Brillouin amplification supports 1× 10 −20 accuracy in optical frequency transfer over 1400~km of underground fibre
BBrillouin amplification supports × − accuracy in optical frequency transfer over1400 km of underground fibre Sebastian M. F. Raupach, ∗ Andreas Koczwara, and Gesine Grosche Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, D-38116 Braunschweig, Germany (Dated: October 3, 2018)We investigate optical frequency transfer over a 1400 km loop of underground fibre connectingBraunschweig and Strasbourg. Largely autonomous fibre Brillouin amplifiers (FBA) are the onlymeans of intermediate amplification, allowing phase-continuous measurements over periods up toseveral days. Over a measurement period of about three weeks we find a weighted mean of thetransferred frequency’s fractional offset of (1 . ± . × − . In the best case we find an instabilityof 6 . × − and a fractional frequency offset of 4 . × − at an averaging time of around 30 000 s.These results represent an upper limit for the achievable uncertainty over 1400 km when using achain of remote Brillouin amplifiers, and allow us to investigate systematic effects at the 10 − -level. The transfer of optical frequencies [1–6] is requirede.g. for comparing the ultrastable frequency signalsgenerated by optical atomic clocks. Latest reportsstate record clock instabilities and accuracies on the10 − − level [7–9]. Transferring their ultrastable opticalfrequency, as required for clock validation via remotecomparison as well as for applications in relativisticgeodesy [10–12], is challenging. Optical frequency trans-fer can also serve to disseminate an optical referencefrequency to remote users [6, 13]. Taking advantage ofphase synchronicity at the sending and receiving endwithin the bandwidth of the link stabilization [14], itcan be used for the common-mode suppression of theDick-effect in optical clock comparisons via synchronoussampling [8, 15, 16].The noise added by the transmission path can beminimized by using underground fibre links and besuppressed further by actively stabilizing the phase ofthe transferred signal [1, 2, 5]. Alternatively the two-waytechnique can be employed [17–19], where applicable.The fibre’s attenuation is traditionally compensated forby broad-band Erbium doped fibre amplifiers (EDFA).For ultrastable optical frequency transfer they haveto be operated without isolators to ensure symmetryof the optical path in both directions [20, 21]. Thisbidirectional operation typically restricts the gain toaround 17 dB to avoid spontaneous lasing.Over long distances, this leads to excess losses, andin some long-distance, bidirectional EDFA links thesignal phase is lost at least several times per hour[4, 5]. Very recently, an instability (as estimated by themodified Allan deviation) of 3 × − was reported forphase-stabilized frequency transfer over a 540 km loop ofcascaded fibre links [19]; an accuracy was not reported.However, in view of clock (in-)accuracies on the 10 − -level, hitherto demonstrated inaccuracy contributions oflong-distance optical frequency transfer of several times10 − [2–6] can no longer be neglected. ∗ Electronic address: [email protected]
Here we present results from a measurement campaignperformed over a 1400 km fibre loop from Braunschweig(Germany) to Strasbourg (France) and back. Thisfibre link will become part of the future internationallink PTB (Germany) / LNE-SYRTE (France). Itslength corresponds to twice the geographical distanceSydney-Brisbane and to the total length of the link PTB/ LNE-SYRTE.In this Letter we report a signal amplification approachadapted to ultrastable-frequency metrology, whichallows phase-continuous measurements over periods upto several days. We show that it supports an instabilityand inaccuracy better than 10 − . We introduce theΛAllan deviation (ΛADEV) as an improved measure ofuncertainty, well suited for remote clock comparisons.Using separately housed setups at the local and “remote”end, we demonstrate the transfer of an optical frequencyover 1400 km with an inaccuracy of around 2 × − .The link consists of a pair of telecommunicationfibres connecting PTB in Braunschweig to Universit´e deStrasbourg (UDS)over a fibre length of around 710 km.The fibres are patched together at UDS to form a loop ofaround 1400 km length, where a cascade of fieldable fibreBrillouin amplifiers (FBA) is the only means of interme-diate amplification. These have been developed at PTBafter early demonstrations of Brillouin-amplificationassisted optical frequency transfer [2, 22]. In contrast toEDFA, the FBA also in bidirectional operation allow again of 40 dB and more, without losing the signal phaseover periods up to several days [6, 20].The fibre loop starts and ends in the same laboratory atPTB to facilitate the characterisation of the link. Foractive phase stabilization, the link is set up as a fibreMichelson interferometer. As a frequency source, weuse a laser at 194.4 THz locked to a cavity-stabilized1 Hz master laser. The local interferometer used forstabilization of the link, and the setup for detecting the“remote” beat frequency between the transferred andthe source light are located in separate but adjacent,thermally insulated housings. We use bidirectionalEDFA as booster amplifiers for the outgoing and theincoming light. Beat frequencies are recorded using a r X i v : . [ phy s i c s . op ti c s ] A p r Kassel ω ω -55 MHz +37 MHz 90%
18 MHz 36 MHz „remote“ local
EDFA
EDFA
FBA
FBA
FBA Giessen Karlsruhe Strasbourg
Braunschweig
FBA lock
FIG. 1: Schematic sketch of the the measurement setup and the 1400 km Brillouin link PTB - Universit´e de Strasbourg - PTB.
K&K FXE dead-time-free totalizing counters with aninternal gate time of 1 ms [23]. The counters are set toreport the frequency values at 1 second intervals. Thefrequency values are reported both as unweighted aver-ages (Π-mode) and as triangularly weighted, overlappingaverages (phase-averaging- or “Λ”-mode [24]). Due tothe spectral response of the triangle function, the Λ-typeaveraging more strongly suppresses Fourier frequencieslarger than the reciprocal of the gate time, acting like alow pass filter (see [24, 25] for a related discussion). Theoverall measurement setup at PTB is described in [6].Along the link three fieldable FBA are the only meansof intermediate amplification. They are located in serverrooms of Kassel University, Giessen University and theKarlsruhe Institute of Technology. While they do allowremote control, they normally operate autonomously.During one pass through this loop the signal experi-ences seven Brillouin amplifications, corresponding toan average inter-amplifier distance of 200 km. Theindividual lengths bridged and their attenuations are205 km/44 dB (Braunschweig-Kassel), 160 km/33 dB(Kassel-Giessen), 231 km/47 dB (Giessen-Karlsruhe)and around 2 ×
114 km/54 dB (Karlsruhe-Strasbourg-Karlsruhe), respectively. Note that the first fibre stretchhas been shortened slightly since the measurementsdescribed in [6].Each FBA contains one pump laser, the light of whichis split into four paths, where in two of the paths thefrequency is shifted by one acousto-optic modulator toaccommodate the frequency shift of the signal returningfrom the remote end. Thus each FBA simultaneouslyamplifies the signal in both directions per fibre and inboth fibres of the loop. The frequency of the pumplaser is locked to the incoming, amplified signal at anoffset frequency corresponding to the fibre’s Brillouinfrequency ( ≈
11 GHz). The FBA allow remote opti-mization of the pump lights polarization and the offsetlock frequency. Without polarization adjustment, allFBA stay in lock at least several days, often about oneweek or more. Each FBA can be relocked remotely.To assess the accuracy of the optical frequency transfer, we calculate the unweighted mean of the differencebetween the expected and the measured beat frequencyat the “remote” end.We have performed two measurement campaigns fromDecembre 10, 2014 to Decembre 18, 2014, and fromDecembre 23, 2014 to January 2, 2015, covering aperiod of about three weeks. During the second cam-paign the stabilization of the link failed during five1-second-intervals, during the first campaign we foundan average of about four invalid data points per day.This demonstrates a high reliability and very low cycleslip rate. During all campaigns, the FBA were runningunattended.Results for optical frequency transfer over the 1400 kmare shown in figure 2. The filled circles illustrate theinstability (Allan deviation, ADEV [26]) of unweightedaverages of Π-data [24]. We find an unweighted mean ofthe transfer-induced frequency offset of 2 . × − , wellwithin the instability of 1 . × − indicated by the lastvalue of the Allan deviation.We apply the Allan deviation formalism also to the datareported in Λ-mode. The slope of 1 /τ of the instabilitycurve remains unchanged. The overall instability issmaller than the ADEV of the Π-data, benefitingfrom the low-pass characteristic of Λ-type averaging.To distinguish this instability curve from the genuineADEV, we label it ΛADEV. Here we find an instability(ΛADEV) at an averaging time τ of around 97 000 s of1 . × − , and an unweighted mean of the Λ-data of1 . × − .Also shown are the modified Allan deviations(ModADEV [24, 26]) of the remote and inloop fre-quencies, calculated from the Λ-data. The modifiedAllan deviation effectively continues the triangular,overlapping Λ-type averaging over the averaging interval τ , benefiting from its low-pass behaviour [24]. Contraryto the ADEV it distinguishes white phase noise fromflicker phase noise and reveals noise processes otherwisecovered by white phase noise. Thus the ModADEVhelps to gain an approximate idea of the achievableuncertainty. For averaging times τ up to about 10 s, the FIG. 2: Instability of the optical frequency transferover the stabilized 1400 km ”Brillouin-Link” Braunschweig-Strasbourg-Braunschweig. The frequency data are reportedonce per second simultaneously in Π- and in Λ-mode usingtotalizing dead-time-free counters (K&K); filled circles: Al-lan deviation of the frequency transfer (Π-type data); filledtriangles: Allan deviation formalism applied to Λ-type re-mote frequency offset data (ΛADEV); open triangles modifiedAllan deviation of the transferred frequency; open squares:modified Allan deviation of the return signal (inloop signal);dashed line: instability of the most recent side-by-side opti-cal clock comparisons [8, 9]; dotted line: instability withoutlink (“optical short-cut”); the error bars of each ADEV point σ y( τ ) are calculated as σ y( τ ) / (cid:112) N ( τ ) [26], with N ( τ ) beingthe number of averaging intervals at τ . ModADEV drops as 1 /τ [4].For averaging times beyond around 100 s the ModADEVis similar to the differential instability between theseparately housed local and “remote” setup, whichshows some variability in the 10 − range. In fig. 2we show one measurement of this relative instability,obtained by optically short-cutting the link (ModADEV,dotted line).The dashed line in fig. 2 indicates the instability of themost recent side-by-side or self-comparison of opticalclocks [8, 9]. It illustrates that using Π-type data for aclock comparison would yield an unweighted frequencyaverage dominated by the instability of the transfer upto the longest averaging times. This is in contrast toΛ-type data, where for averaging times larger than about100 s the optical clocks start to dominate the instability.Depending on the application, we may increase theΛ-type averaging interval to exploit the strong decreasein instability, thus “sliding down” along the ModADEVcurve for continuous measurements (see fig. 3). Forcomparing the mean frequencies of e.g. optical clocks,the Λ-type averaging interval may be maximized. Thisachieves a lower instability (ΛADEV) and thus a betterestimate of the unweighted average. FIG. 3: Optical frequency transfer instability, different mea-surement and demonstration of a numerically extended Λ av-eraging interval. Filled triangles: ΛADEV of the frequencytransfer for Λ-type data averaged over 1s; filled diamonds:ΛADEV of the frequency transfer for Λ-type data, where thetime for Λ-type averaging has been extended numerically to10 s (grey circles: 100 s); open triangles: modified Allan de-viation of the transferred frequency; dashed line: instabilityof optical clock comparison as in fig. 2; dash-dotted line:ModADEV of the fiber link stabilization’s correction signal:the fiber noise is suppressed by six orders of magnitude forthe longest averaging time.
The effect of a Λ-extension is demonstrated in fig. 3.It shows data taken over a period of 145.000 seconds(measurement 3 in fig. 4, which covers a slightly smallerperiod due to our Λ-extension algorithm). At the longestaveraging times the ΛADEV of the 1 s Λ-data is aboutsix times larger then the instability floor as estimated bythe ModADEV. We note, that for the longest averagingtime of around 36 000 s we observe a noise suppressionby about six orders of magnitude, close to the predicteddelay limit for f = 36 000 − s − according to [25].We numerically increase the Λ-type averaging to aninterval of 10 s, the typical minimum interval at whichan optical clock’s instability starts to average down.We obtain an unweighted mean of these 10 s Λ-data of1 . × − and an instability (ΛADEV) of 1 . × − at τ ≈
36 000 s. At this extended Λ-interval, thetransfer instability is smaller than that reported for a local clock comparison [8] already for averaging times of10 s onwards.For the data shown in fig. 2, numerically increasingthe Λ-averaging interval to 10 s yields an instability(ΛADEV) at the longest averaging time of 9 . × − ,and an unweighted mean of 1 . × − .Fig. 4 illustrates the results from all long-termmeasurements during the two measurement campaigns.Here, we numerically extended the Λ-type averaginginterval to 2000 s for all measurements. The durations k s k s k s k s k s k s k s k s k s k s k s k s k s FIG. 4: Overview over all measurements during the periodfrom Decembre 10, 2014 to January 2, 2015. The blacksquares indicate the unweighted means for numerically ex-tended Λ − type averaging intervals of 2000 s, the respectivemeasurement times are indicated in dark gray. The errors bars ± s indicate the last value s of the corresponding ΛADEVs.The mean of these data weighted by 1 /s is (1 . ± . × − .For comparison, the open diamonds correspond to the un-weighted mean of the fibre-induced frequency offset during therespective measurements, multiplied by a factor of − × − .This factor corresponds to the relative frequency differencebetween outgoing and return light. of the measurements are indicated in dark gray (inkiloseconds). The observed residual offsets scatter overa range of less than ± × − , their weighted mean is(1 . ± . × − . In the best case, during a measure-ment period of around 30 000 s, we obtain an instability(ΛADEV) of 6 . × − and an unweighted mean of thetransferred frequency’s offset of 4 . × − . We find,that the offset of the transferred frequency during somemeasurements significantly differs from Zero by up to2 × − . We do not observe a significant offset of theinloop beat frequency. Thus, the observed offsets mostlikely indicate out-of-loop processes or non-reciprocaleffects along the link.Due to the 2 ×
37 MHz shift by the “remote” AOM,the outgoing“remote” light and the returning roundtriplight exhibit a relative frequency difference of 3 . × − .As the frequency shift is positive on the return path,we expect an over-compensation of the frequency offsetobserved at the remote end by around 2 × − [27] (seealso eq. 1) as shown in figure 4. We do not observe theexpected behaviour, indicating the presence of other,competing processes.One process could be the variation of the Brillouingain curve relative to the signal with temperature, inparticular as the “remote” FBA amplifies one directiononly. To estimate this effect, we use the frequencydeviation of the AOM employed for link stabilization as a measure of the temperature variation d T / d t in thefibre according to:∆ ν Link = − π d φ d t ≈ − Lλ k n d T d t , (1)where we neglected the effect of the thermal expansionof the fibre ( δL/δT ). We use a thermo-optic coefficientof k n = δn/δT = 1 . × − / K [28], a fibre length L of 1 . × m and assume a temperature dependenceof the Brillouin frequency of k BT = 1 . k φ of the signal to theBrillouin frequency variation we deliberately modulatethe “remote” FBA pump frequency over a range of about6 MHz at a rate of several tens of kilohertz per second.We find k φ ≈ − × − rad/Hz. This yields a scalingfactor of:∆ ν BrillouinSignal∆ ν Link ≈ − k BT k φ λ πk n L = 8 . × − . (2)This effect is too small to compensate for the expectedeffect of asymmetric frequencies and hence does notlimit us yet. We conservatively estimate the overalleffect of the Brillouin amplification on the instability tobe smaller than 5 × − . From the noise spectrum the“remote” FBA’s lock we expect its instability contribu-tion to be at least one order of magnitude smaller.Other effects that may play a role are the finite sup-pression of the fibre noise [25] as well as the relativefluctuations between the separate local and “remote”setups. These are subject to further investigations.Using a loop consisting of a patched pair of telecommu-nication fibres connecting Braunschweig to Strasbourg,we have investigated optical frequency transfer over 1400km with three FBA as the only means of remote am-plification. We have introduced the ΛADEV as a morestringent measure of instability. We have found that Bril-louin amplification supports an inaccuracy and instabil-ity better than 1 × − , where the statistical precision isindicated by the instability [30]. Using separately housedlocal and “remote” setups, over a period of around threeweeks we observe an (in-)accuracy of the transferred op-tical frequency of about (1 . ± . × − . We do notobserve the effect expected from the relative frequencyshift between the outgoing and returning light.To our knowledge, the results presented here are the firstdemonstration of frequency transfer at the 10 − accu-racy level over a continental-scale distance. This fibrelink supports remote comparisons of the world’s best op-tical clocks. We note that for applications in relativis-tic geodesy, the achieved level of accuracy and stabilitywould correspond to a relativistic height resolution ofaround 100 µ m.We thank H. Schnatz and F. Riehle at PTB for theirlong-standing support and are indebted to Paul-Eric Pot-tie and colleagues for enabling the cooperation with Uni-versit´e de Strasbourg. We thank P. Gris, B. Moya andcolleagues from UDS, O. Bier from ARTE, T. Vetter,H. Klatte, and U. Koc from Kassel University, K. Ack-ermann and colleagues from Justus Liebig University inGiessen, B. Hoeft and colleagues from the Karlsruhe In-stitute of Technology, and F. Hack and colleagues fromGasline GmbH, as well as C. Grimm and colleagues fromDeutsches Forschungsnetz e.V. (DFN) and Emilie Camis-ard from RENATER. We are grateful to Thomas Legero for operating the cavity-stabilized laser, and to AndreUhde, J¨orn Falke, Mattias Misera, and Marion Wengelfor excellent technical support. This work is supportedby the European Metrology Programme (EMRP) SIB-02(NEAT-FT). The EMRP is jointly funded by the EMRPparticipating countries within EURAMET and the Eu-ropean Union. [1] O. Lopez, Opt. Express , 441 (2012).[3] O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar,C. Chardonnet, A. Amy-Klein, and G. Santarelli, App.Phys. B
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