Abstract

We present theoretical predictions and experimental measurements for the achievable phase noise, timing jitter, and frequency stability in the coherent transport of an optical frequency over a fiber-optic link. Both technical and fundamental limitations to the coherent transfer are discussed. Measurements of the coherent transfer of an optical carrier over links ranging from 38 to 251 km demonstrate good agreement with theory. With appropriate experimental design and bidirectional transfer on a single optical fiber, the frequency instability at short times can reach the fundamental limit imposed by delay-unsuppressed phase noise from the fiber link, yielding a frequency instability that scales as link length to the 3/2 power. For two-way transfer on separate outgoing and return fibers, the instability is severely limited by differential fiber noise.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2007 (6)

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

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
[CrossRef]

S. T. Dawkins, J. J. McFerran, and 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).
[CrossRef]

J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kartner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett. 32, 1044-1046 (2007).
[CrossRef]

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).
[CrossRef]

2006 (4)

B. S. Sheard, M. B. Gray, and D. E. McClelland, “High-bandwidth laser frequency stabilization to a fiber-optic delay line,” Appl. Phys. Lett. 45, 8491-8499 (2006).

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 064701 (2006).
[CrossRef]

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

2005 (2)

E. Rubiola, “On the measurement of frequency and of its sample variance with high-resolution counters,” Rev. Sci. Instrum. 76, 054703 (2005).
[CrossRef]

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

2003 (1)

2001 (1)

S.-T. Lee and C.-J. Chae, “Low-cost bidirectional optical amplifier using a unidirectional Er-doped fiber amplifier and a fiber Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 13, 76-78 (2001).

1999 (1)

P. A. Williams, “Modulation phase-shift measurement of PMD using only four launched polarisation states: A new algorithm,” Electron. Lett. 35, 1578-1579 (1999).
[CrossRef]

1994 (1)

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Achkar, J.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).

Allan, D. W.

D. B. Sullivan, D. W. Allan, D. A. Howe, and F. L. Walls, “Characterization of clocks and oscillators,” in NIST Technical Note 1337 (National Institute of Standards and Technology, 1990).

Amy-Klein, A.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 064701 (2006).
[CrossRef]

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” (2007), http://arxiv.org/abs/0711.0933v3.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

Bauch, A.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

Bergquist, J.

W. C. Swann, L. Lorini, J. Bergquist, and N. R. Newbury, “Narrow linewidth 1.5 μm sources and the thermal limit,” in Digest of IEEE LEOS Summer Topical Meetings (IEEE, 2007), pp. 165-166.

Bergquist, J. C.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

J. Ye, J.-L. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L.-S. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20, 1459-1467 (2003).
[CrossRef]

J. C. Bergquist, W. M. Itano, and D. J. Wineland, in International School of Physics “Enrico Fermi,” W.Hansch and M.Inguscio, eds. (North-Holland, 1992), p. 359.

Bize, S.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 064701 (2006).
[CrossRef]

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

J. Ye, J.-L. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L.-S. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20, 1459-1467 (2003).
[CrossRef]

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Calonico, D.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

Chae, C.-J.

S.-T. Lee and C.-J. Chae, “Low-cost bidirectional optical amplifier using a unidirectional Er-doped fiber amplifier and a fiber Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 13, 76-78 (2001).

Chambon, D.

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

Chardonnet, C.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 064701 (2006).
[CrossRef]

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” (2007), http://arxiv.org/abs/0711.0933v3.

Chen, J.

Clairon, A.

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Clarion, A.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 064701 (2006).
[CrossRef]

Coddington, I.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1992).

Coq, Y. L.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

Dach, R.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

Daussy, C.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 064701 (2006).
[CrossRef]

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” (2007), http://arxiv.org/abs/0711.0933v3.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

Dawkins, S. T.

S. T. Dawkins, J. J. McFerran, and 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).
[CrossRef]

Diddams, S. A.

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
[CrossRef]

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

J. Ye, J.-L. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L.-S. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20, 1459-1467 (2003).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Feder, K. S.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Foreman, S. M.

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
[CrossRef]

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

Gardner, F. M.

F. M. Gardner, Phaselock Techniques (Wiley, 1979).

Goncharov, A.

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

Gray, M. B.

B. S. Sheard, M. B. Gray, and D. E. McClelland, “High-bandwidth laser frequency stabilization to a fiber-optic delay line,” Appl. Phys. Lett. 45, 8491-8499 (2006).

Grosche, G.

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Guinet, M.

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

Hall, J. L.

Hlavac, R.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

Hollberg, L. W.

Holman, K. W.

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Howe, D. A.

D. B. Sullivan, D. W. Allan, D. A. Howe, and F. L. Walls, “Characterization of clocks and oscillators,” in NIST Technical Note 1337 (National Institute of Standards and Technology, 1990).

Hudson, D. D.

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

Ishiguro, M.

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Itano, W. M.

J. C. Bergquist, W. M. Itano, and D. J. Wineland, in International School of Physics “Enrico Fermi,” W.Hansch and M.Inguscio, eds. (North-Holland, 1992), p. 359.

Jones, D. J.

Jones, R. J.

Jungner, P.

Kartner, F. X.

Kikuchi, K.

T. Okoshi and K. Kikuchi, Coherent Optical Fiber Communications (KTK Scientific Publishers, 1988).

Kim, J.

Kitching, J.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Lee, S.-T.

S.-T. Lee and C.-J. Chae, “Low-cost bidirectional optical amplifier using a unidirectional Er-doped fiber amplifier and a fiber Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 13, 76-78 (2001).

Lemonde, P.

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Lipphardt, B.

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Loehl, F.

Lopez, O.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 064701 (2006).
[CrossRef]

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” (2007), http://arxiv.org/abs/0711.0933v3.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

Lorini, L.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

W. C. Swann, L. Lorini, J. Bergquist, and N. R. Newbury, “Narrow linewidth 1.5 μm sources and the thermal limit,” in Digest of IEEE LEOS Summer Topical Meetings (IEEE, 2007), pp. 165-166.

Lours, M.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 064701 (2006).
[CrossRef]

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” (2007), http://arxiv.org/abs/0711.0933v3.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Ludlow, A. D.

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
[CrossRef]

Luiten, A. N.

S. T. Dawkins, J. J. McFerran, and 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).
[CrossRef]

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

Ma, L. S.

Ma, L.-S.

McClelland, D. E.

B. S. Sheard, M. B. Gray, and D. E. McClelland, “High-bandwidth laser frequency stabilization to a fiber-optic delay line,” Appl. Phys. Lett. 45, 8491-8499 (2006).

McFerran, J. J.

S. T. Dawkins, J. J. McFerran, and 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).
[CrossRef]

Miranda, M. H. D.

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Musha, M.

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Nakagawa, K.

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Narbonneau, F.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 064701 (2006).
[CrossRef]

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” (2007), http://arxiv.org/abs/0711.0933v3.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Newbury, N. R.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

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).
[CrossRef]

W. C. Swann, L. Lorini, J. Bergquist, and N. R. Newbury, “Narrow linewidth 1.5 μm sources and the thermal limit,” in Digest of IEEE LEOS Summer Topical Meetings (IEEE, 2007), pp. 165-166.

Nicholson, J. W.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

Oates, C. W.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

Okoshi, T.

T. Okoshi and K. Kikuchi, Coherent Optical Fiber Communications (KTK Scientific Publishers, 1988).

Parker, T.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

Peng, J.-L.

Petit, G.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

Piester, D.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

Quraishi, Q.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

Robertsson, L.

Rubiola, E.

E. Rubiola, “On the measurement of frequency and of its sample variance with high-resolution counters,” Rev. Sci. Instrum. 76, 054703 (2005).
[CrossRef]

Santarelli, G.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 064701 (2006).
[CrossRef]

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” (2007), http://arxiv.org/abs/0711.0933v3.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

Sato, Y.

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Schlarb, H.

Schnatz, H.

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Sheard, B. S.

B. S. Sheard, M. B. Gray, and D. E. McClelland, “High-bandwidth laser frequency stabilization to a fiber-optic delay line,” Appl. Phys. Lett. 45, 8491-8499 (2006).

Stalnaker, J. E.

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
[CrossRef]

Sullivan, D. B.

D. B. Sullivan, D. W. Allan, D. A. Howe, and F. L. Walls, “Characterization of clocks and oscillators,” in NIST Technical Note 1337 (National Institute of Standards and Technology, 1990).

Swann, W. C.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

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).
[CrossRef]

W. C. Swann, L. Lorini, J. Bergquist, and N. R. Newbury, “Narrow linewidth 1.5 μm sources and the thermal limit,” in Digest of IEEE LEOS Summer Topical Meetings (IEEE, 2007), pp. 165-166.

Szymaniec, K.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

Tobar, M. E.

C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

Ueda, A.

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Ueda, K.

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Uhrich, P.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
[CrossRef]

Walls, F. L.

D. B. Sullivan, D. W. Allan, D. A. Howe, and F. L. Walls, “Characterization of clocks and oscillators,” in NIST Technical Note 1337 (National Institute of Standards and Technology, 1990).

Wanser, K. H.

K. H. Wanser, “Theory of thermal phase noise in michelson and Sagnac fiber interferometers,” in Proceedings of the Tenth International Conference on Optical Fiber Sensors (OFS 10), Proc. SPIE 2360, 584-587 (1994).

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Westbrook, P. S.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).

Williams, P. A.

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).
[CrossRef]

P. A. Williams, “Modulation phase-shift measurement of PMD using only four launched polarisation states: A new algorithm,” Electron. Lett. 35, 1578-1579 (1999).
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Wineland, D. J.

J. C. Bergquist, W. M. Itano, and D. J. Wineland, in International School of Physics “Enrico Fermi,” W.Hansch and M.Inguscio, eds. (North-Holland, 1992), p. 359.

Wong, F. N. C.

Ye, J.

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

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
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J. Ye, J.-L. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L.-S. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20, 1459-1467 (2003).
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L. S. Ma, P. Jungner, J. Ye, and J. L. Hall, “Delivering the same optical frequency at two places: Accurate cancellation of phase noise introduced by an optical fiber or other time-varying path,” Opt. Lett. 19, 1777-1779 (1994).

Zhang, Z.

Appl. Phys. B (2)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

B. S. Sheard, M. B. Gray, and D. E. McClelland, “High-bandwidth laser frequency stabilization to a fiber-optic delay line,” Appl. Phys. Lett. 45, 8491-8499 (2006).

Electron. Lett. (1)

P. A. Williams, “Modulation phase-shift measurement of PMD using only four launched polarisation states: A new algorithm,” Electron. Lett. 35, 1578-1579 (1999).
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IEEE Photon. Technol. Lett. (1)

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IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

S. T. Dawkins, J. J. McFerran, and 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).
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A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia 43, 109-120 (2006).
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C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).

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