Optical Frequency Transfer Over a Single-Span1840-km Fiber Link

Stefan Droste, Thomas Udem,Theodor W. Hansch, Ronald Holzwarth

Max-Planck-Institut fur QuantenoptikHans-Kopfermann-Str. 1

85748 Garching, GermanyEmail: stefan.droste@mpq.mpg.de

Filip Ozimek, Sebastian Raupach,Harald Schnatz, Gesine Grosche

Physikalisch-Technische BundesanstaltBundesallee 100

38116 Braunschweig, Germany

Abstract—We demonstrate optical frequency transfer over an1840 km underground optical fiber link using a single-spanstabilization. To compensate for more than 420 dB of opticalattenuation of the light we use twenty Erbium doped fiberamplifiers along the entire link and two additional fiber Brillouinamplifiers. The good passive stability of our fiber link allowsus to reach short term instabilities expressed as the modifiedAllan deviation of 3 × 10−15 for a gate time τ of 1 s reaching4 × 10−19 in just 100 s. By comparing the sent and transferredfrequencies we find no systematic offset within the statisticaluncertainty of about 3 × 10−19. The spectral noise distributionof our fiber link at low Fourier frequencies leads to a τ−2 slopein the modified Allan deviation.

I. INTRODUCTION

The development of optical frequency standards [1], [2]raises a demand for transferring highly stable optical signalsover continental distances. Such transfer would enable newexperiments in fundamental physics such as in quantum elec-trodynamics or to verify the constancy of fundamental con-stants. Also applications in navigation or relativistic geodesywill strongly benefit from those stable frequency references.Besides this, the transfer of highly stable optical signals willbe mandatory for a future redefinition of the SI-second basedon an optical atomic transition. Well-established satellite-basedtechniques for frequency comparisons and dissemination donot reach the required stability and accuracy to compare opticalclocks. In recent years, optical fiber links have been inves-tigated extensively [3]–[7] and are considered as a possibletransfer medium for stable optical signals.

II. EXPERIMENTAL SETUP

We investigate an optical frequency transfer over an1840 km fiber link connecting the Max-Planck-Institut furQuantenoptik (MPQ) and the Physikalisch-Technische Bunde-sanstalt (PTB). The link spans a significant part of Germanyand consists of a dedicated fiber which is set up in a loopconfiguration with sender and receiver being located at MPQ.We use a commercial cw fiber laser emitting at 1542.5 nmthat is stabilized to a high-finesse optical reference cavitymade from ultra-low expansion (ULE) material to transfer anoptical carrier at 194 THz over the fiber link. To overcomethe optical attenuation of more than 420 dB of the light in thefiber we use twenty Erbium-doped fiber amplifiers (EDFA)

that are distributed equally along the entire link and a fiberBrillouin amplifier (FBA) [8] at each institute. The EDFAs areremotely controlled by using an amplitude modulated 1310 nmcommunication signal that is sent simultaneously through thesame fiber. Additionally, the EDFAs are fully bi-directional andspecially designed for low input signal powers. The fiber link issubject to temperature induced optical path length variationsand acoustic noise that impose Doppler frequency shifts onthe transmitted signals. An interferometric stabilization schemesimilar to the one described in [9] is used to detect andcompensate for those Doppler shifts.

In contrast to cascading multiple fiber links where eachsection is phase stabilized separately [4], [10] we investigate along-distance fiber link by using a single-span stabilization ofthe whole 1840 km link. While the latter approach comprisesa simpler setup as no stable lasers or intermediate regenerationstations have to be installed and operated along the link, thelarge propagation delay of the light in the fiber yields a stronglyreduced bandwidth for the suppression of fiber-induced noise.The round-trip time of the light for the 1840 km loop is closeto 18 ms, limiting the noise suppression bandwidth to < 27 Hz.

To characterize the performance of the frequency transferover the fiber link we generate a heterodyne beat note atMPQ between the sent light and light that has been transferredthrough the fiber link. To record the beat note we use dead timefree frequency counters [11], that can operate in two differentmodes: the so called Π- and Λ-modes [12]. In contrast to aΠ-type counter, a Λ-type counter averages many frequencysamples within a gate time, thus noise is effectively suppressedand more accurate data is produced.

III. RESULTS

Figure 1 shows the stability of the transferred frequencyafter 1840 km of fiber when the link transfer is stabilized.The stability is expressed as the Allan deviation (ADEV)measured with a Π-type counter as well as the modified ADEVmeasured with a Λ-type counter. Despite the severely reducedservo bandwidth for the suppression of fiber-induced noise,the low intrinsic noise of the fiber link together with activenoise cancellation allows for 1-s instabilities of a few parts in1015 and about 4 × 10−19 after 100 s of measurement time. Itcan be seen that even todays most stable optical clocks can becompared over the distance of 1840 km within a few minutes

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Fig. 1. Fractional frequency instability of the 1840 km fiber link. ADEVmeasured with a Π-type counter and modified ADEV measured with a Λ-typecounter when the link transfer is stabilized. For comparison the instability ofstate-of-the-art optical clocks is depicted.

of measurement time using our fiber link. The noise of ourlink peaks at around 15 Hz and is lower at smaller frequencieswhich leads to a τ−2 dependency in the modified ADEV asshown in Figure 1. We attribute the noise maximum around15 Hz to building and ground vibrations.

To assess potential systematic frequency shifts, we analyzedthe mean deviation of the transferred frequency from theinput frequency, and found agreement within the statisticaluncertainty of 2.6 × 10−19. The results illustrate that for aremote comparison of state-of-the-art optical clocks, the short-term instability contribution of the stabilized ≈ 2000 km linkis negligible within one minute of measurement time.

IV. CONCLUSION

We demonstrated optical frequency transfer along an1840 km optical fiber link with an instability of 2.7 × 10−15

at 1 s reaching 4 × 10−19 after 100 s of measurementtime. The residual uncertainty exceeds the requirements fora comparison of todays most stable clocks by more than oneorder of magnitude. Our fiber link is provided by a commercialtelecommunication supplier and passes several metropolitanareas and computing centers. Despite these environmentalconditions active noise cancellation and carefully adjusted in-line amplification can yet provide high-performance frequencytransfer over continental distances. We demonstrate that remotecomparisons of state-of-the-art optical clocks are possible evenif the clocks are separated by nearly 2000 kilometers. Thiswork can be seen as a testbed for a European wide fiber linknetwork to connect metrology institutes across Europe. Theability to compare those modern optical frequency standardsopens a variety of applications, including relativistic geodesy[13], tests of the constancy of fundamental constants andquantum electrodynamics.

ACKNOWLEDGMENT

This work was supported by the European MetrologyResearch Programme (EMRP) under SIB-02 NEAT-FT. The

EMRP is jointly funded by the EMRP participating countrieswithin EURAMET and the European Union. We thank K.Predehl for establishing the fiber link; J. Alnis and Th. Legerofor setting up the ultra-stable reference cavities; O. Terra forhis work on the fiber Brillouin amplifiers and the membersof Deutsches Forschungsnetz in Berlin, Leipzig, and Erlangen,Germany, as well as Gasline GmbH for a fruitful collaboration.We also thank the excellence cluster QUEST for financialsupport. T.W.H. acknowledges support by the Max PlanckFoundation.

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