Free-space interferometer design for optical frequency dissemination and out-of-loop characterization below the 10−21-level

Thomas Jürss; Gesine Grosche; Sebastian Koke

doi:10.1364/PRJ.485899

[1] LIGO Scientific, B. Abbott, Virgo Collaboration, R. Abbott, T. Abbott. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett., 116, 061102(2016).

[2] K. U. Schreiber, J.-P. R. Wells. Invited review article: large ring lasers for rotation sensing. Rev. Sci. Instrum., 84, 041101(2013).

[3] N. Kuramoto, K. Fujii, K. Yamazawa. Volume measurements of ²⁸Si spheres using an interferometer with a flat etalon to determine the Avogadro constant. Metrologia, 48, S83-S95(2011).

[4] A. Nicolaus, G. Bartl, A. Peter, E. Kuhn, T. Mai. Volume determination of two spheres of the new ²⁸Si crystal of PTB. Metrologia, 54, 512-515(2017).

[5] https://www.bipm.org/en/home

[6] L.-S. Ma, P. Jungner, J. Ye, 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).

[7] S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, J. Ye. Remote transfer of ultrastable frequency references via fiber networks. Rev. Sci. Instrum., 78, 021101(2007).

[8] P. A. Williams, W. C. Swann, N. R. Newbury. High-stability transfer of an optical frequency over long fiber-optic links. J. Opt. Soc. Am. B, 25, 1284-1293(2008).

[9] G. Grosche, O. Terra, K. Predehl, R. Holzwarth, B. Lipphardt, F. Vogt, U. Sterr, H. Schnatz. Optical frequency transfer via 146 km fiber link with 10⁻¹⁹ relative accuracy. Opt. Lett., 34, 2270-2272(2009).

[10] 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, F. Levi. High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link. Appl. Phys. B, 117, 979-986(2014).

[11] N. Chiodo, N. Quintin, F. Stefani, F. Wiotte, E. Camisard, C. Chardonnet, G. Santarelli, A. Amy-Klein, P.-E. Pottie, O. Lopez. Cascaded optical fiber link using the internet network for remote clocks comparison. Opt. Express, 23, 33927-33937(2015).

[12] S. M. F. Raupach, A. Koczwara, 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).

[13] S. Koke, A. Kuhl, T. Waterholter, S. M. F. Raupach, O. Lopez, E. Cantin, N. Quintin, A. Amy-Klein, P.-E. Pottie, 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).

[14] C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, P.-E. Pottie. A clock network for Geodesy and fundamental science. Nat. Commun., 7, 12443(2016).

[15] M. Takamoto, I. Ushijima, N. Ohmae, T. Yahagi, K. Kokado, H. Shinkai, H. Katori. Test of general relativity by a pair of transportable optical lattice clocks. Nat. Photonics, 14, 411-415(2020).

[16] C. W. Chou, D. B. Hume, T. Rosenband, D. J. Wineland. Optical clocks and relativity. Science, 329, 1630-1633(2010).

[17] I. Ushijima, M. Takamoto, M. Das, T. Ohkubo, H. Katori. Cryogenic optical lattice clocks. Nat. Photonics, 9, 185-189(2015).

[18] T. Nicholson, S. Campbell, R. Hutson, G. Marti, B. Bloom, R. McNally, W. Zhang, M. Barrett, M. Safronova, G. Strouse, W. Tew, J. Ye. Systematic evaluation of an atomic clock at 2 × 10⁻¹⁸ total uncertainty. Nat. Commun., 6, 6896(2015).

[19] N. Huntemann, C. Sanner, B. Lipphardt, C. Tamm, E. Peik. Single-ion atomic clock with 3 × 10⁻¹⁸ systematic uncertainty. Phys. Rev. Lett., 116, 063001(2016).

[20] W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, A. D. Ludlow. Atomic clock performance enabling Geodesy below the centimetre level. Nature, 564, 87-90(2018).

[21] S. Brewer, J.-S. Chen, A. Hankin, E. Clements, C. Chou, D. Wineland, D. Hume, D. Leibrandt. ²⁷Al⁺ quantum-logic clock with a systematic uncertainty below 10⁻¹⁸. Phys. Rev. Lett., 123, 033201(2019).

[22] F. Riehle. Towards a redefinition of the second based on optical atomic clocks. C. R. Phys., 16, 506-515(2015).

[23] P. Gill. Is the time right for a redefinition of the second by optical atomic clocks?. J. Phys. Conf. Ser., 723, 012053(2016).

[24] T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, H. Katori. Geopotential measurements with synchronously linked optical lattice clocks. Nat. Photonics, 10, 662-666(2016).

[25] J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Barbieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, D. Calonico. Geodesy and metrology with a transportable optical clock. Nat. Phys., 14, 437-441(2018).

[26] T. E. Mehlstäubler, G. Grosche, C. Lisdat, P. O. Schmidt, H. Denker. Atomic clocks for geodesy. Rep. Prog. Phys., 81, 064401(2018).

[27] P. Delva, J. Lodewyck, S. Bilicki, E. Bookjans, G. Vallet, R. Le Targat, P.-E. Pottie, C. Guerlin, F. Meynadier, C. Le Poncin-Lafitte, O. Lopez, A. Amy-Klein, W.-K. Lee, N. Quintin, C. Lisdat, A. Al-Masoudi, S. Dörscher, C. Grebing, G. Grosche, A. Kuhl, S. Raupach, U. Sterr, I. R. Hill, R. Hobson, W. Bowden, J. Kronjäger, G. Marra, A. Rolland, F. N. Baynes, H. S. Margolis, P. Gill. Test of special relativity using a fiber network of optical clocks. Phys. Rev. Lett., 118, 221102(2017).

[28] B. M. Roberts, P. Delva, A. Al-Masoudi, A. Amy-Klein, C. Bærentsen, C. F. A. Baynham, E. Benkler, S. Bilicki, S. Bize, W. Bowden, J. Calvert, V. Cambier, E. Cantin, E. A. Curtis, S. Dörscher, M. Favier, F. Frank, P. Gill, R. M. Godun, G. Grosche, C. Guo, A. Hees, I. R. Hill, R. Hobson, N. Huntemann, J. Kronjäger, S. Koke, A. Kuhl, R. Lange, T. Legero, B. Lipphardt, C. Lisdat, J. Lodewyck, O. Lopez, H. S. Margolis, H. Álvarez-Martínez, F. Meynadier, F. Ozimek, E. Peik, P.-E. Pottie, N. Quintin, C. Sanner, L. De Sarlo, M. Schioppo, R. Schwarz, A. Silva, U. Sterr, C. Tamm, R. Le Targat, P. Tuckey, G. Vallet, T. Waterholter, D. Xu, P. Wolf. Search for transient variations of the fine structure constant and dark matter using fiber-linked optical atomic clocks. New J. Phys., 22, 093010(2020).

[29] F. Stefani, O. Lopez, A. Bercy, W.-K. Lee, C. Chardonnet, G. Santarelli, P.-E. Pottie, A. Amy-Klein. Tackling the limits of optical fiber links. J. Opt. Soc. Am. B, 32, 787-797(2015).

[30] D. Xu, P. Delva, O. Lopez, A. Amy-Klein, P.-E. Pottie. Reciprocity of propagation in optical fiber links demonstrated to 10⁻²¹. Opt. Express, 27, 36965-36975(2019).

[31] D. Xu, O. Lopez, A. Amy-Klein, P.-E. Pottie. Non-reciprocity in optical fiber links: experimental evidence. Opt. Express, 29, 17476-17490(2021).

[32] J. Guéna, S. Weyers, M. Abgrall, C. Grebing, V. Gerginov, P. Rosenbusch, S. Bize, B. Lipphardt, H. Denker, N. Quintin, S. M. F. Raupach, D. Nicolodi, F. Stefani, N. Chiodo, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, C. Chardonnet, Y. Le Coq, M. Lours, G. Santarelli, A. Amy-Klein, R. Le Targat, O. Lopez, P. E. Pottie, G. Grosche. First international comparison of fountain primary frequency standards via a long distance optical fiber link. Metrologia, 54, 348-354(2017).

[33] J. Lodewyck, R. Le Targat, P.-E. Pottie, E. Benkler, S. Koke, J. Kronjäger. Universal formalism for data sharing and processing in clock comparison networks. Phys. Rev. Res., 2, 043269(2020).

[34] E. Benkler, B. Lipphardt, T. Puppe, R. Wilk, F. Rohde, U. Sterr. End-to-end topology for fiber comb based optical frequency transfer at the 10⁻²¹ level. Opt. Express, 27, 36886-36902(2019).

[35] S. Häfner, S. Herbers, S. Vogt, S. Vogt, C. Lisdat, U. Sterr. Transportable interrogation laser system with an instability of mod σ_y = 3 × 10⁻¹⁶. Opt. Express, 28, 16407-16416(2020).

[36] T. Akatsuka, T. Goh, H. Imai, K. Oguri, A. Ishizawa, I. Ushijima, N. Ohmae, M. Takamoto, H. Katori, T. Hashimoto, H. Gotoh, T. Sogawa. Optical frequency distribution using laser repeater stations with planar lightwave circuits. Opt. Express, 28, 9186-9197(2020).

[37] E. Cantin, M. Tønnes, R. L. Targat, A. Amy-Klein, O. Lopez, P.-E. Pottie. An accurate and robust metrological network for coherent optical frequency dissemination. New J. Phys., 23, 053027(2021).

[38] G. Grosche. Eavesdropping time and frequency: phase noise cancellation along a time-varying path, such as an optical fiber. Opt. Lett., 39, 2545-2548(2014).

[39] C. E. Calosso, E. Bertacco, D. Calonico, C. Clivati, G. A. Costanzo, M. Frittelli, F. Levi, A. Mura, A. Godone. Frequency transfer via a two-way optical phase comparison on a multiplexed fiber network. Opt. Lett., 39, 1177-1180(2014).

[40] F. Guillou-Camargo, V. Ménoret, E. Cantin, O. Lopez, N. Quintin, E. Camisard, V. Salmon, J.-M. L. Merdy, G. Santarelli, A. Amy-Klein, P.-E. Pottie, B. Desruelle, C. Chardonnet. First industrial-grade coherent fiber link for optical frequency standard dissemination. Appl. Opt., 57, 7203-7210(2018).

[41] S. Droste. Optical frequency transfer via telecommunication fiber links for metrological applications(2014).

[42] H. Jiang, F. Kéfélian, S. Crane, O. Lopez, M. Lours, J. Millo, D. Holleville, P. Lemonde, C. Chardonnet, A. Amy-Klein, G. Santarelli. Long-distance frequency transfer over an urban fiber link using optical phase stabilization. J. Opt. Soc. Am. B, 25, 2029-2035(2008).

[43] C. Clivati, P. Savio, S. Abrate, V. Curri, R. Gaudino, M. Pizzocaro, D. Calonico. Robust optical frequency dissemination with a dual-polarization coherent receiver. Opt. Express, 28, 8494-8511(2020).

[44] M. Notcutt, L.-S. Ma, J. Ye, J. L. Hall. Simple and compact 1-Hz laser system via an improved mounting configuration of a reference cavity. Opt. Lett., 30, 1815-1817(2005).

[45] F. T. Ghaemi. Ultra-high-precision alignment of the elastomerically mounted elements of the science camera lenses for the Mars Science Laboratory (MSL) rover. Appl. Opt., 50, 5108-5114(2011).

[46] S. T. Dawkins, J. J. McFerran, A. N. Luiten. Considerations on the measurement of the stability of oscillators with frequency counters. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 54, 918-925(2007).

[47] E. Benkler, C. Lisdat, U. Sterr. On the relation between uncertainties of weighted frequency averages and the various types of Allan deviations. Metrologia, 52, 565(2015).

[48] R. Noe, H. Heidrich, D. Hoffmann. Endless polarization control systems for coherent optics. J. Lightwave Technol., 6, 1199-1208(1988).

[49] W. Aarts, G.-D. Khoe. New endless polarization control method using three fiber squeezers. J. Lightwave Technol., 7, 1033-1043(1989).

[50] . Schott optical glass collection datasheets(2019).

[51] G. Ghosh. Model for the pressure-optic coefficients in optical materials. Phys. Rev. B, 57, 8178-8180(1998).

[52] . Corning HPFS 7979, 7980, 8655 fused silica–optical materials product information(2015).

[53] . Guide to optical glass used at Thorlabs(2023).

[54] G. Ghosh. Handbook of Thermo-Optic Coefficients of Optical Materials with Applications(1998).

[55] P. E. Ciddor. Refractive index of air: new equations for the visible and near infrared. Appl. Opt., 35, 1566-1573(1996).

[56] M. Polyanskiy. https://github.com/polyanskiy/refractiveindex.info-scripts/blob/6e7febc6ea8ca76936cdfa23208f74321f018938/scripts/Ciddor 1996-air.py(2017). https://github.com/polyanskiy/refractiveindex.info-scripts/blob/6e7febc6ea8ca76936cdfa23208f74321f018938/scripts/Ciddor 1996-air.py

[57] B. Edlén. The refractive index of air. Metrologia, 2, 71(1966).

[58] K. P. Birch, M. J. Downs. Correction to the updated Edlén equation for the refractive index of air. Metrologia, 31, 315-316(1994).

[59] A. Tourigny-Plante, V. Michaud-Belleau, N. B. Hébert, H. Bergeron, J. Genest, J.-D. Deschênes. An open and flexible digital phase-locked loop for optical metrology. Rev. Sci. Instrum., 89, 093103(2018).

[60] G. Wanner, G. Heinzel, E. Kochkina, C. Mahrdt, B. S. Sheard, S. Schuster, K. Danzmann. Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams. Opt. Commun., 285, 4831-4839(2012).

[61] K.-S. Isleif, L. Bischof, S. Ast, D. Penkert, T. S. Schwarze, G. F. Barranco, M. Zwetz, S. Veith, J.-S. Hennig, M. Tröbs, J. Reiche, O. Gerberding, K. Danzmann, G. Heinzel. Towards the LISA backlink: experiment design for comparing optical phase reference distribution systems. Classical Quantum Gravity, 35, 085009(2018).

[62] K.-S. Isleif. Laser interferometry for LISA and satellite geodesy missions(2018).

[63] R. Fleddermann, C. Diekmann, F. Steier, M. Tröbs, G. Heinzel, K. Danzmann. Sub-pm√hZ^-1 non-reciprocal noise in the LISA backlink fiber. Classical Quantum Gravity, 35, 075007(2018).

[64] J. W. Berthold, S. F. Jacobs. Ultraprecise thermal expansion measurements of seven low expansion materials. Appl. Opt., 15, 2344-2347(1976).

[65] https://doi.org/10.5281/zenodo.7859474. https://doi.org/10.5281/zenodo.7859474