^-18 would be achievable with uni-directional fibers in urban area.

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.

Cascaded optical fiber link using the internet network for remote clocks comparison

We report a cascaded optical link of 1100 km for ultra-stable frequency distribution over an Internet fiber network. The link is composed of four spans for which the propagation noise is actively compensated. The robustness and the performance of the link are ensured by five fully automated optoelectronic stations, two of them at the link ends, and three deployed on the field and connecting the spans. This device coherently regenerates the optical signal with the heterodyne optical phase locking of a low-noise laser diode. Optical detection of the beat-note signals for the laser lock and the link noise compensation are obtained with stable and low-noise fibered optical interferometer. We show 3.5 days of continuous operation of the noise-compensated 4-span cascaded link leading to fractional frequency instability of 4x10(-16) at 1-s measurement time and 1x10(-19) at 2000 s. This cascaded link was extended to 1480-km with the same performance. This work is a significant step towards a sustainable wide area ultra-stable optical frequency distribution and comparison network at a very high level of performance.

Progress toward the first observation of parity violation in chiral molecules by high-resolution laser spectroscopy

Parity violation (PV) effects in chiral molecules have so far never been experimentally observed. To take up this challenge, a consortium of physicists, chemists, theoreticians, and spectroscopists has been established and aims at measuring PV energy differences between two enantiomers by using high-resolution laser spectroscopy. In this article, we present our common strategy to reach this goal, the progress accomplished in the diverse areas, and point out directions for future PV observations. The work of André Collet on bromochlorofluoromethane (1) enantiomers, their synthesis, and their chiral recognition by cryptophanes made feasible the first generation of experiments presented in this article.

Cascaded multiplexed optical link on a telecommunication network for frequency dissemination

We demonstrate a cascaded optical link for ultrastable frequency dissemination comprised of two compensated links of 150 km and a repeater station. Each link includes 114 km of Internet fiber simultaneously carrying data traffic through a dense wavelength division multiplexing technology, and passes through two routing centers of the telecommunication network. The optical reference signal is inserted in and extracted from the communication network using bidirectional optical add-drop multiplexers. The repeater station operates autonomously ensuring noise compensation on the two links and the ultra-stable signal optical regeneration. The compensated link shows a fractional frequency instability of 3 x 10(-15) at one second measurement time and 5 x 10(-20) at 20 hours. This work paves the way to a wide dissemination of ultra-stable optical clock signals between distant laboratories via the Internet network.

High-resolution optical frequency dissemination on a telecommunications network with data traffic

We transferred the frequency of an ultrastable laser over a 108-km-long urban fiber link comprising 22 km of an optical communications network fiber simultaneously carrying Internet data traffic. The metrological signal and the digital data signal were transferred over two different frequency channels in a dense wavelength-division multiplexing scheme. The metrological signal was inserted in and extracted from the communication network using bidirectional off-the-shelf optical add-drop multiplexers. The link-induced phase noise was measured and canceled with a round-trip technique using an all-fiber-based interferometer. The compensated link showed an Allan deviation of a few 10(-16) at 1 s and below 10(-19) at 10,000 s. This work paves the way to a wide dissemination of ultrastable optical clock signals between distant laboratories via the Internet.

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.

Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation

We demonstrate a new, simple technique for measuring IR frequencies near 30 THz by using a femtosecond (fs) laser optical comb and sum-frequency generation. The optical frequency is directly compared with the distance between two modes of the fs laser, and the resultant beat note is used to control this distance, which depends only on the repetition rate of the fs laser. The absolute frequency of a CO2 laser stabilized onto a SF6 two-photon line has been measured for the first time to the authors' knowledge. This line is an attractive alternative to the usual saturated absorption OsO4 resonances used for the stabilization of CO2 lasers. First results demonstrate a fractional Allan deviation of 3 x 10(-14) at 1 s.

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.