Optical frequency transfer with below 10−21 uncertainty using a DFB–laser-based fiber Brillouin amplifier

I. INTRODUCTION

Section:

ChooseTop of pageABSTRACTI. INTRODUCTION <<II. NOVEL FBAM LAYOUTIII. DFB-FBAM CHARACTERIZ...IV. BRILLOUIN FREQUENCY S...V. DISCUSSION AND PERSPEC...REFERENCESPrevious sectionNext sectionModern atomic clocks based on optical transition play a paramount role—due to their high accuracy1–31. T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10−18 total uncertainty,” Nat. Commun. 6, 6896 (2015). https://doi.org/10.1038/ncomms78962. I. Ushijima, M. Takamoto, M. Das, T. Ohkubo, and H. Katori, “Cryogenic optical lattice clocks,” Nat. Photonics 9, 185–189 (2015). https://doi.org/10.1038/nphoton.2015.53. N. Huntemann, C. Sanner, B. Lipphardt, C. Tamm, and E. Peik, “Single-ion atomic clock with 3 × 10−18 systematic uncertainty,” Phys. Rev. Lett. 116, 063001–063005 (2016). https://doi.org/10.1103/PhysRevLett.116.063001—in the view of a future redefinition of the second in the international system of units (SI)4,54. F. Riehle, “Towards a redefinition of the second based on optical atomic clocks,” C. R. Phys. 16, 506–515 (2015). https://doi.org/10.1016/j.crhy.2015.03.0125. H. Margolis, “Timekeepers of the future,” Nat. Phys. 10, 82–83 (2014). https://doi.org/10.1038/nphys2834 and also in many applications such as tests of fundamental physics,6,76. B. M. Roberts, P. Delva, A. Al-Masoudi et al., “Search for transient variations of the fine structure constant and dark matter using fiber-linked optical atomic clocks,” New J. Phys. 22, 093010 (2020). https://doi.org/10.1088/1367-2630/abaace7. R. Lange, N. Huntemann, J. M. Rahm, C. Sanner, H. Shao, B. Lipphardt, C. Tamm, S. Weyers, and E. Peik, “Improved limits for violations of local position invariance from atomic clock comparisons,” Phys. Rev. Lett. 126, 011102 (2021). https://doi.org/10.1103/PhysRevLett.126.011102 relativistic geodesy,8–118. T. E. Mehlstäubler, G. Grosche, C. Lisdat, P. O. Schmidt, and H. Denker, “Atomic clocks for geodesy,” Rep. Prog. Phys. 81, 064401 (2018). https://doi.org/10.1088/1361-6633/aab4099. J. Grotti, S. Koller, S. Vogt et al., “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14, 437–441 (2018). https://doi.org/10.1038/s41567-017-0042-310. C. W. Chou, D. B. Hume, T. Rosenband, and D. J. Wineland, “Optical clocks and relativity,” Science 329, 1630–1634 (2010). https://doi.org/10.1126/science.119272011. T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10, 662–666 (2016). https://doi.org/10.1038/nphoton.2016.159 and remote spectroscopy.1212. B. Chanteau, O. Lopez, W. Zhang, D. Nicolodi, B. Argence, F. Auguste, M. Abgrall, C. Chardonnet, G. Santarelli, B. Darquié, Y. Le Coq, and A. Amy-Klein, “Mid-infrared laser phase-locking to a remote near-infrared frequency reference for high- precision molecular spectroscopy,” New J. Phys. 15, 073003 (2013). https://doi.org/10.1088/1367-2630/15/7/073003 These applications require high accuracy frequency comparisons of remote optical oscillators.13,1413. C. Lisdat, G. Grosche, N. Quintin et al., “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443–12447 (2016). https://doi.org/10.1038/ncomms1244314. M. Schioppo, J. Kronjäger, A. Silva et al., “Comparing ultrastable lasers at 7 × 10−17 fractional frequency instability through a 2220 km optical fibre network,” Nat. Commun. 13, 212 (2022). https://doi.org/10.1038/s41467-021-27884-3 Therefore, dissemination of highly coherent, stable frequencies over long distances is a prerequisite. For microwave atomic clock comparisons, satellite-based microwave links have been employed for coherent frequency transfer.1515. A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavać, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109–120 (2006). https://doi.org/10.1088/0026-1394/43/1/016 However, these links are restricted to an uncertainty greater than 10−16,1616. G. Petit, A. Kanj, S. Loyer, J. Delporte, F. Mercier, and F. Perosanz, “1 × 10−16 frequency transfer by GPS PPP with integer ambiguity resolution,” Metrologia 52, 301–309 (2015). https://doi.org/10.1088/0026-1394/52/2/301 which consequently does not meet the stringent requirement of comparisons of state-of-the-art optical atomic clocks that now achieve uncertainties in the range of ≈10−18.1–31. T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10−18 total uncertainty,” Nat. Commun. 6, 6896 (2015). https://doi.org/10.1038/ncomms78962. I. Ushijima, M. Takamoto, M. Das, T. Ohkubo, and H. Katori, “Cryogenic optical lattice clocks,” Nat. Photonics 9, 185–189 (2015). https://doi.org/10.1038/nphoton.2015.53. N. Huntemann, C. Sanner, B. Lipphardt, C. Tamm, and E. Peik, “Single-ion atomic clock with 3 × 10−18 systematic uncertainty,” Phys. Rev. Lett. 116, 063001–063005 (2016). https://doi.org/10.1103/PhysRevLett.116.063001Optical fiber links have been demonstrated as a powerful method for ultra-stable coherent frequency dissemination,17,1817. P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25, 1284–1293 (2008). https://doi.org/10.1364/josab.25.00128418. S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78, 021101 (2007). https://doi.org/10.1063/1.2437069 supporting frequency transfer uncertainties of ≪10−18 over continental distances.19,2019. N. Chiodo, N. Quintin, F. Stefani, F. Wiotte, E. Camisard, C. Chardonnet, G. Santarelli, A. Amy-Klein, P.-E. Pottie, and O. Lopez, “Cascaded optical fiber link using the internet network for remote clocks comparison,” Opt. Express 23, 33927–33937 (2015). https://doi.org/10.1364/oe.23.03392720. S. M. F. Raupach, A. Koczwara, and G. Grosche, “Brillouin amplification supports 1 × 10−20 uncertainty in optical frequency transfer over 1400 km of underground fiber,” Phys. Rev. A 92, 021801 (2015). https://doi.org/10.1103/physreva.92.021801 Optical fiber links are susceptible to environmental perturbations such as acoustic noise and thermal variations , which introduce frequency and phase fluctuations to the transmitted signal.1717. P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25, 1284–1293 (2008). https://doi.org/10.1364/josab.25.001284 For coherent frequency transfer,21,2221. K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336, 441–444 (2012). https://doi.org/10.1126/science.121844222. E. Cantin, M. Tønnes, R. Le Targat, A. Amy-Klein, O. Lopez, and P.-E. Pottie, “An accurate and robust metrological network for coherent optical frequency dissemination,” New J. Phys. 23, 053027 (2021). https://doi.org/10.1088/1367-2630/abe79e these fluctuations are compensated either by real-time interferometric stabilization schemes17,2317. P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25, 1284–1293 (2008). https://doi.org/10.1364/josab.25.00128423. L.-S. Ma, P. Jungner, J. Ye, and J. L. Hall, “Delivering the same optical frequency at two places: Accurate cancellation of phase noise introduced by an optical fiber or other time-varying path,” Opt. Lett. 19, 1777–1779 (1994). https://doi.org/10.1364/ol.19.001777 or by using a two-way transfer layout.24,2524. A. Bercy, F. Stefani, O. Lopez, C. Chardonnet, P. E. Pottie, and A. Amy-Klein, “Two-way optical frequency comparisons at 5 × 10−21 relative stability over 100-km telecommunication network fibers,” Phys. Rev. A 90, 061802 (2014). https://doi.org/10.1103/physreva.90.06180225. C. E. Calosso, E. Bertacco, D. Calonico, C. Clivati, G. A. Costanzo, M. Frittelli, F. Levi, A. Mura, and A. Godone, “Frequency transfer via a two-way optical phase comparison on a multiplexed fiber network,” Opt. Lett. 39, 1177 (2014). https://doi.org/10.1364/ol.39.001177 Moreover, the attenuation of power in the fiber is another major factor impacting long-haul optical links. In standard single mode fiber (SSMF), the attenuation coefficient is around 0.2 dB/km at 1550 nm wavelength. Erbium-doped fiber amplifiers (EDFAs) have been widely used in many undersea and terrestrial optical fiber communication links. However, bidirectional EDFA (bi-EDFA) as required for interferometric fiber links (IFLs) are subjected to spurious lasing effects caused by the double Rayleigh scattering,2627. D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, “High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117, 979–986 (2014). https://doi.org/10.1007/s00340-014-5917-8 which restricts the bi-EDFA gain to below 20 dB.19,27,2819. N. Chiodo, N. Quintin, F. Stefani, F. Wiotte, E. Camisard, C. Chardonnet, G. Santarelli, A. Amy-Klein, P.-E. Pottie, and O. Lopez, “Cascaded optical fiber link using the internet network for remote clocks comparison,” Opt. Express 23, 33927–33937 (2015). https://doi.org/10.1364/oe.23.03392726. J. Bromage, P. J. Winzer, and R. J. Essiambre, “Multiple path interference and its impact on system design,” in Raman Amplifiers for Telecommunications 2: Sub-Systems and Systems, Springer Series in Optical Sciences, edited by M. N. Islam (Springer, New York, 2004), pp. 491–568.28. O. Terra, G. Grosche, and H. Schnatz, “Brillouin amplification in phase coherent transfer of optical frequencies over 480 km fiber,” Opt. Express 18, 16102 (2010). https://doi.org/10.1364/oe.18.016102Due to the immanent high gain, narrow band, and greatly reduced sensitivity to double Rayleigh scattering, fiber Brillouin amplification (FBA) has been demonstrated as an efficient alternative amplification scheme for coherent frequency transfer.2828. O. Terra, G. Grosche, and H. Schnatz, “Brillouin amplification in phase coherent transfer of optical frequencies over 480 km fiber,” Opt. Express 18, 16102 (2010). https://doi.org/10.1364/oe.18.016102 Optical frequency transfer with an uncertainty lower than 1 × 10−20 was achieved over a 1400 km loop of an underground fiber connection between Braunschweig and Strasbourg using cascaded fiber Brillouin amplifier modules (FBAMs) as the only means of amplification.2020. S. M. F. Raupach, A. Koczwara, and G. Grosche, “Brillouin amplification supports 1 × 10−20 uncertainty in optical frequency transfer over 1400 km of underground fiber,” Phys. Rev. A 92, 021801 (2015). https://doi.org/10.1103/physreva.92.021801 This link is part of the Braunschweig–Strasbourg–Paris-London connection serving for a comparison of microwave and optical clocks.13,14,2913. C. Lisdat, G. Grosche, N. Quintin et al., “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443–12447 (2016). https://doi.org/10.1038/ncomms1244314. M. Schioppo, J. Kronjäger, A. Silva et al., “Comparing ultrastable lasers at 7 × 10−17 fractional frequency instability through a 2220 km optical fibre network,” Nat. Commun. 13, 212 (2022). https://doi.org/10.1038/s41467-021-27884-329. J. Guéna, S. Weyers, M. Abgrall et al., “First international comparison of fountain primary frequency standards via a long distance optical fiber link,” Metrologia 54, 348 (2017). https://doi.org/10.1088/1681-7575/aa65fe The link between Braunschweig and Strasbourg is operated by the Physikalisch Technische Bundesanstalt (PTB). Three cascaded FBAMs installed ≈200 km apart at Kassel University, Giessen University, and the Karlsruhe Institute of Technology are currently being used to compensate for the signal attenuation.20,3020. S. M. F. Raupach, A. Koczwara, and G. Grosche, “Brillouin amplification supports 1 × 10−20 uncertainty in optical frequency transfer over 1400 km of underground fiber,” Phys. Rev. A 92, 021801 (2015). https://doi.org/10.1103/physreva.92.02180130. S. Koke, A. Kuhl, T. Waterholter, S. M. F. Raupach, O. Lopez, E. Cantin, N. Quintin, A. Amy-Klein, P.-E. Pottie, and G. Grosche, “Combining fiber Brillouin amplification with a repeater laser station for fiber-based optical frequency dissemination over 1400 km,” New J. Phys. 21, 123017 (2019). https://doi.org/10.1088/1367-2630/ab5d95The FBAMs exploit the stimulated Brillouin scattering (SBS) nonlinear interaction in the transmission fiber. SBS is one of the lowest threshold nonlinear effects in optical fibers and has many applications in various fields, such as distributed sensing and optical signal processing.31,3231. J. Kadum, R. Das, A. Misra, and T. Schneider, “Brillouin-scattering-induced transparency enabled reconfigurable sensing of RF signals,” Photonics Res. 9, 1486 (2021). https://doi.org/10.1364/prj.42769132. J. E. Kadum, S. Preußler, R. Das, Y. Mandalawi, and T. Schneider, “Temporal disentanglement of wireless signal carriers based on quasi-light-storage,” J. Lightwave Technol. 40, 6762 (2022). https://doi.org/10.1109/jlt.2022.3189429 SBS can be viewed as a nonlinear interaction between two counter-propagating optical waves, a strong pump, and a weak signal. The interaction between the two waves excites, through electrostriction, an acoustic wave that acts as a moving density wave.3333. R. Boyd, Nonlinear Optics (Academic Press, Cambridge, MA, 2008). This acoustic wave then initiates the power coupling from the pump wave to the signal wave. Maximum power transfer takes place if the pump wave is frequency upshifted with respect to the weak signal by the so-called Brillouin frequency shift (BFS). In order to attain maximum Brillouin gain and circumvent the SBS-induced phase shift to the counterpropagating signal, the pump frequency νp has to be stabilized to have a constant frequency at νs+ νBFS, where νBFS and νs are the BFS and signal frequency, respectively. When the pump power is sufficiently high so that it is undepleted, the signal amplitude is amplified exponentially at the output of the optical fiber according toAS(L)=AS(0)expGB(ωS)Leffe−αL/2,(1)where As (L) and As (0) are the signal amplitudes at the output and the input of the fiber amplifier, respectively; Leff = [1 − exp(−αL)]/α is the effective length of the fiber amplifier, and α is the linear loss coefficient. The complex Brillouin gain coefficient GB (ωs) is given by3434. A. Zadok, A. Eyal, and M. Tur, “Stimulated Brillouin scattering slow light in optical fibers [Invited],” Appl. Opt. 50, E38 (2011). https://doi.org/10.1364/ao.50.000e38GB(ωS)=gBAeff12Ap21−2j(Δω−ωBFS)/ΓBs,(2)where gB denotes the material Brillouin coefficient and equals to 5 × 10−11 m/W in SSMF, and Aeff represents the effective area of the optical mode in the fiber. Ap is the pump amplitude, ∆ω/2π is the frequency detuning between the pump and signal waves, ωBFS/2π is the BFS of the fiber, and ΓB/2π is the full width at half-maximum (FWHM) of the Lorentzian shaped Brillouin spectrum. The phonon lifetime τa (≈10 ns) of the acoustic wave in standard Brillouin materials makes the SBS a narrowband process with a gain linewidth of ≈20–30 MHz.3333. R. Boyd, Nonlinear Optics (Academic Press, Cambridge, MA, 2008). The real part of Eq. (2) determines the amplitude gain response of the signal wave. However, due to the Kramers–Kronig relation,3333. R. Boyd, Nonlinear Optics (Academic Press, Cambridge, MA, 2008). the amplitude change is accompanied by a change of the propagation constant; hence, the imaginary part of Eq. (2) represents the frequency-dependent phase change imposed on the signal wave. For very low input pump powers, spontaneous Brillouin scattering (SpBS) is initiated by the acoustic wave that originates from the thermal density fluctuations in the medium,3535. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990). https://doi.org/10.1103/physreva.42.5514 leading to a frequency down-shifted Stokes and a frequency upshifted anti-Stokes spontaneous scattering. For FBA-based IFLs, the SpBS is in the same frequency band as the signal wave , which consequently degrades the signal-to-noise ratio (SNR) of the amplified signal.Currently installed bidirectional FBAMs employ one narrow linewidth (≈1 kHz) laser as a pump source for both the forward and backward signal amplifications.20,28,30,3620. S. M. F. Raupach, A. Koczwara, and G. Grosche, “Brillouin amplification supports 1 × 10−20 uncertainty in optical frequency transfer over 1400 km of underground fiber,” Phys. Rev. A 92, 021801 (2015). https://doi.org/10.1103/physreva.92.02180128. O. Terra, G. Grosche, and H. Schnatz, “Brillouin amplification in phase coherent transfer of optical frequencies over 480 km fiber,” Opt. Express 18, 16102 (2010). https://doi.org/10.1364/oe.18.01610230. S. Koke, A. Kuhl, T. Waterholter, S. M. F. Raupach, O. Lopez, E. Cantin, N. Quintin, A. Amy-Klein, P.-E. Pottie, and G. Grosche, “Combining fiber Brillouin amplification with a repeater laser station for fiber-based optical frequency dissemination over 1400 km,” New J. Phys. 21, 123017 (2019). https://doi.org/10.1088/1367-2630/ab5d9536. S. M. F. Raupach, A. Koczwara, and G. Grosche, “Optical frequency transfer via a 660 km underground fiber link using a remote Brillouin amplifier,” Opt. Express 22, 26537–26547 (2014). https://doi.org/10.1364/oe.22.026537 Moreover, the backward pump wave is frequency shifted using acousto-optic modulators (AOMs) to accommodate for the frequency offset Δν between forward and backward signals, which is introduced to mark the remote end back-reflection.2020. S. M. F. Raupach, A. Koczwara, and G. Grosche, “Brillouin amplification supports 1 × 10−20 uncertainty in optical frequency transfer over 1400 km of underground fiber,” Phys. Rev. A 92, 021801 (2015). https://doi.org/10.1103/physreva.92.021801 This offset is selected depending on the IFL setup and frequency comparison layout. This FBAM design has several drawbacks: first, the AOM based scheme is inflexible since the AOMs have a limited frequency operating range of a few MHz. This requires the AOM frequencies to be tailored to the pre-measured BFS of the deployed fibers around the amplifier site. Second, the AOM based design demands additional radio frequency (RF) generators with very high driving RF power (≈1 W). In addition, due to the power splitting of the pump wave, the insertion loss of the AOM, and the limited output power of the narrow linewidth diode laser, the pump waves experience significant optical losses. Therefore, to reach sufficient optical pump power for amplifying both forward and backward traveling signal waves, additional unidirectional EDFAs are required to compensate for the optical losses. These EDFAs restrict the ad hoc applicability of the demonstrated FBAM to the C-band. Third, phase locking between the pump and signal waves is achieved by using an analog-electronics-based phase locked loop (PLL), which claims a large volume in current FBAMs. Furthermore, an automatic and continuous adaptation of the lock frequency to the temporarily varying effective BFS, which is the average of the strain- and temperature-dependent BFS of the fiber sections within the SBS interaction zone,37,3837. T. R. Parker, M. Farhadiroushan, V. A. Handerek, and A. J. Rogers, “Temperature and strain dependence of the power level and frequency of spontaneous Brillouin scattering in optical fibers,” Opt. Lett. 22, 787 (1997). https://doi.org/10.1364/ol.22.00078738. T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects on the Brillouin frequency shift in jacketed optical silica fibers,” Appl. Opt. 29, 2219 (1990). https://doi.org/10.1364/ao.29.002219 is missing.In summary, the complex configuration of current FBAMs, with their large dimensions and high-power consumption, hinders their straightforward roll-out to other sites. Although several developments have been introduced to FBAMs installed in our IFL,3939. A. Kuhl, T. Waterholter, S. Koke, and G. Grosche, “Polarization-optimized fibre Brillouin amplifier module for the interferometric fibre link between Braunschweig and Strasbourg,” in European Frequency and Time Forum (EFTF), 2020. a compact footprint, power efficient, and cost-effective FBAM that outperforms the existing modules in terms of integrability of the frequency metrology infrastructure with the existing telecom fiber network is still desirable.

In this paper, we present an FBAM based on two distributed feedback (DFB) lasers as pump sources for the forward and backward signal amplifications. These DFBs are cost-effective and commercially available within different frequency bands. As will be described in detail, the employment of DFB lasers in the FBAM allows for IFLs operation in telecommunication channels outside the EDFA’s amplification window. This paves the way toward the possibility of fiber sharing and of creating a long-term infrastructure for sustainable frequency comparison. In the DFB-FBAM, automatic tracking of the BFS is implemented using phase stabilization on a field programmable gate array (FPGA). The performance of the DFB-FBAM in the coherent frequency transfer has been assessed using a novel two-way scheme over an in-lab 100 km long optical fiber link.

V. DISCUSSION AND PERSPECTIVES

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. NOVEL FBAM LAYOUTIII. DFB-FBAM CHARACTERIZ...IV. BRILLOUIN FREQUENCY S...V. DISCUSSION AND PERSPEC... <<REFERENCESPrevious sectionNext sectionThis paper presents for the first time, to the best of our knowledge, the utilization of an FBAM based on DFB pump lasers for optical frequency dissemination. The novel design is compact, cost-effective, and directly applicable without hardware modification at different positions along a fiber link. The phase stabilization between the pump and signal waves is implemented via an FPGA, which includes the capability to track the temporally varying Brillouin frequency shift. These simplifications facilitate the building of FBAM-based IFLs with more frequent amplification stages. As then only lower pump powers are required, the negative impact of SpBS can be mitigated and better SNRs can be achieved. These improvements address the quest to push single span IFL lengths beyond the currently demonstrated 1400 km.2020. S. M. F. Raupach, A. Koczwara, and G. Grosche, “Brillouin amplification supports 1 × 10−20 uncertainty in optical frequency transfer over 1400 km of underground fiber,” Phys. Rev. A 92, 021801 (2015). https://doi.org/10.1103/physreva.92.021801 Using a two-way characterization scheme free from uncompensated optical paths, we observed a frequency instability lower than 9.3 × 10−22 at 10 ks integration time and a zero-compatible fractional frequency uncertainty contribution of below (−2.1 ± 3.3) × 10−22 for averaging times >100 ks. These values exceed the hitherto published FBAM-induced uncertainty characterization by at least one order of magnitude.The presented DFB-FBAM minimizes insertion loss by using only one fiber coupler for injecting both pump waves. Still, signal insertion losses amount to ≈7 dB , which mandates a certain pump power for compensation and, hence, impacts the spontaneous Brillouin scattering background. A further insertion loss reduction of ≈3.5 dB can be achieved by combining the DFB approach with the alternative polarization-based pump injection scheme3939. A. Kuhl, T. Waterholter, S. Koke, and G. Grosche, “Polarization-optimized fibre Brillouin amplifier module for the interferometric fibre link between Braunschweig and Strasbourg,” in European Frequency and Time Forum (EFTF), 2020. suited for IFLs with orthogonal SOP in the forward and backward directions. The optimal pump injection scheme is subject to a trade-off between the frequency transfer errors introduced by a limited SNR and the slight PMD induced non-reciprocity that comes from an orthogonal SOP IFL setup.The DFB-based design also allows for building FBAMs in frequency bands off of the well populated ITU C-band. This feature is especially interesting for building IFLs over fiber connections shared with telecommunication data traffic.51,5251. O. Lopez, A. Haboucha, F. Kéfélian, H. Jiang, B. Chanteau, V. Roncin, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Cascaded multiplexed optical link on a telecommunication network for frequency dissemination,” Opt. Express 18, 16849 (2010). https://doi.org/10.1364/oe.18.01684952. A. Amy-Klein, O. Lopez, F. Kéfélian, C. Chardonnet, H. Jiang, and G. Santarelli, “High-resolution optical frequency dissemination on a telecommunication network,” in 2009 IEEE International Frequency Control Symposium Joint with the 22nd European Frequency and Time Forum (IEEE, 2009), Vol. 34, pp. 813–814. Therefore, the DFB-FBA unfolds new opportunities to establish a frequency metrology infrastructure within existing telecommunication fiber networks.With the achieved results and the promising features, we believe the DFB-based FBAM will in the future serve to compare today’s state-of-the-art atomic optical clocks. This will support pursuing the roadmap toward a future redefinition of the SI-second and applications such as relativistic geodesy.6–96. B. M. Roberts, P. Delva, A. Al-Masoudi et al., “Search for transient variations of the fine structure constant and dark matter using fiber-linked optical atomic clocks,” New J. Phys. 22, 093010 (2020). https://doi.org/10.1088/1367-2630/abaace7. R. Lange, N. Huntemann, J. M. Rahm, C. Sanner, H. Shao, B. Lipphardt, C. Tamm, S. Weyers, and E. Peik, “Improved limits for violations of local position invariance from atomic clock comparisons,” Phys. Rev. Lett. 126, 011102 (2021). https://doi.org/10.1103/PhysRevLett.126.0111028. T. E. Mehlstäubler, G. Grosche, C. Lisdat, P. O. Schmidt, and H. Denker, “Atomic clocks for geodesy,” Rep. Prog. Phys. 81, 064401 (2018). https://doi.org/10.1088/1361-6633/aab4099. J. Grotti, S. Koller, S. Vogt et al., “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14, 437–441 (2018). https://doi.org/10.1038/s41567-017-0042-3

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