Abstract

We present a powerful jitter analysis method for timing-distribution and remote-laser synchronization systems based on feedback flow between setup elements. We synchronize two different mode-locked lasers in a master-slave configuration locally and remotely over a timing-stabilized fiber link network. Local synchronization reveals the inherent jitter of the slave laser as 2.1 fs RMS (>20 kHz), whereas remote synchronization exhibits an out-of-loop jitter of 8.55 fs RMS integrated for 1 Hz - 1 MHz. Our comprehensive feedback model yields excellent agreement with the experimental results and identifies seven uncorrelated noise sources, out of which the slave laser’s jitter dominates with 8.19 fs RMS.

© 2016 Optical Society of America

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2016 (3)

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(6), 063001 (2016).
[Crossref] [PubMed]

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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

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 6(2), 021016 (2016).
[Crossref]

2015 (3)

K. Şafak, M. Xin, P. T. Callahan, M. Y. Peng, and F. X. Kärtner, “All fiber-coupled, long-term stable timing distribution for free-electron lasers with few-femtosecond jitter,” Struct. Dyn. 2(4), 041715 (2015).
[Crossref] [PubMed]

E. Prat and S. Reiche, “Simple method to generate terawatt-attosecond X-ray free-electron-laser pulses,” Phys. Rev. Lett. 114(24), 244801 (2015).
[Crossref] [PubMed]

S. Schulz, I. Grguraš, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Prędki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015).
[Crossref] [PubMed]

2014 (4)

P. Kómár, E. M. Kessler, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin, “A quantum network of clocks,” Nat. Phys. 10(8), 582–587 (2014).
[Crossref]

H. Kim, P. Qin, Y. Song, H. Yang, J. Shin, C. Kim, K. Jung, C. Wang, and J. Kim, “Sub-20-attosecond timing jitter mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 260–267 (2014).
[Crossref]

B. Ning, S. Y. Zhang, D. Hou, J. T. Wu, Z. B. Li, and J. Y. Zhao, “High-precision distribution of highly stable optical pulse trains with 8.8×10−19 instability,” Sci. Rep. 4, 5109 (2014).
[Crossref] [PubMed]

M. Xin, K. Şafak, M. Y. Peng, P. T. Callahan, and F. X. Kärtner, “One-femtosecond, long-term stable remote laser synchronization over a 3.5-km fiber link,” Opt. Express 22(12), 14904–14912 (2014).
[Crossref] [PubMed]

2013 (3)

M. Y. Peng, P. T. Callahan, A. H. Nejadmalayeri, S. Valente, M. Xin, L. Grüner-Nielsen, E. M. Monberg, M. Yan, J. M. Fini, and F. X. Kärtner, “Long-term stable, sub-femtosecond timing distribution via a 1.2-km polarization-maintaining fiber link: approaching 10-21 link stability,” Opt. Express 21(17), 19982–19989 (2013).
[Crossref] [PubMed]

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(11), 110801 (2013).
[Crossref] [PubMed]

P. Delva and J. Lodewyck, “Atomic clocks: new prospects in metrology and geodesy,” Acta Futura 7, 67–78 (2013).

2012 (4)

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
[Crossref]

J. Ullrich, A. Rudenko, and R. Moshammer, “Free-electron lasers: new avenues in molecular physics and photochemistry,” Annu. Rev. Phys. Chem. 63(1), 635–660 (2012).
[Crossref] [PubMed]

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(6080), 441–444 (2012).
[Crossref] [PubMed]

O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express 20(21), 23518–23526 (2012).
[Crossref] [PubMed]

2011 (1)

G. Mourou and T. Tajima, “The extreme light infrastructure: optics’ next horizon,” Opt. Photonics News 22(7), 47–51 (2011).
[Crossref]

2010 (1)

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

2008 (2)

J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
[Crossref]

L.-J. Chen, A. J. Benedick, J. R. Birge, M. Y. Sander, and F. Kärtner, “Octave-spanning, dual-output 2.166 GHz Ti:sapphire laser,” Opt. Express 16(25), 20699–20705 (2008).
[Crossref] [PubMed]

2007 (1)

2005 (1)

2004 (1)

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10(-19) level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

2003 (1)

2002 (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

2001 (1)

S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001).
[Crossref] [PubMed]

2000 (2)

A. H. Zewail, “Femtochemistry: Atomic-scale dynamics of the chemical bond,” J. Phys. Chem. A 104, 5660–5694 (2000).
[Crossref] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[Crossref] [PubMed]

Abgrall, M.

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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Akre, R.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Al-Masoudi, A.

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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Alnis, J.

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(6080), 441–444 (2012).
[Crossref] [PubMed]

Amy-Klein, A.

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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express 20(21), 23518–23526 (2012).
[Crossref] [PubMed]

Arthur, J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Bartels, A.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10(-19) level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

Baumann, E.

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 6(2), 021016 (2016).
[Crossref]

Behrens, C.

S. Schulz, I. Grguraš, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Prędki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015).
[Crossref] [PubMed]

Benedick, A. J.

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
[Crossref]

L.-J. Chen, A. J. Benedick, J. R. Birge, M. Y. Sander, and F. Kärtner, “Octave-spanning, dual-output 2.166 GHz Ti:sapphire laser,” Opt. Express 16(25), 20699–20705 (2008).
[Crossref] [PubMed]

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 6(2), 021016 (2016).
[Crossref]

Bergquist, J. C.

S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001).
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Bi, Z.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10(-19) level,” Science 303(5665), 1843–1845 (2004).
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Bilicki, S.

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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Bionta, R.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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Birge, J.

Birge, J. R.

Bishof, M.

P. Kómár, E. M. Kessler, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin, “A quantum network of clocks,” Nat. Phys. 10(8), 582–587 (2014).
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Bookjans, E.

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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Bostedt, C.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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Brachmann, A.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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Bromberger, H.

S. Schulz, I. Grguraš, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Prędki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015).
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P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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Camisard, E.

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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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S. Schulz, I. Grguraš, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Prędki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015).
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Cermak, M.

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 6(2), 021016 (2016).
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Chanteau, B.

Chardonnet, C.

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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express 20(21), 23518–23526 (2012).
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Chen, J.

J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
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J. Kim, J. Chen, J. Cox, and F. X. Kärtner, “Attosecond-resolution timing jitter characterization of free-running mode-locked lasers,” Opt. Lett. 32(24), 3519–3521 (2007).
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Chen, L.-J.

Chiodo, N.

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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Coddington, I.

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 6(2), 021016 (2016).
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Coffee, R.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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Costello, J. T.

S. Schulz, I. Grguraš, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Prędki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015).
[Crossref] [PubMed]

Cox, J.

Cox, J. A.

J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
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Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[Crossref] [PubMed]

Curtis, E. A.

S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001).
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Czwalinna, M. K.

S. Schulz, I. Grguraš, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Prędki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015).
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Decker, F.-J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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P. Delva and J. Lodewyck, “Atomic clocks: new prospects in metrology and geodesy,” Acta Futura 7, 67–78 (2013).

Denker, H.

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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Deschênes, J.-D.

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 6(2), 021016 (2016).
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Diddams, S. A.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10(-19) level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001).
[Crossref] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[Crossref] [PubMed]

Ding, Y.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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Dörscher, S.

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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Dowell, D.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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Droste, S.

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(11), 110801 (2013).
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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(6080), 441–444 (2012).
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Drullinger, R. E.

S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001).
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Edstrom, S.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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Ell, R.

Emma, P.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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Felber, M.

S. Schulz, I. Grguraš, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Prędki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015).
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Fini, J. M.

Fisher, A.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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Frisch, J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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Galayda, J.

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Haboucha, A.

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P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
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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(11), 110801 (2013).
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T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
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B. Ning, S. Y. Zhang, D. Hou, J. T. Wu, Z. B. Li, and J. Y. Zhao, “High-precision distribution of highly stable optical pulse trains with 8.8×10−19 instability,” Sci. Rep. 4, 5109 (2014).
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Itano, W. M.

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P. Kómár, E. M. Kessler, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin, “A quantum network of clocks,” Nat. Phys. 10(8), 582–587 (2014).
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Kalaydzhyan, A.

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P. Kómár, E. M. Kessler, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin, “A quantum network of clocks,” Nat. Phys. 10(8), 582–587 (2014).
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H. Kim, P. Qin, Y. Song, H. Yang, J. Shin, C. Kim, K. Jung, C. Wang, and J. Kim, “Sub-20-attosecond timing jitter mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 260–267 (2014).
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H. Kim, P. Qin, Y. Song, H. Yang, J. Shin, C. Kim, K. Jung, C. Wang, and J. Kim, “Sub-20-attosecond timing jitter mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 260–267 (2014).
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H. Kim, P. Qin, Y. Song, H. Yang, J. Shin, C. Kim, K. Jung, C. Wang, and J. Kim, “Sub-20-attosecond timing jitter mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 260–267 (2014).
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J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
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J. Kim, J. Chen, J. Cox, and F. X. Kärtner, “Attosecond-resolution timing jitter characterization of free-running mode-locked lasers,” Opt. Lett. 32(24), 3519–3521 (2007).
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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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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E. Prat and S. Reiche, “Simple method to generate terawatt-attosecond X-ray free-electron-laser pulses,” Phys. Rev. Lett. 114(24), 244801 (2015).
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L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10(-19) level,” Science 303(5665), 1843–1845 (2004).
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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, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Sanner, C.

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(6), 063001 (2016).
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IEEE J. Sel. Top. Quantum Electron. (1)

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Figures (10)

Fig. 1
Fig. 1 (a) Schematic of the Kerr-lens mode-locked Ti:sa laser. (b) Experimental setup for characterizing the timing jitter of the Ti:sa laser. The right panel shows the measured TC-BOC response as a function of the time delay between the two input pulse trains. Abbreviations: cDCM: concave DCM; fDCM: flat DCM; Ti:sa: titanium-sapphire crystal; BaF2: barium fluoride plate; OC: output coupler; PZT: piezo-electric transducer; λ/2: half-wave plate; SM: silver mirror; DBC: dichroic beam combiner; DBS: dichroic beam splitter; BBO: beta barium borate crystal; IF: interference filter; BPD: balanced photodetector.
Fig. 2
Fig. 2 Timing jitter characterization results of the Ti:sa laser. Left axes: timing jitter spectral density Sjitter and its integrated jitter δjitter for different feedback gains. The color map on the top indicates the feedback gain value. Right axes: equivalent single-sideband (SSB) phase noise L(f) and its integrated phase error δphase scaled to 10-GHz carrier frequency.
Fig. 3
Fig. 3 Feedback model for BOC-based laser synchronization. JM and JS: free-running jitter of the master and the slave laser; JO: relative jitter between the two lasers at the BOC input; HBOC, HBPD, HPI and HPZT: transfer functions of the BOC, BPD, PI controller and slave laser’s PZT, respectively; EBOC and EPI: electronic noise of the BOC and the PI controller, respectively.
Fig. 4
Fig. 4 Simulation results of BOC-based laser synchronization. (a) Transfer coefficient |1/(1 + H)|2 of the master and slave laser’s inherent jitter. (b) Transfer coefficient |H/(1 + H)|2 of the electronic noise jitter. The color map on the top indicates the feedback gain values for individual curves in (a) and (b). (c) (i) Calculated free-running jitter of the Ti:sa laser using Eq. (6) and (ii) measured jitter between the master and slave laser at 0-dB gain. Integrated jitter is shown on a logarithmic scale.
Fig. 5
Fig. 5 (a) Experimental setup for the synchronization of the Ti:sa laser on a timing link network with a total length of 4.7 km. (b) Individual elements of the timing stabilized fiber links. Abbreviations: RF: RF reference; FC: fiber collimator; MDL: motorized delay line; PM-FS: polarization-maintaining fiber stretcher; PM-DCF: PM dispersion-compensated fiber; EDFA: bidirectional erbium-doped fiber amplifier; PRM: partially reflecting fiber mirror.
Fig. 6
Fig. 6 Out-of-loop measurements between the remotely synchronized Ti:sa laser and timing link 2 output. (a) Timing drift below 1 Hz. (b) Calculated relative timing instability from the drift data. (c) Jitter spectral density Sjitter and its integrated jitter δjitter; right axes: equivalent SSB phase noise L(f) and its integrated phase δphase scaled to a 10-GHz carrier frequency. The gray curve shows the noise floor of the free-running TC-BOC2.
Fig. 7
Fig. 7 Feedback model for (a) stabilization of timing link 1, (b) remote synchronization of the Ti:sa laser via timing link 1, (c) stabilization of timing link 2, and (d) out-of-loop jitter measurement between the Ti:sa laser and timing link 2. JE: total environmental jitter imposed on the link for one-way travel; JI: timing jitter detected by the in-loop BOC; JF: equivalent jitter generated by the feedback loop to maintain the lock; JO: out-of-loop jitter between the Ti:sa laser and timing link 2 output; τ: one-way fiber link travel time, s = jω: complex frequency. Subscripts L1, L2, and S after each abbreviation refer to timing link 1, timing link 2 and the Ti:sa laser, respectively.
Fig. 8
Fig. 8 Calculated transfer coefficients in Eq. (21) for varying TC-BOC1 feedback gain. Coefficients are given as following: (a) master laser’s inherent jitter; (b) slave laser’s inherent jitter; environmental noise imposed on (c) timing link 1 and (d) timing link 2; electronic feedback noise from (e) TC-BOC1 lock, (f) OC-BOC1 lock and (g) OC-BOC2 lock. The color map on the right-hand side is common for all figures.
Fig. 9
Fig. 9 (a) Simulation results of individual jitter contributions. The legend on the right shows the color code of the jitter spectral densities and their integrated jitter from 100 Hz to 1 MHz. Integrated jitter in this graph is shown on a logarithmic scale. (b) Comparison between (i) the sum of all simulated jitter sources and (ii) the out-of-loop jitter measurement.
Fig. 10
Fig. 10 Noise model of the PI controller. Vin and Vout: input and output voltage; Vn: input voltage noise of the PI controller; Rin and ith,Rin: input impedance and its thermal noise current; Rf and ith,Rf: feedback gain resistance and its thermal noise current; C: integrating capacitance.

Tables (1)

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Table 1 Experimental parameters used in the feedback loop analysis

Equations (25)

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J O = J M + J S +[ ( J O H BOC + E BOC ) H BPD H PI + E PI ]
J N = E BOC H BOC + E PI H BOC H BPD H PI
H= H BOC H BPD H PI H PZT
J O =( 1 1+H )[ J M + J S ]+( H 1+H ) J N
J O 2 ¯ = | 1 1+H | 2 [   J M 2 ¯ + J S 2 ¯ ]+ | H 1+H | 2 J N 2 ¯
J S 2 ¯ = | 1+H | 2 J O 2 ¯ J M 2 ¯ | H | 2 J N 2 ¯
J I,L1 = J M [ 1+exp( 2s τ L1 )  ]+ J F,L1 [ 1+exp( 2s τ L1 ) ]+ J E,L1 [ 1+exp( s τ L1 ) ]
J I, S = J M exp( s τ L1 )+ J F,L1 exp( s τ L1 )+ J E,L1 J S + J F,S
J I,L2 = J M [ 1+exp( 2s τ L2 ) ]+ J F,L2 [ 1+exp( 2s τ L2 ) ]+ J E,L2 [ 1+exp( s τ L2 ) ]
J O = J M exp( s τ L2 )+ J F,L2 exp( s τ L2 )+ J E,L2 J I,S
J N,i = E BOC,i H BOC, i + E PI,i H BOC,i H BPD,i H PI,i
H i = H BOC,i H BPD,i H PI,i H PZT,i
J O = C M   J M + C S   J S + C E,L1   J E,L1 + C E,L2   J E,L2 + C N,S   J N,S + C N,L1   J N,L1 + C N,L2   J N,L2
C M = ( 1+2 H L2 )exp( s τ L2 ) 1+ H L2 ( 1+exp( 2s τ L2 ) ) 1 1+ H S ( 1+2 H L1 )exp( s τ L1 ) 1+ H L1 ( 1+exp( 2s τ L1 ) )
C S = 1 1+ H S
C E,L1 = 1 1+ H S 1+ H L1 [ 1exp( s τ L1 ) ] 1+ H L1 [ 1+exp( 2s τ L1 ) ]
C E,L2 = 1+ H L2 [ 1exp( s τ L2 ) ] 1+ H L2 [ 1+exp( 2s τ L2 ) ]
C N,S = H S 1+ H S
C N,L1 = 1 1+ H S H L1 exp( s τ L1 ) 1+ H L1 [ 1+exp( 2s τ L1 ) ]
C N,L2 = H L2 exp( s τ L2 ) 1+ H L2 [ 1+exp( 2s τ L2 ) ]
J O 2 ¯ = | C M | 2   J M 2 ¯ + | C S | 2   J S 2 ¯ + | C E,L1 | 2   J E,L1 2 ¯ + | C E,L2 | 2   J E,L2 2 ¯ + | C N,S | 2   J N,S 2 ¯ + | C N,L1 | 2   J N,L1 2 ¯ + | C N,L2 | 2   J N,L2 2 ¯
H= H BOC H BPD H PI H PZT
J N = E BOC H BOC + E PI H BOC H BPD H PI
H BOC = k BOC H PI = k PI ( s+2π f PI s ) H BPD = ( 1+ s 2π f BW ) 1 H PZT = k PZT f rep s ( ( 2π f res ) 2 s 2 +ζs+ ( 2π f res ) 2 )
E PI 2 = Z f 2 4 k B T R in +4 k B T R f + ( 1+ Z f R in ) 2 V n 2   where Z f = 1/ R f  jsC 1/ R f + s 2 C 2

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