Abstract

Coherently bridging across wide spectral regions in the optical domain with ultra-high precision will enable progress in optical spectroscopy and time and frequency metrology. We report optical frequency synthesis at the 1018 instability level based on a novel technique actively canceling the differential phase noise of a dual-branch Er-fiber based optical frequency comb spanning 500–2200 nm. We validate the method with an out-of-loop measurement demonstrating the stability transfer from 1560 nm to 780 nm with an instability level at 3×1018 at 1 s averaging time and 1×1019 at 1000 s (approximately averaging on 1×1017/τ), limited mainly by uncompensated optical interferometers used to detect optical beatnotes. To confirm this limitation, we propose an experimental setup that eliminates the excess noise induced by uncompensated optical paths and show that the proposed method exhibits an ultimate unprecedented instability level at 6×1019 at 1 s averaging time when two optical signals can share a common photodetector. The system realized becomes a powerful and universal tool for optical frequency comparison and spectral purity transfer across the visible and infrared domains.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (3)

G. E. Marti, R. B. Hutson, A. Goban, S. L. Campbell, N. Poli, and J. Ye, “Imaging optical frequencies with 100  μHz precision and 1.1  μm resolution,” Phys. Rev. Lett. 120, 103201 (2018).
[Crossref]

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

K. Kashiwagi, Y. Nakajima, M. Wada, S. Okubo, and H. Inaba, “Multi-branch fiber comb with relative frequency uncertainty at 10−20using fiber noise difference cancellation,” Opt. Express 26, 8831–8840 (2018).
[Crossref]

2017 (10)

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (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]

N. Ohmae, N. Kuse, M. E. Fermann, and H. Katori, “All-polarization-maintaining, single-port Er:fiber comb for high-stability comparison of optical lattice clocks,” Appl. Phys. Express 10, 062503 (2017).
[Crossref]

H. Leopardi, J. Davila-Rodriguez, F. Quinlan, J. Olson, J. A. Sherman, S. A. Diddams, and T. M. Fortier, “Single-branch Er:fiber frequency comb for precision optical metrology with 10−18 fractional instability,” Optica 4, 879–885 (2017).
[Crossref]

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

O. Gobron, K. Jung, N. Galland, K. Predehl, R. L. Targat, A. Ferrier, P. Goldner, S. Seidelin, and Y. L. Coq, “Dispersive heterodyne probing method for laser frequency stabilization based on spectral hole burning in rare-earth doped crystals,” Opt. Express 25, 15539–15548 (2017).
[Crossref]

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. 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 358, 90–94 (2017).
[Crossref]

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

B. M. Roberts, G. Blewitt, C. Dailey, M. Murphy, M. Pospelov, A. Rollings, J. Sherman, W. Williams, and A. Derevianko, “Search for domain wall dark matter with atomic clocks on board global positioning system satellites,” Nat. Commun. 8, 1195 (2017).
[Crossref]

2016 (9)

S. Kolkowitz, I. Pikovski, N. Langellier, M. D. Lukin, R. L. Walsworth, and J. Ye, “Gravitational wave detection with optical lattice atomic clocks,” Phys. Rev. D 94, 124043 (2016).
[Crossref]

C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and C. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563–569 (2016).
[Crossref]

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

N. Nemitz, T. Ohkubo, M. Takamoto, I. Ushijima, M. Das, N. Ohmae, and H. Katori, “Frequency ratio of Yb and Sr clocks with 5 × 10−17 uncertainty at 150 seconds averaging time,” Nat. Photonics 10, 258–261 (2016).
[Crossref]

G. D. Cole, W. Zhang, B. J. Bjork, D. Follman, P. Heu, C. Deutsch, L. Sonderhouse, J. Robinson, C. Franz, A. Alexandrovski, M. Notcutt, O. H. Heckl, J. Ye, and M. Aspelmeyer, “High-performance near- and mid-infrared crystalline coatings,” Optica 3, 647–656 (2016).
[Crossref]

Y. Yao, Y. Jiang, H. Yu, Z. Bi, and L. Ma, “Optical frequency divider with division uncertainty at the 10−21 level,” Nat. Sci. Rev. 3, 463–469 (2016).
[Crossref]

T. M. Fortier, A. Rolland, F. Quinlan, F. N. Baynes, A. J. Metcalf, A. Hati, A. D. Ludlow, N. Hinkley, M. Shimizu, T. Ishibashi, J. C. Campbell, and S. A. Diddams, “Optically referenced broadband electronic synthesizer with 15 digits of resolution,” Laser Photon. Rev. 10, 780–790 (2016).
[Crossref]

T. D. Shoji, W. Xie, K. L. Silverman, A. Feldman, T. Harvey, R. P. Mirin, and T. R. Schibli, “Ultra-low-noise monolithic mode-locked solid-state laser,” Optica 3, 995–998 (2016).
[Crossref]

N. Kuse, J. Jiang, C.-C. Lee, T. R. Schibli, and M. Fermann, “All polarization-maintaining Er fiber-based optical frequency combs with nonlinear amplifying loop mirror,” Opt. Express 24, 3095–3102 (2016).
[Crossref]

2015 (5)

N. Kuse, C.-C. Lee, J. Jiang, C. Mohr, T. R. Schibli, and M. Fermann, “Ultra-low noise all polarization-maintaining Er fiber-based optical frequency combs facilitated with a graphene modulator,” Opt. Express 23, 24342–24350 (2015).
[Crossref]

B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall, C. Chardonnet, C. Daussy, B. Darquié, Y. Le Coq, and A. Amy-Klein, “Quantum cascade laser frequency stabilization at the sub-Hz level,” Nat. Photonics 9, 456–460 (2015).
[Crossref]

L. A. M. Johnson, P. Gill, and H. S. Margolis, “Evaluating the performance of the NPL femtosecond frequency combs: agreement at the 10−21 level,” Metrologia 52, 62–71 (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]

S. Cook, T. Rosenband, and D. R. Leibrandt, “Laser-frequency stabilization based on steady-state spectral-hole burning in Eu3+:Y2SiO5,” Phys. Rev. Lett. 114, 253902 (2015).
[Crossref]

2014 (5)

A. Derevianko and M. Pospelov, “Hunting for topological dark matter with atomic clocks,” Nat. Phys. 10, 933–936 (2014).
[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]

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10−18 level,” Nature 506, 71–75 (2014).
[Crossref]

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113, 210801 (2014).
[Crossref]

N. Huntemann, B. Lipphardt, C. Tamm, V. Gerginov, S. Weyers, and E. Peik, “Improved limit on a temporal variation of mp/me from comparisons of Yb+ and Cs atomic clocks,” Phys. Rev. Lett. 113, 210802 (2014).
[Crossref]

2013 (2)

N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, and A. D. Ludlow, “An atomic clock with 10−18 instability,” Science 341, 1215–1218 (2013).
[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]

2012 (2)

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, “A sub-40-MHz-linewidth laser based on a silicon single-crystal optical cavity,” Nat. Photonics 6, 687–692 (2012).
[Crossref]

J. G. Bohnet, Z. Chen, J. W. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref]

2011 (2)

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

M. J. Thorpe, L. Rippe, T. M. Fortier, M. S. Kirchner, and T. Rosenband, “Frequency stabilization to 6 × 10−16 via spectral-hole burning,” Nat. Photonics 5, 688–693 (2011).
[Crossref]

2010 (2)

2009 (1)

2007 (2)

T. M. Fortier, N. Ashby, J. C. Bergquist, M. J. Delaney, S. A. Diddams, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, K. Kim, F. Levi, L. Lorini, W. H. Oskay, T. E. Parker, J. Shirley, and J. E. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
[Crossref]

C. Langrock, M. M. Fejer, I. Hartl, and M. E. Fermann, “Generation of octave-spanning spectra inside reverse-proton-exchanged periodically poled lithium niobate waveguides,” Opt. Lett. 32, 2478–2480 (2007).
[Crossref]

2004 (1)

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

2000 (2)

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

1990 (1)

Abgrall, M.

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

B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall, C. Chardonnet, C. Daussy, B. Darquié, Y. Le Coq, and A. Amy-Klein, “Quantum cascade laser frequency stabilization at the sub-Hz level,” Nat. Photonics 9, 456–460 (2015).
[Crossref]

Alexandre, C.

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
[Crossref]

Alexandrovski, A.

Al-Masoudi, A.

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

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

C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and C. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563–569 (2016).
[Crossref]

Amy-Klein, A.

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

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

B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall, C. Chardonnet, C. Daussy, B. Darquié, Y. Le Coq, and A. Amy-Klein, “Quantum cascade laser frequency stabilization at the sub-Hz level,” Nat. Photonics 9, 456–460 (2015).
[Crossref]

Argence, B.

B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall, C. Chardonnet, C. Daussy, B. Darquié, Y. Le Coq, and A. Amy-Klein, “Quantum cascade laser frequency stabilization at the sub-Hz level,” Nat. Photonics 9, 456–460 (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]

Ashby, N.

T. M. Fortier, N. Ashby, J. C. Bergquist, M. J. Delaney, S. A. Diddams, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, K. Kim, F. Levi, L. Lorini, W. H. Oskay, T. E. Parker, J. Shirley, and J. E. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
[Crossref]

Aspelmeyer, M.

Barbieri, P.

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

Bartels, A.

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

Baynes, F.

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

Baynes, F. N.

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

T. M. Fortier, A. Rolland, F. Quinlan, F. N. Baynes, A. J. Metcalf, A. Hati, A. D. Ludlow, N. Hinkley, M. Shimizu, T. Ishibashi, J. C. Campbell, and S. A. Diddams, “Optically referenced broadband electronic synthesizer with 15 digits of resolution,” Laser Photon. Rev. 10, 780–790 (2016).
[Crossref]

Beloy, K.

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]

N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, and A. D. Ludlow, “An atomic clock with 10−18 instability,” Science 341, 1215–1218 (2013).
[Crossref]

Bergquist, J. C.

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

T. M. Fortier, N. Ashby, J. C. Bergquist, M. J. Delaney, S. A. Diddams, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, K. Kim, F. Levi, L. Lorini, W. H. Oskay, T. E. Parker, J. Shirley, and J. E. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
[Crossref]

Bi, Z.

Y. Yao, Y. Jiang, H. Yu, Z. Bi, and L. Ma, “Optical frequency divider with division uncertainty at the 10−21 level,” Nat. Sci. Rev. 3, 463–469 (2016).
[Crossref]

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

Bigler, E.

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

Bilicki, S.

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

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

Bishof, M.

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10−18 level,” Nature 506, 71–75 (2014).
[Crossref]

Bjork, B. J.

Blewitt, G.

B. M. Roberts, G. Blewitt, C. Dailey, M. Murphy, M. Pospelov, A. Rollings, J. Sherman, W. Williams, and A. Derevianko, “Search for domain wall dark matter with atomic clocks on board global positioning system satellites,” Nat. Commun. 8, 1195 (2017).
[Crossref]

Bloom, B. J.

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 358, 90–94 (2017).
[Crossref]

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10−18 level,” Nature 506, 71–75 (2014).
[Crossref]

Bohnet, J. G.

J. G. Bohnet, Z. Chen, J. W. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref]

Bongs, K.

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113, 210801 (2014).
[Crossref]

Bookjans, E.

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

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

Bouchand, R.

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
[Crossref]

Boudot, R.

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

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34, 3707–3709 (2009).
[Crossref]

Bourgeois, P. Y.

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

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34, 3707–3709 (2009).
[Crossref]

Bowden, W.

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

Bregolin, F.

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

Bromley, S. L.

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10−18 level,” Nature 506, 71–75 (2014).
[Crossref]

Brown, R. C.

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]

Calenico, D.

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

Camisard, E.

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

Campbell, J. C.

T. M. Fortier, A. Rolland, F. Quinlan, F. N. Baynes, A. J. Metcalf, A. Hati, A. D. Ludlow, N. Hinkley, M. Shimizu, T. Ishibashi, J. C. Campbell, and S. A. Diddams, “Optically referenced broadband electronic synthesizer with 15 digits of resolution,” Laser Photon. Rev. 10, 780–790 (2016).
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X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
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C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Supplementary Material (1)

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Figures (3)

Fig. 1.
Fig. 1. (a) Representation of the proposed approach to compare two optical frequencies separated by more than an octave in a fiber noise cancelled dual-branch frequency comb. See text for details. (b) Diagram of the proposed method. Two CW lasers are linked through the dual-branch frequency comb with no excessive noise due to non-common optical path. DM, dichroic mirror; EDFA, erbium-doped fiber amplifier; PPLN, periodically poled lithium niobate; SHG, second-harmonic generation. IR PBS, infrared polarization beam splitter; VIS PBS, visible polarization beam splitter. (c) Optical spectra of the dual-branch frequency comb spanning 500 nm to 2200 nm. (d) RF spectra of optical beatnotes at 698 nm (black), 780 nm (red), 1064 nm (blue), and 1560 nm (green), measured with 100 kHz resolution bandwidth in free-running operation. (e) Phase noise power spectral density of the residual error of the servo locking of f ceo (blue) and f rep (red). (f) Fractional frequency instability in terms of Allan deviation of the residual error of the servo locking of f ceo (blue) and f rep (red) (raw data acquired with a Λ -type frequency counter with 1 s gate time).
Fig. 2.
Fig. 2. (a) Experimental setup to evaluate the residual noise of the proposed method in this paper. A 1560 nm CW laser is used to stabilize the frequency comb. This laser is also doubled to 780 nm through a PPLN, and this doubled CW light is then compared to a comb mode at 780 nm. (b) Phase noise power spectral density of the setup in the non-fiber cancelled configuration (red) and fiber cancelled configuration (blue). (c) Fractional frequency instability in terms of Allan deviation of the setup in the non-fiber cancelled configuration (red) and fiber cancelled configuration (blue) (raw data acquired with a Λ -type frequency counter with 1 s gate time).
Fig. 3.
Fig. 3. (a) Experimental setup, to evaluate the residual noise of the proposed method, overcoming the excess noise from non-common path optical interferometers. A 1064 nm CW laser beats with the stitched visible and infrared branch on a common photodetector as well as with the dual-branch f ceo detection. (b) RF spectrum of the signal photodetected exhibiting the two optical beatnotes f IR and f VIS , and f ceo . Resolution bandwidth is 100 kHz. (c) Phase noise power spectral density of the out-of-loop beatnote f VIS . (d) Fractional frequency instability in terms of Allan deviation of the out-of-loop beatnote f VIS . This instability level reveals the lower limit of the proposed method (raw data acquired with a Λ -type frequency counter with 1 s gate time).

Equations (8)

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{ ϕ A ( t ) = ϕ ceo ( t ) + ( ϕ τ VIS ( t ) ϕ τ IR ( t ) ) ϕ B ( t ) = ϕ ceo ( t ) + ϕ τ IR ( t ) ϕ C ( t ) = n ϕ rep ( t ) + ϕ ceo ( t ) + ϕ τ IR ( t ) ϕ ν IR ( t ) ϕ D ( t ) = m ϕ rep ( t ) + 2 ϕ ceo ( t ) + ϕ τ VIS ( t ) ϕ ν VIS ( t ) ,
{ ϕ A ( t ) = 0 ϕ ceo ( t ) = ( ϕ τ IR ( t ) ϕ τ VIS ( t ) ) ϕ B ( t ) = ( 2 ϕ τ IR ( t ) ϕ τ VIS ( t ) ) ϕ C ( t ) = n ϕ rep ( t ) + ( 2 ϕ τ IR ( t ) ϕ τ VIS ( t ) ) ϕ ν IR ( t ) ϕ D ( t ) = m ϕ rep ( t ) + ( 2 ϕ τ IR ( t ) ϕ τ VIS ( t ) ) ϕ ν VIS ( t ) .
Δ ( t ) = ( 2 ϕ τ IR ( t ) ϕ τ VIS ( t ) ) .
ϕ D ( t ) = m n ϕ ν IR ( t ) ϕ ν VIS ( t ) + ( 1 m n ) Δ ( t ) .
{ ϕ C ( t ) ϕ B ( t ) = n ϕ rep ( t ) ϕ ν IR ( t ) ϕ D ( t ) ϕ B ( t ) = m ϕ rep ( t ) ϕ ν VIS ( t ) .
ϕ D ( t ) ϕ B ( t ) = m n ϕ ν IR ( t ) ϕ ν VIS ( t ) .
{ ϕ C ( t ) ϕ B ( t ) = n ϕ rep ( t ) ϕ ν 1560 ( t ) ϕ D ( t ) ϕ B ( t ) = 2 n ϕ rep ( t ) ϕ ν 780 ( t ) ,
n ϕ rep ( t ) ϕ ν 1560 ( t ) = 2 n ϕ rep ( t ) ϕ ν 780 ( t ) .