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Physical Review Letters

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

Stefan Droste, Filip Ozimek, Thomas Udem, Katharina Predehl, Theodor W. Hänsch, H. Schnatz, Gesine Grosche, Ronald Holzwarth

Published Sep 12, 2013• 314 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.111.110801

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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×\else\texttimes\fi10\ensuremath−152\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}2\ifmmode×\else\texttimes\fi10\ensuremath−15 for a gate time \ensuremathτ\ensuremath{\tau}\ensuremathτ of 1 s reaching 4\ifmmode×\else\texttimes\fi10\ensuremath−194\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}4\ifmmode×\else\texttimes\fi10\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×\else\texttimes\fi10\ensuremath−193\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}3\ifmmode×\else\texttimes\fi10\ensuremath−19. The spectral noise distribution of our fiber link at low Fourier frequencies leads to a \ensuremathτ\ensuremath−2{\ensuremath{\tau}}^{\ensuremath{-}2}\ensuremathτ\ensuremath−2 slope in the modified Allan deviation, which is also derived theoretically.
We demonstrate optical frequency transfer over an 1840 km underground optical fiber link using a single-span stabilization. To compensate for more than 420 dB of optical attenuation of the light we use twenty Erbium doped fiber amplifiers along the entire link and two additional fiber Brillouin amplifiers. The good passive stability of our fiber link allows us to reach short term instabilities expressed as the modified Allan deviation of 3 × 10-15for a gate time τ of 1 s reaching 4 × 10-19in just 100 s. By comparing the sent and transferred frequencies we find no systematic offset within the statistical uncertainty of about 3 × 10-19. The spectral noise distribution of our fiber link at low Fourier frequencies leads to a τ-2slope in the modified Allan deviation.
We investigated the transfer of a 194 THz optical frequency along a 1840 km fiber link. The fractional frequency instability expressed as the modified Allan deviation is 2.7 × 10−15 at 1 s with 4 × 10−19 after 100 s. The transferred frequency shows no systematic offset within an uncertainty of 3 × 10−19. Analyzing the underlying noise structure reveals a τ−2 response in the modified Allan deviation, which is confirmed by calculations of the frequency instability from frequency counter data as well as from phase noise data.
We demonstrate the long-distance transmission of an ultrastable optical frequency derived directly from a state-of-the-art optical frequency standard. Using an active stabilization system we deliver the frequency via a 146-km-long underground fiber link with a fractional instability of 3 x 10(-15) at 1 s, which is close to the theoretical limit for our transfer experiment. After 30,000 s, the relative uncertainty for the transfer is at the level of 1 x 10(-19). Tests with a very short fiber show that noise in our stabilization system contributes fluctuations that are 2 orders of magnitude lower, namely, 3 x 10(-17) at 1 s, reaching 10(-20) after 4,000 s.
We realized a coherent optical fiber link in Italy, with a fiber haul of 642 km. To characterize the link, we doubled the link to 1284 km, demonstrating a characterization technique based on the double round trip on a single fiber. The link is intended to significantly improve the frequency references used in radio-astronomy and precision measurements in atomic physics. The data analysis is based on the Allan deviation, whose expression is theoretically derived from the noise power spectrum. The demonstrated resolution is 3×10−19 in 1000 s and the uncertainty of the transfer is 5×10−19. The arming of a second fiber is avoided, and this could be rather beneficial to long hauls realizations for a continental fiber network for frequency and time metrology.
In long-distance, optical continuous-wave frequency transfer via fiber, remote bidirectional Er³ ⁺ -doped fiber amplifiers are commonly used to mitigate signal attenuation. We demonstrate for the first time the ultrastable transfer of an optical frequency using a remote fiber Brillouin amplifier, placed in a server room along the link. Using it as the only means of remote amplification, on a 660 km loop of installed underground fiber we bridge distances of 250 km and 160 km between amplifications. Over several days of uninterrupted measurement, we find an instability of the frequency transfer (Allan deviation of Λ-weighted data with 1 s gate time) of around 1 × 10(-19) and less for averaging times longer than 3000 s. The modified Allan deviation reaches 3 × 10(-19) at an averaging time of 100 s. Beyond 100 s it follows the interferometer noise floor, and for averaging times longer than 1000 s the modified Allan deviation is in the 10(-20) range. A conservative value of the overall accuracy is 1 × 10(-19)