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Optics Letters

Unidirectional two-way optical frequency comparison and its fundamental limitations

Dan Xu, Olivier Lopez, Anne Amy‐Klein, Paul-Éric Pottie

Published Oct 5, 2020• 8 citations
Publisher

Abstract

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 × 43 k m 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 10 6 s 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.

DOI
10.1364/ol.404866

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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 × 43 k m 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 10 6 s 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.
By using two-way frequency transfer, we demonstrate ultra-high resolution comparison of optical frequencies over a telecommunication fiber link of 100 km operating simultaneously digital data transfer. We first propose and experiment a bi-directional scheme using a single fiber. We show that the relative stability at 1 s integration time is 7 10^18 and scales down to 5 10^21. The same level of performance is reached when an optical link is implemented with an active compensation of the fiber noise. We also implement a real-time two-way frequency comparison over a uni-directional telecommunication network using a pair of parallel fibers. The relative frequency stability is 10^15 at 1 s integration time and reaches 2 10^17 at 40 000 s. The fractional uncertainty of the frequency comparisons was evaluated for the best case to 2 10^20. These results open the way to accurate and high resolution frequency comparison of optical clocks over intercontinental fiber networks.
By using two-way frequency transfer, we implement a real-time frequency comparison over a uni-directional telecommunication network of 100 km using a pair of parallel fibers with simultaneous digital data transfer. The relative frequency stability is ${10}^{\ensuremath{-}15}$ at 1-s integration time and reaches $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ at 40 000 s, three orders of magnitude below the one-way fiber instability. We also demonstrate ultrahigh-resolution comparison of optical frequencies with a bidirectional scheme using a single fiber. We show that the relative stability at 1-s integration time is $7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$ and scales down to $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$. The same level of performance is reached when an optical link is implemented with an active compensation of the fiber noise. The fractional uncertainty of the frequency comparisons was evaluated for the best case to $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$. These results open the way to accurate and high-resolution frequency comparison of optical clocks over intercontinental fiber networks.
We present the first experimental demonstration over a 43-km-long urban fiber network of a local two-way optical frequency comparison, which does not require any synchronization of the measurements. It was combined with a regular active-noise compensation on another parallel fiber leading to a very reliable and robust frequency transfer. This hybrid scheme enables us to investigate the major limiting factors of the local two-way comparison. We analyze the contribution to the phase noise of the recovered signal by the interferometers at local and remote places. By using the ability of this set up to be injected by a single laser or two independent lasers, we measure the contribution to the long-term instability by the demodulated laser instabilities. We show that a fractional frequency instability level of 1 × 10 −20 at 10 000 s can be obtained with this simple setup after 43-km-long propagation in an urban area.
We present the experimental demonstration of a local two-way optical frequency comparison over a 43-km-long urban fiber network without any requirement for measurement synchronization. We combined the local two-way scheme with a regular active noise compensation scheme that was implemented on another parallel fiber leading to a highly reliable and robust frequency transfer. This hybrid scheme allowed us to investigate the major limiting factors of the local two-way comparison. We analyzed the contributions of the interferometers at both local and remote locations to the phase noise of the local two-way signal. Using the ability of this setup to be injected by either a single laser or two independent lasers, we measured the contributions of the demodulated laser instabilities to the long-term instability. We show that a fractional frequency instability level of 10 −20 at 10,000 s can be obtained using this simple setup after propagation over a distance of 43 km in an urban area.
Two-way frequency transfer on optical fibers is a powerful technique for the comparison of distant clocks over long and ultra-long hauls. In contrast to traditional Doppler noise cancellation, it is capable of sustaining higher link attenuation, mitigating the need of optical amplification and regeneration and thus reducing the setup complexity. We investigate the ultimate limitations of the two-way approach on a 300 km multiplexed fiber haul, considering fully independent setups and acquisition systems at the two link ends. We derive a theoretical model to predict the performance deterioration due to a bad synchronisation of the measurements, which is confirmed by experimental results. This study demonstrates that two-way optical frequency transfer is a reliable and performing technique, capable of sustaining remote clocks comparisons at the resolution, and is relevant for the development of a fiber network of continental scale for frequency metrology in Europe.
Bidirectional phase-stabilized optical fiber links allow state-of-the-art optical clocks to be compared on a continental scale.However, intercontinental comparisons are still based on satellite techniques, preventing optical clocks from being compared without degradation.We performed the first optical frequency transfer experiment over submarine links, measuring levels of environmentally induced noise substantially lower than for on-land links.From these measurements, we predict the transfer stability that can be achieved over transoceanic links.We also performed the first optical frequency transfer over fibers installed in power cables, observing optical perturbations caused by the high-voltage field.Finally, we show that the low background noise of fibers on the seafloor allows applications in geophysical sensing.