Abstract

The ability to distribute the precise time and frequency from an optical clock to remote platforms could enable future precise navigation and sensing systems. Here, we demonstrate tight, real-time synchronization of a remote microwave clock to a master optical clock over a turbulent 4 km open-air path via optical two-way time–frequency transfer. Once synchronized, the 10 GHz frequency signals generated at each site agree to 10−14 at 1 s and below 10−17 at 1000 s. In addition, the two clock times are synchronized to ±13 fs over an 8-hour period. The ability to phase-synchronize 10 GHz signals across platforms supports future distributed coherent sensing, while the ability to time-synchronize multiple microwave-based clocks to a high-performance master optical clock supports future precision navigation/timing systems.

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References

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    [Crossref]

2016 (1)

C. Robert, J.-M. Conan, and P. Wolf, “Impact of turbulent phase noise on frequency transfer with asymmetric two-way ground-satellite coherent optical links,” Phys. Rev. A 93, 033860 (2016).

2015 (4)

L. C. Sinclair, J.-D. Deschênes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “Invited Article: A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86, 081301 (2015).
[Crossref]

O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Phys. 16, 531–539 (2015).
[Crossref]

S. Droste, C. Grebing, J. Leute, S. M. F. Raupach, A. Matveev, T. W. Hänsch, A. Bauch, R. Holzwarth, and G. Grosche, “Characterization of a 450 km baseline GPS carrier-phase link using an optical fiber link,” New J. Phys. 17, 083044 (2015).
[Crossref]

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
[Crossref]

2014 (2)

2013 (3)

A. Hati, C. W. Nelson, C. Barnes, D. Lirette, T. Fortier, F. Quinlan, J. A. Desalvo, A. Ludlow, S. A. Diddams, and D. A. Howe, “State-of-the-art RF signal generation from optical frequency division,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60, 1796–1803 (2013).
[Crossref]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7, 434–438 (2013).
[Crossref]

S. Droste, F. Ozimek, T. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett. 111, 110801 (2013).
[Crossref]

2012 (1)

L. Sliwczynski, P. Krehlik, L. Buczek, and M. Lipinski, “Frequency transfer in electronically stabilized fiber optic link exploiting bidirectional optical amplifiers,” IEEE Trans. Instrum. Meas. 61, 2573–2580 (2012).
[Crossref]

2011 (4)

S. Doeleman, T. Mai, A. E. E. Rogers, J. G. Hartnett, M. E. Tobar, and N. Nand, “Adapting a cryogenic sapphire oscillator for very long baseline interferometry,” Publ. Astron. Soc. Pac. 123, 582–595 (2011).
[Crossref]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[Crossref]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654–3656 (2011).
[Crossref]

N. R. Nand, J. G. Hartnett, E. N. Ivanov, and G. Santarelli, “Ultra-stable very-low phase-noise signal source for very long baseline interferometry using a cryocooled sapphire oscillator,” IEEE Trans. Microwave Theory Tech. 59, 2978–2986 (2011).
[Crossref]

2010 (2)

S. Grop, P.-Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46, 420–422 (2010).
[Crossref]

K. Djerroud, O. Acef, A. Clairon, P. Lemonde, C. N. Man, E. Samain, and P. Wolf, “Coherent optical link through the turbulent atmosphere,” Opt. Lett. 35, 1479–1481 (2010).
[Crossref]

2009 (2)

2008 (1)

S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
[Crossref]

2007 (1)

2006 (1)

J.-F. Cliche and B. Shillue, “Precision timing control for radioastronomy: maintaining femtosecond synchronization in the Atacama large millimeter array,” IEEE Control Syst. 26, 19–26 (2006).
[Crossref]

2001 (1)

M. Calhoun, R. Sydnor, and W. Diener, “A stabilized 100-megahertz and 1-gigahertz reference frequency distribution for Cassini radio science,” Interplanet. Netw. Prog. Rep. 148, 1–11 (2001).

2000 (1)

M. Sushchik, N. Rulkov, L. Larson, L. Tsimring, H. Abarbanel, K. Yao, and A. Volkovskii, “Chaotic pulse position modulation: a robust method of communicating with chaos,” IEEE Commun. Lett. 4, 128–130 (2000).
[Crossref]

1994 (1)

1971 (1)

1960 (1)

R. E. Kalman, “A new approach to linear filtering and prediction problems,” Trans. ASME J. Basic Eng. 82, 35–45 (1960).
[Crossref]

Abarbanel, H.

M. Sushchik, N. Rulkov, L. Larson, L. Tsimring, H. Abarbanel, K. Yao, and A. Volkovskii, “Chaotic pulse position modulation: a robust method of communicating with chaos,” IEEE Commun. Lett. 4, 128–130 (2000).
[Crossref]

Acef, O.

Achkar, J.

O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Phys. 16, 531–539 (2015).
[Crossref]

Albanese, D.

E. Samain, P. Exertier, P. Guillemot, F. Pierron, D. Albanese, J. Paris, J.-M. Torre, I. Petitbon, and S. Leon, “Time transfer by laser link T2L2 first results,” in Joint Meeting of the European Frequency and Time Forum (EFTF) and the IEEE International Frequency Control Symposium (FCS), Besancon, France, 2009, pp. 194–198.

Alighanbari, S.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
[Crossref]

Amy-Klein, A.

O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Phys. 16, 531–539 (2015).
[Crossref]

Andrews, L. C.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

Barnes, C.

A. Hati, C. W. Nelson, C. Barnes, D. Lirette, T. Fortier, F. Quinlan, J. A. Desalvo, A. Ludlow, S. A. Diddams, and D. A. Howe, “State-of-the-art RF signal generation from optical frequency division,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60, 1796–1803 (2013).
[Crossref]

Barwood, G. P.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
[Crossref]

Bauch, A.

S. Droste, C. Grebing, J. Leute, S. M. F. Raupach, A. Matveev, T. W. Hänsch, A. Bauch, R. Holzwarth, and G. Grosche, “Characterization of a 450 km baseline GPS carrier-phase link using an optical fiber link,” New J. Phys. 17, 083044 (2015).
[Crossref]

Baumann, E.

L. C. Sinclair, J.-D. Deschênes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “Invited Article: A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86, 081301 (2015).
[Crossref]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7, 434–438 (2013).
[Crossref]

J.-D. Deschênes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X (in press).

Baynes, F. N.

Bercy, A.

O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Phys. 16, 531–539 (2015).
[Crossref]

Bergeron, H.

J.-D. Deschênes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X (in press).

Bergquist, J. C.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[Crossref]

Bize, S.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
[Crossref]

Bock, D. C.-J.

S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
[Crossref]

Bongs, K.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
[Crossref]

Boudot, R.

S. Grop, P.-Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46, 420–422 (2010).
[Crossref]

Bourgeois, P.-Y.

S. Grop, P.-Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46, 420–422 (2010).
[Crossref]

Bower, G. C.

S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
[Crossref]

Buczek, L.

L. Sliwczynski, P. Krehlik, L. Buczek, and M. Lipinski, “Frequency transfer in electronically stabilized fiber optic link exploiting bidirectional optical amplifiers,” IEEE Trans. Instrum. Meas. 61, 2573–2580 (2012).
[Crossref]

Byrd, J. M.

Calhoun, M.

M. Calhoun, R. Sydnor, and W. Diener, “A stabilized 100-megahertz and 1-gigahertz reference frequency distribution for Cassini radio science,” Interplanet. Netw. Prog. Rep. 148, 1–11 (2001).

Campbell, J. C.

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S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Phys. 16, 531–539 (2015).
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O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Phys. 16, 531–539 (2015).
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F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7, 434–438 (2013).
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C. Robert, J.-M. Conan, and P. Wolf, “Impact of turbulent phase noise on frequency transfer with asymmetric two-way ground-satellite coherent optical links,” Phys. Rev. A 93, 033860 (2016).

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S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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A. Hati, C. W. Nelson, C. Barnes, D. Lirette, T. Fortier, F. Quinlan, J. A. Desalvo, A. Ludlow, S. A. Diddams, and D. A. Howe, “State-of-the-art RF signal generation from optical frequency division,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60, 1796–1803 (2013).
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L. C. Sinclair, J.-D. Deschênes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “Invited Article: A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86, 081301 (2015).
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J.-D. Deschênes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X (in press).

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F. Quinlan, F. N. Baynes, T. M. Fortier, Q. Zhou, A. Cross, J. C. Campbell, and S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39, 1581–1584 (2014).
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A. Hati, C. W. Nelson, C. Barnes, D. Lirette, T. Fortier, F. Quinlan, J. A. Desalvo, A. Ludlow, S. A. Diddams, and D. A. Howe, “State-of-the-art RF signal generation from optical frequency division,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60, 1796–1803 (2013).
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T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
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M. Calhoun, R. Sydnor, and W. Diener, “A stabilized 100-megahertz and 1-gigahertz reference frequency distribution for Cassini radio science,” Interplanet. Netw. Prog. Rep. 148, 1–11 (2001).

Djerroud, K.

Doeleman, S.

S. Doeleman, T. Mai, A. E. E. Rogers, J. G. Hartnett, M. E. Tobar, and N. Nand, “Adapting a cryogenic sapphire oscillator for very long baseline interferometry,” Publ. Astron. Soc. Pac. 123, 582–595 (2011).
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S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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Droste, S.

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S. Droste, F. Ozimek, T. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett. 111, 110801 (2013).
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A. Hati, C. W. Nelson, C. Barnes, D. Lirette, T. Fortier, F. Quinlan, J. A. Desalvo, A. Ludlow, S. A. Diddams, and D. A. Howe, “State-of-the-art RF signal generation from optical frequency division,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60, 1796–1803 (2013).
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F. Quinlan, F. N. Baynes, T. M. Fortier, Q. Zhou, A. Cross, J. C. Campbell, and S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39, 1581–1584 (2014).
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T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
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S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7, 434–438 (2013).
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J.-D. Deschênes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X (in press).

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S. Droste, C. Grebing, J. Leute, S. M. F. Raupach, A. Matveev, T. W. Hänsch, A. Bauch, R. Holzwarth, and G. Grosche, “Characterization of a 450 km baseline GPS carrier-phase link using an optical fiber link,” New J. Phys. 17, 083044 (2015).
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S. Droste, C. Grebing, J. Leute, S. M. F. Raupach, A. Matveev, T. W. Hänsch, A. Bauch, R. Holzwarth, and G. Grosche, “Characterization of a 450 km baseline GPS carrier-phase link using an optical fiber link,” New J. Phys. 17, 083044 (2015).
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S. Droste, F. Ozimek, T. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett. 111, 110801 (2013).
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Guillemot, P.

E. Samain, P. Exertier, P. Guillemot, F. Pierron, D. Albanese, J. Paris, J.-M. Torre, I. Petitbon, and S. Leon, “Time transfer by laser link T2L2 first results,” in Joint Meeting of the European Frequency and Time Forum (EFTF) and the IEEE International Frequency Control Symposium (FCS), Besancon, France, 2009, pp. 194–198.

Haboucha, A.

O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Phys. 16, 531–539 (2015).
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S. Droste, F. Ozimek, T. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett. 111, 110801 (2013).
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S. Doeleman, T. Mai, A. E. E. Rogers, J. G. Hartnett, M. E. Tobar, and N. Nand, “Adapting a cryogenic sapphire oscillator for very long baseline interferometry,” Publ. Astron. Soc. Pac. 123, 582–595 (2011).
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N. R. Nand, J. G. Hartnett, E. N. Ivanov, and G. Santarelli, “Ultra-stable very-low phase-noise signal source for very long baseline interferometry using a cryocooled sapphire oscillator,” IEEE Trans. Microwave Theory Tech. 59, 2978–2986 (2011).
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A. Hati, C. W. Nelson, C. Barnes, D. Lirette, T. Fortier, F. Quinlan, J. A. Desalvo, A. Ludlow, S. A. Diddams, and D. A. Howe, “State-of-the-art RF signal generation from optical frequency division,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60, 1796–1803 (2013).
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K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
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S. Droste, C. Grebing, J. Leute, S. M. F. Raupach, A. Matveev, T. W. Hänsch, A. Bauch, R. Holzwarth, and G. Grosche, “Characterization of a 450 km baseline GPS carrier-phase link using an optical fiber link,” New J. Phys. 17, 083044 (2015).
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S. Droste, F. Ozimek, T. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett. 111, 110801 (2013).
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O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Phys. 16, 531–539 (2015).
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O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Phys. 16, 531–539 (2015).
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S. Grop, P.-Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46, 420–422 (2010).
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L. C. Sinclair, J.-D. Deschênes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “Invited Article: A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86, 081301 (2015).
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T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
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Li, Z.

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O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Phys. 16, 531–539 (2015).
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Singh, Y.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
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Sliwczynski, L.

L. Sliwczynski, P. Krehlik, L. Buczek, and M. Lipinski, “Frequency transfer in electronically stabilized fiber optic link exploiting bidirectional optical amplifiers,” IEEE Trans. Instrum. Meas. 61, 2573–2580 (2012).
[Crossref]

Smith, L.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
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Smythe, D. L.

S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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Sonderhouse, L.

L. C. Sinclair, J.-D. Deschênes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “Invited Article: A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86, 081301 (2015).
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Staples, J. W.

Stefani, F.

O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Phys. 16, 531–539 (2015).
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Sterr, U.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
[Crossref]

Strittmatter, P.

S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
[Crossref]

Stuhler, J.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
[Crossref]

Sushchik, M.

M. Sushchik, N. Rulkov, L. Larson, L. Tsimring, H. Abarbanel, K. Yao, and A. Volkovskii, “Chaotic pulse position modulation: a robust method of communicating with chaos,” IEEE Commun. Lett. 4, 128–130 (2000).
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Swann, W. C.

L. C. Sinclair, J.-D. Deschênes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “Invited Article: A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86, 081301 (2015).
[Crossref]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7, 434–438 (2013).
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I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent linear optical sampling at 15 bits of resolution,” Opt. Lett. 34, 2153–2155 (2009).
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N. R. Newbury, P. A. Williams, and W. C. Swann, “Coherent transfer of an optical carrier over 251 km,” Opt. Lett. 32, 3056–3058 (2007).
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J.-D. Deschênes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X (in press).

Swierad, D.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
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M. Calhoun, R. Sydnor, and W. Diener, “A stabilized 100-megahertz and 1-gigahertz reference frequency distribution for Cassini radio science,” Interplanet. Netw. Prog. Rep. 148, 1–11 (2001).

Targat, R. L.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
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T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[Crossref]

Tilanus, R. P. J.

S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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Tino, G. M.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
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Titus, M.

S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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Tobar, M. E.

S. Doeleman, T. Mai, A. E. E. Rogers, J. G. Hartnett, M. E. Tobar, and N. Nand, “Adapting a cryogenic sapphire oscillator for very long baseline interferometry,” Publ. Astron. Soc. Pac. 123, 582–595 (2011).
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E. Samain, P. Exertier, P. Guillemot, F. Pierron, D. Albanese, J. Paris, J.-M. Torre, I. Petitbon, and S. Leon, “Time transfer by laser link T2L2 first results,” in Joint Meeting of the European Frequency and Time Forum (EFTF) and the IEEE International Frequency Control Symposium (FCS), Besancon, France, 2009, pp. 194–198.

Tsimring, L.

M. Sushchik, N. Rulkov, L. Larson, L. Tsimring, H. Abarbanel, K. Yao, and A. Volkovskii, “Chaotic pulse position modulation: a robust method of communicating with chaos,” IEEE Commun. Lett. 4, 128–130 (2000).
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Udem, T.

S. Droste, F. Ozimek, T. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett. 111, 110801 (2013).
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Venon, B.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
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Vogt, S.

K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
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Volkovskii, A.

M. Sushchik, N. Rulkov, L. Larson, L. Tsimring, H. Abarbanel, K. Yao, and A. Volkovskii, “Chaotic pulse position modulation: a robust method of communicating with chaos,” IEEE Commun. Lett. 4, 128–130 (2000).
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S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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Werthimer, D.

S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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Whitney, A. R.

S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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Wilcox, R.

Williams, P. A.

Wolf, P.

C. Robert, J.-M. Conan, and P. Wolf, “Impact of turbulent phase noise on frequency transfer with asymmetric two-way ground-satellite coherent optical links,” Phys. Rev. A 93, 033860 (2016).

K. Djerroud, O. Acef, A. Clairon, P. Lemonde, C. N. Man, E. Samain, and P. Wolf, “Coherent optical link through the turbulent atmosphere,” Opt. Lett. 35, 1479–1481 (2010).
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S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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Yan, L.

Yao, K.

M. Sushchik, N. Rulkov, L. Larson, L. Tsimring, H. Abarbanel, K. Yao, and A. Volkovskii, “Chaotic pulse position modulation: a robust method of communicating with chaos,” IEEE Commun. Lett. 4, 128–130 (2000).
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Ye, J.

Young, K. H.

S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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Zhang, W.

Zhou, Q.

Ziurys, L. M.

S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck, R. Freund, R. P. J. Tilanus, P. Friberg, L. M. Ziurys, J. M. Moran, B. Corey, K. H. Young, D. L. Smythe, M. Titus, D. P. Marrone, R. J. Cappallo, D. C.-J. Bock, G. C. Bower, R. Chamberlin, G. R. Davis, T. P. Krichbaum, J. Lamb, H. Maness, A. E. Niell, A. Roy, P. Strittmatter, D. Werthimer, A. R. Whitney, and D. Woody, “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature 455, 78–80 (2008).
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K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Swierad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. L. Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, and the SOC2 team, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16, 553–564 (2015).
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Supplementary Material (1)

NameDescription
Supplement 1: PDF (594 KB)      Description and figure detailing stabilization architecture for the microwave clock.

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Figures (7)
Fig. 1.
Fig. 1. (a) Conceptual multistatic synthetic aperture radar where an array of microwave oscillators are synchronized to a single master optical oscillator; LO, local oscillator. (b) The master site’s clock is based on a laser stabilized to an optical cavity (optical oscillator). The remote site’s clock is based on a combined quartz oscillator and DRO. This remote microwave clock is tightly synchronized to the optical clock over a folded 4 km long air path via O-TWTFT. The time and the frequency outputs from each clock are compared in a separate measurement to verify femtosecond time offsets and high phase coherence of the synchronized signals.

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Fig. 2.
Fig. 2. Schematic of the experimental setup. A master optical clock (blue shaded region) consists of a frequency comb phase-locked to a 195 THz cavity-stabilized laser. A remote synchronized microwave-based clock (red shaded region) consists of a frequency comb phase-locked to a 10 GHz oscillator. Each site produces a 10.037 GHz frequency output. At the master optical clock site, this 10 GHz signal corresponds to the 50th harmonic of the 200 MHz repetition rate frequency comb and is generated by optical frequency division. At the microwave clock site, it is the direct output of a quartz/DRO microwave oscillator. At both sites, the time output is defined by the arrival of the labeled optical pulses from the respective frequency combs at a common reference plane. (This step requires a separate calibration with a shorted link.) The two clocks are synchronized by a Kalman-filter-based loop filter that uses the input time offset, as measured through O-TWTFT, to steer the frequency of the DRO. DDS, direct digital synthesizer; f r , repetition frequency of the frequency comb.

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Fig. 3.
Fig. 3. System operation during dropouts. (a) Schematic of the Kalman-filter-based loop filter; PI, proportional and integral. (b) Measured out-of-loop time offset (black trace), in-loop time offset measured via the O-TWTFT system (red circles), and predicted in-loop timing offset from the loop filter (orange trace). During the shaded gray regions, the received power over the single-mode link was below threshold, leading to a dropout in the measured in-loop time offset. (c) Correction applied to the frequency of the 10 GHz signal (blue trace).

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Fig. 4.
Fig. 4. (a) Time offset (gated operation) between the optical and microwave clocks. (b) Link availability. (c) Turbulence strength as measured by the turbulence structure function C n 2 . All data is averaged over a 1 s window.

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Fig. 5.
Fig. 5. Time deviation calculated from the measured time offset between the microwave and optical clock for gated operation (light blue curve) and for continuous operation (dark blue curve). The data for gated operation agrees with previous optical-to-optical synchronization (dashed green curve) [11] out to 100 s.

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Fig. 6.
Fig. 6. Single-sideband PSD for differential phase noise of the 10 GHz outputs from the optical and microwave clocks without synchronization (purple curve), while synchronized over the 4 km link (red curve), and while synchronized over a shorted link (gray curve). The integrated phase noise is 375 μrad (6 fs) for the red curve from 100 μHz out to the synchronization bandwidth of 100 Hz. In addition, the PSD calculated from the optical time outputs is shown (in blue).

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Fig. 7.
Fig. 7. Fractional instability (modified Allan deviation) of the frequency difference between the remote site and master site clocks during continuous operation for the synchronized 10 GHz microwave outputs (red trace) and for the optical time offsets (blue trace).

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