Abstract

Frequency doublers are widely used in high-resolution spectroscopy to shift the operation wavelength of a laser to a more easily accessible or otherwise preferable spectral region. We investigate the use of a periodically-poled lithium niobate (PPLN) waveguide frequency doubler in an optical clock. We focus on the phase evolution between the fundamental (1396 nm) and frequency-doubled (698 nm) light and its effect on clock performance. We find that the excess phase noise of the doubler under steady-state operation is at least two orders of magnitude lower than the noise of today’s best interrogation lasers. Phase chirps related to changes of the optical power in the doubler unit and their influence on the accuracy of optical clocks are evaluated. We also observe substantial additional noise when characterizing the doubler unit with an optical frequency comb instead of using two identical waveguide doublers.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, “An  27Al + quantum-logic clock with systematic uncertainty below 10−18,” Phys. Rev. Lett. 123, 033201 (2019).

C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, “Optical clock comparison test of Lorentz symmetry,” Nature 567, 204–208 (2019).
[Crossref] [PubMed]

2018 (3)

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
[Crossref] [PubMed]

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

T. Mehlstäubler, G. Grosche, C. Lisdat, P. Schmidt, and H. Denker, “Atomic clocks for geodesy,” Rep. Prog. Phys. 81, 064401 (2018).
[Crossref] [PubMed]

2017 (4)

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
[Crossref]

S. B. Koller, J. Grotti, S. Vogt, A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, “Transportable optical lattice clock with 7×10−17 uncertainty,” Phys. Rev. Lett. 118, 073601 (2017).
[Crossref]

M. Delehaye, J. Millo, P.-Y. Bourgeois, R. B. Lucas Groult, E. Rubiola, E. Bigler, Y. Kersalé, and C. Lacroûte, “Residual phase noise measurement of optical second harmonic generation in PPLN waveguides,” IEEE Phot. Tech. Lett. 29, 1639–1642 (2017).
[Crossref]

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 μm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118, 263202 (2017).
[Crossref]

2015 (4)

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

S. Häfner, S. Falke, C. Grebing, S. Vogt, T. Legero, M. Merimaa, C. Lisdat, and U. Sterr, “8 ×10−17 fractional laser frequency instability with a long room-temperature cavity,” Opt. Lett. 40, 2112–2115 (2015).
[Crossref]

A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, “Noise and instability of an optical lattice clock,” Phys. Rev. A 92, 063814 (2015).
[Crossref]

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

2014 (1)

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8, 219–223 (2014).
[Crossref]

2013 (3)

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62, 1556–1562 (2013).
[Crossref]

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. B. Wübbena, O. Mandel, and P. O. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113, 233–242 (2013).
[Crossref]

G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, “Tenfold reduction of Brownian noise in optical interferometry,” Nat. Photonics 7, 644–650 (2013).
[Crossref]

2012 (3)

D. Yeaton-Massey and R. X. Adhikari, “A new bound on excess frequency noise in second harmonic generation in PPKTP at the 10−19 level,” Opt. Exp. 20, 21019–21024 (2012).
[Crossref]

S. Falke, M. Misera, U. Sterr, and C. Lisdat, “Delivering pulsed and phase stable light to atoms of an optical clock,” Appl. Phys. B 107, 301–311 (2012).
[Crossref]

T. Kessler, T. Legero, and U. Sterr, “Thermal noise in optical cavities revisited,” J. Opt. Soc. Am. B 29, 178–184 (2012).
[Crossref]

2010 (1)

P. G. Westergaard, J. Lodewyck, and P. Lemonde, “Minimizing the Dick effect in an optical lattice clock,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 57, 623–628 (2010).
[Crossref] [PubMed]

2007 (1)

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. Blatt, T. Zanon-Willette, S. M. Foreman, and J. Ye, “Nuclear spin effects in optical lattice clocks,” Phys. Rev. A 76, 022510 (2007).
[Crossref]

2002 (1)

J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultra-precise measurement of optical frequency ratios,” Phys. Rev. Lett. 88, 073601 (2002).
[Crossref]

1993 (1)

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: Population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[Crossref] [PubMed]

Adhikari, R. X.

D. Yeaton-Massey and R. X. Adhikari, “A new bound on excess frequency noise in second harmonic generation in PPKTP at the 10−19 level,” Opt. Exp. 20, 21019–21024 (2012).
[Crossref]

Al-Masoudi, A.

S. B. Koller, J. Grotti, S. Vogt, A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, “Transportable optical lattice clock with 7×10−17 uncertainty,” Phys. Rev. Lett. 118, 073601 (2017).
[Crossref]

A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, “Noise and instability of an optical lattice clock,” Phys. Rev. A 92, 063814 (2015).
[Crossref]

Amairi, S.

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. B. Wübbena, O. Mandel, and P. O. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113, 233–242 (2013).
[Crossref]

Argence, B.

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8, 219–223 (2014).
[Crossref]

Aspelmeyer, M.

G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, “Tenfold reduction of Brownian noise in optical interferometry,” Nat. Photonics 7, 644–650 (2013).
[Crossref]

Barbieri, P.

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

Barrett, M. D.

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

Baynes, F. N.

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

Beloy, K.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
[Crossref] [PubMed]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
[Crossref]

Bergquist, J. C.

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: Population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[Crossref] [PubMed]

Bigler, E.

M. Delehaye, J. Millo, P.-Y. Bourgeois, R. B. Lucas Groult, E. Rubiola, E. Bigler, Y. Kersalé, and C. Lacroûte, “Residual phase noise measurement of optical second harmonic generation in PPLN waveguides,” IEEE Phot. Tech. Lett. 29, 1639–1642 (2017).
[Crossref]

Blatt, S.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. Blatt, T. Zanon-Willette, S. M. Foreman, and J. Ye, “Nuclear spin effects in optical lattice clocks,” Phys. Rev. A 76, 022510 (2007).
[Crossref]

Bloom, B. J.

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

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science xtbf358, 90–94 (2017).
[Crossref]

Bollinger, J. J.

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: Population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[Crossref] [PubMed]

Bourgeois, P.-Y.

M. Delehaye, J. Millo, P.-Y. Bourgeois, R. B. Lucas Groult, E. Rubiola, E. Bigler, Y. Kersalé, and C. Lacroûte, “Residual phase noise measurement of optical second harmonic generation in PPLN waveguides,” IEEE Phot. Tech. Lett. 29, 1639–1642 (2017).
[Crossref]

Boyd, M. M.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. Blatt, T. Zanon-Willette, S. M. Foreman, and J. Ye, “Nuclear spin effects in optical lattice clocks,” Phys. Rev. A 76, 022510 (2007).
[Crossref]

Bregolin, F.

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

Brewer, S. M.

S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, “An  27Al + quantum-logic clock with systematic uncertainty below 10−18,” Phys. Rev. Lett. 123, 033201 (2019).

Brown, R. C.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
[Crossref] [PubMed]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
[Crossref]

Calonico, D.

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

Campbell, S. L.

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

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science xtbf358, 90–94 (2017).
[Crossref]

Chen, J.-S.

S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, “An  27Al + quantum-logic clock with systematic uncertainty below 10−18,” Phys. Rev. Lett. 123, 033201 (2019).

Chou, C. W.

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W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: Population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
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W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
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S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, “An  27Al + quantum-logic clock with systematic uncertainty below 10−18,” Phys. Rev. Lett. 123, 033201 (2019).

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C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, “Optical clock comparison test of Lorentz symmetry,” Nature 567, 204–208 (2019).
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S. Amairi, T. Legero, T. Kessler, U. Sterr, J. B. Wübbena, O. Mandel, and P. O. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113, 233–242 (2013).
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D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 μm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118, 263202 (2017).
[Crossref]

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[Crossref]

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. B. Wübbena, O. Mandel, and P. O. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113, 233–242 (2013).
[Crossref]

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S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, “An  27Al + quantum-logic clock with systematic uncertainty below 10−18,” Phys. Rev. Lett. 123, 033201 (2019).

Lemke, N.

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62, 1556–1562 (2013).
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J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Barbieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, and D. Calonico, “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14, 437–441 (2018).
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J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Barbieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, and D. Calonico, “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14, 437–441 (2018).
[Crossref]

T. Mehlstäubler, G. Grosche, C. Lisdat, P. Schmidt, and H. Denker, “Atomic clocks for geodesy,” Rep. Prog. Phys. 81, 064401 (2018).
[Crossref] [PubMed]

S. B. Koller, J. Grotti, S. Vogt, A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, “Transportable optical lattice clock with 7×10−17 uncertainty,” Phys. Rev. Lett. 118, 073601 (2017).
[Crossref]

A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, “Noise and instability of an optical lattice clock,” Phys. Rev. A 92, 063814 (2015).
[Crossref]

S. Häfner, S. Falke, C. Grebing, S. Vogt, T. Legero, M. Merimaa, C. Lisdat, and U. Sterr, “8 ×10−17 fractional laser frequency instability with a long room-temperature cavity,” Opt. Lett. 40, 2112–2115 (2015).
[Crossref]

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[Crossref]

S. Falke, M. Misera, U. Sterr, and C. Lisdat, “Delivering pulsed and phase stable light to atoms of an optical clock,” Appl. Phys. B 107, 301–311 (2012).
[Crossref]

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P. G. Westergaard, J. Lodewyck, and P. Lemonde, “Minimizing the Dick effect in an optical lattice clock,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 57, 623–628 (2010).
[Crossref] [PubMed]

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[Crossref]

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W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
[Crossref] [PubMed]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
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[Crossref]

Mandel, O.

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. B. Wübbena, O. Mandel, and P. O. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113, 233–242 (2013).
[Crossref]

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J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Barbieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, and D. Calonico, “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14, 437–441 (2018).
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T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2×10−18 total uncertainty,” Nat. Com. 6, 6896 (2015).
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[Crossref]

Martin, M. J.

G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, “Tenfold reduction of Brownian noise in optical interferometry,” Nat. Photonics 7, 644–650 (2013).
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D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 μm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118, 263202 (2017).
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McGrew, W. F.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
[Crossref] [PubMed]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
[Crossref]

McNally, R. L.

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

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science xtbf358, 90–94 (2017).
[Crossref]

Mehlstäubler, T.

T. Mehlstäubler, G. Grosche, C. Lisdat, P. Schmidt, and H. Denker, “Atomic clocks for geodesy,” Rep. Prog. Phys. 81, 064401 (2018).
[Crossref] [PubMed]

Merimaa, M.

Milan, G.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
[Crossref] [PubMed]

Milani, G.

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
[Crossref]

Millo, J.

M. Delehaye, J. Millo, P.-Y. Bourgeois, R. B. Lucas Groult, E. Rubiola, E. Bigler, Y. Kersalé, and C. Lacroûte, “Residual phase noise measurement of optical second harmonic generation in PPLN waveguides,” IEEE Phot. Tech. Lett. 29, 1639–1642 (2017).
[Crossref]

Misera, M.

S. Falke, M. Misera, U. Sterr, and C. Lisdat, “Delivering pulsed and phase stable light to atoms of an optical clock,” Appl. Phys. B 107, 301–311 (2012).
[Crossref]

Moore, F. L.

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: Population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[Crossref] [PubMed]

Nicholson, T. L.

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

Nicolodi, D.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
[Crossref] [PubMed]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
[Crossref]

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8, 219–223 (2014).
[Crossref]

Oates, C. W.

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
[Crossref]

Peik, E.

C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, “Optical clock comparison test of Lorentz symmetry,” Nature 567, 204–208 (2019).
[Crossref] [PubMed]

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

Phillips, N. B.

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
[Crossref]

Pizzocaro, M.

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

Porsev, S. G.

C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, “Optical clock comparison test of Lorentz symmetry,” Nature 567, 204–208 (2019).
[Crossref] [PubMed]

Raizen, M. G.

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: Population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[Crossref] [PubMed]

Rauf, B.

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

Riehle, F.

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 μm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118, 263202 (2017).
[Crossref]

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62, 1556–1562 (2013).
[Crossref]

Robinson, J. M.

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 μm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118, 263202 (2017).
[Crossref]

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science xtbf358, 90–94 (2017).
[Crossref]

Rolland, A.

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

Rubiola, E.

M. Delehaye, J. Millo, P.-Y. Bourgeois, R. B. Lucas Groult, E. Rubiola, E. Bigler, Y. Kersalé, and C. Lacroûte, “Residual phase noise measurement of optical second harmonic generation in PPLN waveguides,” IEEE Phot. Tech. Lett. 29, 1639–1642 (2017).
[Crossref]

Safronova, M. S.

C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, “Optical clock comparison test of Lorentz symmetry,” Nature 567, 204–208 (2019).
[Crossref] [PubMed]

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

Sanner, C.

C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, “Optical clock comparison test of Lorentz symmetry,” Nature 567, 204–208 (2019).
[Crossref] [PubMed]

Santarelli, G.

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8, 219–223 (2014).
[Crossref]

Schäffer, S. A.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
[Crossref] [PubMed]

Schioppo, M.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
[Crossref] [PubMed]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
[Crossref]

Schmidt, P.

T. Mehlstäubler, G. Grosche, C. Lisdat, P. Schmidt, and H. Denker, “Atomic clocks for geodesy,” Rep. Prog. Phys. 81, 064401 (2018).
[Crossref] [PubMed]

Schmidt, P. O.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. B. Wübbena, O. Mandel, and P. O. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113, 233–242 (2013).
[Crossref]

Schnatz, H.

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62, 1556–1562 (2013).
[Crossref]

J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultra-precise measurement of optical frequency ratios,” Phys. Rev. Lett. 88, 073601 (2002).
[Crossref]

Sherman, J. A.

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
[Crossref]

Sonderhouse, L.

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 μm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118, 263202 (2017).
[Crossref]

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science xtbf358, 90–94 (2017).
[Crossref]

Stenger, J.

J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultra-precise measurement of optical frequency ratios,” Phys. Rev. Lett. 88, 073601 (2002).
[Crossref]

Sterr, U.

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

S. B. Koller, J. Grotti, S. Vogt, A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, “Transportable optical lattice clock with 7×10−17 uncertainty,” Phys. Rev. Lett. 118, 073601 (2017).
[Crossref]

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 μm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118, 263202 (2017).
[Crossref]

S. Häfner, S. Falke, C. Grebing, S. Vogt, T. Legero, M. Merimaa, C. Lisdat, and U. Sterr, “8 ×10−17 fractional laser frequency instability with a long room-temperature cavity,” Opt. Lett. 40, 2112–2115 (2015).
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A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, “Noise and instability of an optical lattice clock,” Phys. Rev. A 92, 063814 (2015).
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C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62, 1556–1562 (2013).
[Crossref]

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. B. Wübbena, O. Mandel, and P. O. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113, 233–242 (2013).
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T. Kessler, T. Legero, and U. Sterr, “Thermal noise in optical cavities revisited,” J. Opt. Soc. Am. B 29, 178–184 (2012).
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S. Falke, M. Misera, U. Sterr, and C. Lisdat, “Delivering pulsed and phase stable light to atoms of an optical clock,” Appl. Phys. B 107, 301–311 (2012).
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Strouse, G. F.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2×10−18 total uncertainty,” Nat. Com. 6, 6896 (2015).
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Sutherland, R. L.

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, 2003), 2nd ed.
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Tamm, C.

C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, “Optical clock comparison test of Lorentz symmetry,” Nature 567, 204–208 (2019).
[Crossref] [PubMed]

J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultra-precise measurement of optical frequency ratios,” Phys. Rev. Lett. 88, 073601 (2002).
[Crossref]

Tampellini, A.

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

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8, 219–223 (2014).
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Telle, H. R.

J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultra-precise measurement of optical frequency ratios,” Phys. Rev. Lett. 88, 073601 (2002).
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Tew, W. L.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2×10−18 total uncertainty,” Nat. Com. 6, 6896 (2015).
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J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Barbieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, and D. Calonico, “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14, 437–441 (2018).
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J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Barbieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, and D. Calonico, “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14, 437–441 (2018).
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J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Barbieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, and D. Calonico, “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14, 437–441 (2018).
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S. B. Koller, J. Grotti, S. Vogt, A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, “Transportable optical lattice clock with 7×10−17 uncertainty,” Phys. Rev. Lett. 118, 073601 (2017).
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S. Häfner, S. Falke, C. Grebing, S. Vogt, T. Legero, M. Merimaa, C. Lisdat, and U. Sterr, “8 ×10−17 fractional laser frequency instability with a long room-temperature cavity,” Opt. Lett. 40, 2112–2115 (2015).
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J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Barbieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, and D. Calonico, “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14, 437–441 (2018).
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P. G. Westergaard, J. Lodewyck, and P. Lemonde, “Minimizing the Dick effect in an optical lattice clock,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 57, 623–628 (2010).
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D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 μm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118, 263202 (2017).
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S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, “An  27Al + quantum-logic clock with systematic uncertainty below 10−18,” Phys. Rev. Lett. 123, 033201 (2019).

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: Population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
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Wübbena, J. B.

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. B. Wübbena, O. Mandel, and P. O. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113, 233–242 (2013).
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Ye, J.

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 μm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118, 263202 (2017).
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G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, “Tenfold reduction of Brownian noise in optical interferometry,” Nat. Photonics 7, 644–650 (2013).
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M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. Blatt, T. Zanon-Willette, S. M. Foreman, and J. Ye, “Nuclear spin effects in optical lattice clocks,” Phys. Rev. A 76, 022510 (2007).
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Yeaton-Massey, D.

D. Yeaton-Massey and R. X. Adhikari, “A new bound on excess frequency noise in second harmonic generation in PPKTP at the 10−19 level,” Opt. Exp. 20, 21019–21024 (2012).
[Crossref]

Yoon, T. H.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
[Crossref] [PubMed]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
[Crossref]

Zampaolo, M.

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

Zanon-Willette, T.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. Blatt, T. Zanon-Willette, S. M. Foreman, and J. Ye, “Nuclear spin effects in optical lattice clocks,” Phys. Rev. A 76, 022510 (2007).
[Crossref]

Zelevinsky, T.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. Blatt, T. Zanon-Willette, S. M. Foreman, and J. Ye, “Nuclear spin effects in optical lattice clocks,” Phys. Rev. A 76, 022510 (2007).
[Crossref]

Zhang, W.

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 μm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118, 263202 (2017).
[Crossref]

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

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8, 219–223 (2014).
[Crossref]

G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, “Tenfold reduction of Brownian noise in optical interferometry,” Nat. Photonics 7, 644–650 (2013).
[Crossref]

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science xtbf358, 90–94 (2017).
[Crossref]

Zhang, X.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
[Crossref] [PubMed]

Zucco, M.

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

Appl. Phys. B (2)

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. B. Wübbena, O. Mandel, and P. O. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113, 233–242 (2013).
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S. Falke, M. Misera, U. Sterr, and C. Lisdat, “Delivering pulsed and phase stable light to atoms of an optical clock,” Appl. Phys. B 107, 301–311 (2012).
[Crossref]

IEEE Phot. Tech. Lett. (1)

M. Delehaye, J. Millo, P.-Y. Bourgeois, R. B. Lucas Groult, E. Rubiola, E. Bigler, Y. Kersalé, and C. Lacroûte, “Residual phase noise measurement of optical second harmonic generation in PPLN waveguides,” IEEE Phot. Tech. Lett. 29, 1639–1642 (2017).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62, 1556–1562 (2013).
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IEEE Trans. Ultrason. Ferroelectr. Freq. Control. (1)

P. G. Westergaard, J. Lodewyck, and P. Lemonde, “Minimizing the Dick effect in an optical lattice clock,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 57, 623–628 (2010).
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J. Opt. Soc. Am. B (1)

Nat. Com. (1)

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

Nat. Photonics (3)

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultra-stable optical clock with two cold-atom ensembles,” Nat. Photonics 11, 48–52 (2017).
[Crossref]

G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, “Tenfold reduction of Brownian noise in optical interferometry,” Nat. Photonics 7, 644–650 (2013).
[Crossref]

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8, 219–223 (2014).
[Crossref]

Nat. Phys. (1)

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

Nature (2)

C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, “Optical clock comparison test of Lorentz symmetry,” Nature 567, 204–208 (2019).
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W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milan, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance beyond the geodetic limit,” Nature 564, 87–90 (2018).
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Opt. Exp. (1)

D. Yeaton-Massey and R. X. Adhikari, “A new bound on excess frequency noise in second harmonic generation in PPKTP at the 10−19 level,” Opt. Exp. 20, 21019–21024 (2012).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (3)

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. Blatt, T. Zanon-Willette, S. M. Foreman, and J. Ye, “Nuclear spin effects in optical lattice clocks,” Phys. Rev. A 76, 022510 (2007).
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W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: Population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
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A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, “Noise and instability of an optical lattice clock,” Phys. Rev. A 92, 063814 (2015).
[Crossref]

Phys. Rev. Lett. (4)

S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, “An  27Al + quantum-logic clock with systematic uncertainty below 10−18,” Phys. Rev. Lett. 123, 033201 (2019).

S. B. Koller, J. Grotti, S. Vogt, A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, “Transportable optical lattice clock with 7×10−17 uncertainty,” Phys. Rev. Lett. 118, 073601 (2017).
[Crossref]

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 μm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118, 263202 (2017).
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J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultra-precise measurement of optical frequency ratios,” Phys. Rev. Lett. 88, 073601 (2002).
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Rep. Prog. Phys. (1)

T. Mehlstäubler, G. Grosche, C. Lisdat, P. Schmidt, and H. Denker, “Atomic clocks for geodesy,” Rep. Prog. Phys. 81, 064401 (2018).
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Rev. Mod. Phys. (1)

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

Other (4)

R. C. Hilborn, “Einstein coefficients, cross sections, f values, dipole moments, and all that,” arXiv:physics/0202029 [physics.atom-ph] (2002). This is a revised (February, 2002) version of a paper that originally appeared in Am. J. Phys. 50, 982–986 (1982).

G. J. Dick, “Local oscillator induced instabilities in trapped ion frequency standards,” in Proceedings of 19thAnnu. Precise Time and Time Interval Meeting, Redendo Beach, 1987, (U.S. Naval Observatory, Washington, DC, 1988), pp. 133–147.

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science xtbf358, 90–94 (2017).
[Crossref]

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, 2003), 2nd ed.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Schematic sketch of the experimental setup used to determine the excess phase noise of two second-harmonic generator (SHG) modules. BS: beam splitter, DM: dichroic mirror, PD: photodiode, AOM: acousto-optical modulator, f/2 frequency divider, DDS: direct digital synthesizer, M: frequency mixer, FPGA: field-programmable gate array. FC: fiber coupler.
Fig. 2
Fig. 2 Power spectral density (PSD) of the electronic noise of the experimental setup (green line), PSD of phase noise between fundamental and doubled light of SHG modules Δνexc (blue line), and PSD of laser noise of a laser stabilized to PTB’s silicon cavity (red line) [14].
Fig. 3
Fig. 3 Schematic sketch of the experimental setup to determine the excess phase noise of a second-harmonic generation (SHG) module and a frequency comb. BS: beam splitter, DM: dichroic mirror, DG: diffraction grating, PD: photo diode, tracker: narrow-band filter (band width 500 kHz) and amplifier consisting of a phase-locked loop using a voltage-controlled oscillator that follows the input frequency, PFC: phase frequency comparator, AOM: acousto-optical modulator, f/2 frequency divider, DDS: direct digital synthesizer, M: frequency mixer, FPGA: field-programmable gate array, FC: fiber coupler.
Fig. 4
Fig. 4 Power spectral density (PSD) of the electronic noise of the experimental setup (green line), PSD of phase noise from the comb measurement (blue line) and the SHG module measurement in section 2 (light blue line), PSD of laser noise ofa laser stabilized to PTB’s silicon cavity (red line) [14]
Fig. 5
Fig. 5 Sketch of a simple path length stabilization including a second harmonic generation (SHG) module. RM: reference mirror BS: beam splitter, AOM: acousto-optical modulator, DM: dichroic mirror, PD: photo diode, Ref.: 100 MHz reference signal PFC: phase frequency comparator, VCO: voltage-controlled oscillator, DDS: direct digital synthesizer.
Fig. 6
Fig. 6 Schematic sketch of the phase difference between fundamental and frequency-doubled light (blue line) in response to a input power step (red line).
Fig. 7
Fig. 7 Phase difference per 1 mW of laser power over a duration t t 0   ' after a power switching event, starting 25 ms after the power step. Black diamonds represent measured data averaged over ten samples. A model with exponential settling of the phase has been fitted to the data (red line).
Fig. 8
Fig. 8 Schematic phase difference between fundamental and frequency-doubled light for a Rabi (blue line) and Ramsey (red line) scheme.
Fig. 9
Fig. 9 Fractional frequency shift Δy caused by phase evolution during Rabi interrogation with a duration Tπ = T (blue line) and for Ramsey interrogation with dark time Td = T and Tπ/2 = 1 ms, for a conversion efficiency η = 3.8 W−1 and a waist radius w0 = 100 µm. Note that Δy is approximately proportional to w0.

Equations (10)

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ν L ( t ) = ν 0 + Δ ν ( t ) ,
ν L   ' ( t ) = ν 0 + Δ ν ( t ) + f 0 + Δ f ( t ) .
f IR = ν L   ' ν L = f 0 + Δ f ( t )
f red = 2 ( ν L   ' + Δ ν SHG , 1 ) 2 ( ν L + Δ ν SHG , 2 ) = 2 f 0 + 2 Δ f + 2 Δ ν SHG , 1 2 Δ ν SHG , 2 ,
Δ ν exc = Δ ν SHG , 1 Δ ν SHG , 2 .
ν n = ν CEO + Δ ν CEO + n ( f rep + Δ f rep ) ,
ν m = 2 × ( ν CEO + Δ ν CEO ) + m ( f rep + Δ f rep ) + Δ ν SFG , m .
Δ ν exc , 2 = Δ ν SHG , 1 Δ ν SFG , m
Δ ϕ settle ( t ) = A ( 1 e t / τ ) .
P red = π 4 h ν 3 w 0 2 3 A ki c 2 × T π 2

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