Abstract

We report a bound on the relative frequency fluctuations in nonlinear second harmonic generation. A 1064nm Nd:YAG laser is used to read out the phase of a Mach-Zehnder interferometer while PPKTP, a nonlinear crystal, is placed in each arm to generate second harmonic light. By comparing the arm length difference of the Mach Zehnder as read out by the fundamental 1064 nm light, and its second harmonic at 532 nm, we can bound the excess frequency noise introduced in the harmonic generation process. We report an amplitude spectral density of frequency noise with total RMS frequency deviation of 3mHz and a minimum value of 20 μHz/Hz1/2 over 250 seconds with a measurement bandwidth of 128 Hz, corresponding to an Allan deviation of 10−19 at 20 seconds.

© 2012 OSA

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2012 (2)

A. J. Mullavey, B. J. J. Slagmolen, J. Miller, M. Evans, P. Fritschel, D. Sigg, S. J. Waldman, D. A. Shaddock, and D. E. McClelland, “Arm-length stabilisation for interferometric gravitational-wave detectors using frequency-doubled auxiliary lasers,” Opt. Express20, 81–89 (2012).
[CrossRef] [PubMed]

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

2011 (2)

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D83, 062003 (2011).
[CrossRef]

D. Heinert, A. G. Gurkovsky, R. Nawrodt, S. P. Vyatchanin, and K. Yamamoto, “Thermorefractive noise of finite-sized cylindrical test masses,” Phys. Rev. D84, 062001 (2011).
[CrossRef]

2009 (2)

LIGO Scientific Collaboration, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Rep. Prog. Phys.72, 076901 (2009).

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B: Lasers Opt.97, 541–551 (2009). 10.1007/s00340-009-3653-2.
[CrossRef]

2008 (2)

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef]

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fibre-based femtosecond lasers,” Euro. Phys. J. D.48, 27–33 (2008).
[CrossRef]

2007 (5)

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[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] [PubMed]

E. J. Zang, J. P. Cao, Y. Li, C. Y. Li, Y. K. Deng, and C. Q. Gao, “Realization of four-pass I2 absorption cell in 532-nm optical frequency standard,” IEEE Trans. Instrumen. Meas.56, 673–676 (2007).
[CrossRef]

Y. Levin, “Fluctuation–dissipation theorem for thermo-refractive noise,” Phys. Lett. A372, 1941–1944 (2007).
[CrossRef]

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[CrossRef]

2006 (1)

2004 (1)

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

2002 (1)

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

2001 (1)

L. Robertsson, “International comparison of 127I2-stabilized frequency-doubled Nd:YAG lasers between the BIPM, the NRLM and the BNM-INM,” Metrologia38 (2001).

1998 (1)

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Adhikari, R. X.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Arai, K.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
[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] [PubMed]

Barr, B.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

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,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Bergquist, J. C.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[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] [PubMed]

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[CrossRef]

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[CrossRef]

Betzwieser, J.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Bi, Z.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Brooks, A.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Brusch, A.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef]

Byer, R. L.

Camp, J. B.

Cao, J. P.

E. J. Zang, J. P. Cao, Y. Li, C. Y. Li, Y. K. Deng, and C. Q. Gao, “Realization of four-pass I2 absorption cell in 532-nm optical frequency standard,” IEEE Trans. Instrumen. Meas.56, 673–676 (2007).
[CrossRef]

Chen, Y.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D83, 062003 (2011).
[CrossRef]

Chou, C. W.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef]

Coddington, I.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[CrossRef]

Dahl, K.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Danilishin, S.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D83, 062003 (2011).
[CrossRef]

Delaney, M. J.

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] [PubMed]

Delany, M. J.

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[CrossRef]

Deng, Y. K.

E. J. Zang, J. P. Cao, Y. Li, C. Y. Li, Y. K. Deng, and C. Q. Gao, “Realization of four-pass I2 absorption cell in 532-nm optical frequency standard,” IEEE Trans. Instrumen. Meas.56, 673–676 (2007).
[CrossRef]

Diddams, S. A.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[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] [PubMed]

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[CrossRef]

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[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,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Doravari, S.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Driggers, J. C.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Drullinger, R. E.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Evans, M.

Feder, K. S.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[CrossRef]

Fortier, T. M.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[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] [PubMed]

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[CrossRef]

Fritschel, P.

Gao, C. Q.

E. J. Zang, J. P. Cao, Y. Li, C. Y. Li, Y. K. Deng, and C. Q. Gao, “Realization of four-pass I2 absorption cell in 532-nm optical frequency standard,” IEEE Trans. Instrumen. Meas.56, 673–676 (2007).
[CrossRef]

Grosche, G.

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B: Lasers Opt.97, 541–551 (2009). 10.1007/s00340-009-3653-2.
[CrossRef]

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fibre-based femtosecond lasers,” Euro. Phys. J. D.48, 27–33 (2008).
[CrossRef]

Gurkovsky, A. G.

D. Heinert, A. G. Gurkovsky, R. Nawrodt, S. P. Vyatchanin, and K. Yamamoto, “Thermorefractive noise of finite-sized cylindrical test masses,” Phys. Rev. D84, 062001 (2011).
[CrossRef]

Gustafson, E. K.

Heavner, T. P.

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[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] [PubMed]

Heinert, D.

D. Heinert, A. G. Gurkovsky, R. Nawrodt, S. P. Vyatchanin, and K. Yamamoto, “Thermorefractive noise of finite-sized cylindrical test masses,” Phys. Rev. D84, 062001 (2011).
[CrossRef]

Hollberg, L.

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[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] [PubMed]

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,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Holzwarth, R.

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B: Lasers Opt.97, 541–551 (2009). 10.1007/s00340-009-3653-2.
[CrossRef]

Hume, D. B.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef]

Itano, W. M.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[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] [PubMed]

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[CrossRef]

Izumi, K.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Jefferts, S. R.

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[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] [PubMed]

Khalili, F.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D83, 062003 (2011).
[CrossRef]

Kim, K.

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[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] [PubMed]

King, P. J.

Korth, W. Z.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Le Coq, Y.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[CrossRef]

Legero, T.

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B: Lasers Opt.97, 541–551 (2009). 10.1007/s00340-009-3653-2.
[CrossRef]

Leonhardt, V.

Levi, F.

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[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] [PubMed]

Levin, Y.

Y. Levin, “Fluctuation–dissipation theorem for thermo-refractive noise,” Phys. Lett. A372, 1941–1944 (2007).
[CrossRef]

Li, C. Y.

E. J. Zang, J. P. Cao, Y. Li, C. Y. Li, Y. K. Deng, and C. Q. Gao, “Realization of four-pass I2 absorption cell in 532-nm optical frequency standard,” IEEE Trans. Instrumen. Meas.56, 673–676 (2007).
[CrossRef]

Li, Y.

E. J. Zang, J. P. Cao, Y. Li, C. Y. Li, Y. K. Deng, and C. Q. Gao, “Realization of four-pass I2 absorption cell in 532-nm optical frequency standard,” IEEE Trans. Instrumen. Meas.56, 673–676 (2007).
[CrossRef]

Lipphardt, B.

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B: Lasers Opt.97, 541–551 (2009). 10.1007/s00340-009-3653-2.
[CrossRef]

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fibre-based femtosecond lasers,” Euro. Phys. J. D.48, 27–33 (2008).
[CrossRef]

Lorini, L.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef]

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[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] [PubMed]

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[CrossRef]

Ma, L.-S.

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,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

McClelland, D. E.

Miao, H.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D83, 062003 (2011).
[CrossRef]

Miller, J.

Mullavey, A. J.

Müller-Ebhardt, H.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D83, 062003 (2011).
[CrossRef]

Nawrodt, R.

D. Heinert, A. G. Gurkovsky, R. Nawrodt, S. P. Vyatchanin, and K. Yamamoto, “Thermorefractive noise of finite-sized cylindrical test masses,” Phys. Rev. D84, 062001 (2011).
[CrossRef]

Newbury, N. R.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef]

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[CrossRef]

Nicholson, J. W.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[CrossRef]

Oates, C.

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,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Oates, C. W.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[CrossRef]

Oskay, W. H.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[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] [PubMed]

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[CrossRef]

Parker, T. E.

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[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).
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Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
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Predehl, K.

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B: Lasers Opt.97, 541–551 (2009). 10.1007/s00340-009-3653-2.
[CrossRef]

Quraishi, Q.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[CrossRef]

Robertsson, L.

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,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

L. Robertsson, “International comparison of 127I2-stabilized frequency-doubled Nd:YAG lasers between the BIPM, the NRLM and the BNM-INM,” Metrologia38 (2001).

Rollins, J.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Rosenband, T.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef]

Rubiola,

Rubiola, Phase Noise and Frequency Stability in Oscillators (Cambridge University Press, 2008).
[CrossRef]

Savage, J. R. L.

Schmidt, P. O.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef]

Schnatz, H.

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B: Lasers Opt.97, 541–551 (2009). 10.1007/s00340-009-3653-2.
[CrossRef]

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fibre-based femtosecond lasers,” Euro. Phys. J. D.48, 27–33 (2008).
[CrossRef]

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

Seel, S. U.

Shaddock, D. A.

Shirley, J.

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] [PubMed]

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[CrossRef]

Sigg, D.

Slagmolen, B. J. J.

Stalnaker, J. E.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[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] [PubMed]

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[CrossRef]

Stenger, J.

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

Sterr, U.

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B: Lasers Opt.97, 541–551 (2009). 10.1007/s00340-009-3653-2.
[CrossRef]

Swann, W. C.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef]

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[CrossRef]

Tamm, C.

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

Telle, H. R.

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

Terra, O.

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B: Lasers Opt.97, 541–551 (2009). 10.1007/s00340-009-3653-2.
[CrossRef]

Uehara, N.

Vass, S.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Vyatchanin, S. P.

D. Heinert, A. G. Gurkovsky, R. Nawrodt, S. P. Vyatchanin, and K. Yamamoto, “Thermorefractive noise of finite-sized cylindrical test masses,” Phys. Rev. D84, 062001 (2011).
[CrossRef]

Waldman, S. J.

Westbrook, P. S.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[CrossRef]

Willke, B.

Wilpers, G.

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,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Windeler, R. S.

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,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Wineland, D. J.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef]

Yamamoto, K.

D. Heinert, A. G. Gurkovsky, R. Nawrodt, S. P. Vyatchanin, and K. Yamamoto, “Thermorefractive noise of finite-sized cylindrical test masses,” Phys. Rev. D84, 062001 (2011).
[CrossRef]

Yeaton-Massey, D.

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Zang, E. J.

E. J. Zang, J. P. Cao, Y. Li, C. Y. Li, Y. K. Deng, and C. Q. Gao, “Realization of four-pass I2 absorption cell in 532-nm optical frequency standard,” IEEE Trans. Instrumen. Meas.56, 673–676 (2007).
[CrossRef]

Zhao, C.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D83, 062003 (2011).
[CrossRef]

Zucco, M.

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,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. B: Lasers Opt. (2)

J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B: Lasers Opt.89, 167–176 (2007).
[CrossRef]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B: Lasers Opt.97, 541–551 (2009). 10.1007/s00340-009-3653-2.
[CrossRef]

Euro. Phys. J. D. (1)

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fibre-based femtosecond lasers,” Euro. Phys. J. D.48, 27–33 (2008).
[CrossRef]

IEEE Trans. Instrumen. Meas. (1)

E. J. Zang, J. P. Cao, Y. Li, C. Y. Li, Y. K. Deng, and C. Q. Gao, “Realization of four-pass I2 absorption cell in 532-nm optical frequency standard,” IEEE Trans. Instrumen. Meas.56, 673–676 (2007).
[CrossRef]

Metrologia (1)

L. Robertsson, “International comparison of 127I2-stabilized frequency-doubled Nd:YAG lasers between the BIPM, the NRLM and the BNM-INM,” Metrologia38 (2001).

Nat. Photonics (1)

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le 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. Photonics1, 283–287 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Lett. A (1)

Y. Levin, “Fluctuation–dissipation theorem for thermo-refractive noise,” Phys. Lett. A372, 1941–1944 (2007).
[CrossRef]

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Phys. Rev. D (2)

D. Heinert, A. G. Gurkovsky, R. Nawrodt, S. P. Vyatchanin, and K. Yamamoto, “Thermorefractive noise of finite-sized cylindrical test masses,” Phys. Rev. D84, 062001 (2011).
[CrossRef]

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D83, 062003 (2011).
[CrossRef]

Phys. Rev. Lett. (2)

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

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] [PubMed]

Rep. Prog. Phys. (1)

LIGO Scientific Collaboration, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Rep. Prog. Phys.72, 076901 (2009).

Science (2)

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[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,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Other (3)

K. Izumi, K. Arai, B. Barr, J. Betzwieser, A. Brooks, K. Dahl, S. Doravari, J. C. Driggers, W. Z. Korth, H. Miao, J. Rollins, S. Vass, D. Yeaton-Massey, and R. X. Adhikari, “Multi-wavelength cavity metrology,” arXiv:1205.1257 (2012)

Rubiola, Phase Noise and Frequency Stability in Oscillators (Cambridge University Press, 2008).
[CrossRef]

I. R. C. Committee, “Characterization of Frequency and Phase Noise,” Report (1986).

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Figures (4)

Fig. 1
Fig. 1

Experimental layout - A dual wavelength Mach-Zehnder Interferometer. Some readout mirrors for harmonic separation are not shown. See text for a more complete description.

Fig. 2
Fig. 2

Example time series of the Mach-Zehnder output. The RMS phase noise over the one hour period was 6 mrad RMS at 532 nm and 3 mrad RMS at 1064 nm

Fig. 3
Fig. 3

On the left we see the full noise budget of the experiment: θ 1064 A θ 1064 B (in red) (which is the in-loop signal of the Mach-Zehnder), θ 532 A θ 532 B (in green) (which contains excess phase noise), and the subtraction residual (in black). The total RMS frequency fluctuation in the measurement band is 3 mHz. On the right we have a comparison of this work with previous bounds. These bounds show up as frequency noise [13], timing error [5], and phase noise [4].

Fig. 4
Fig. 4

The Allan deviations from this experiment (green and black) were obtained from the power spectrum as described in [20]. Bounds from previous work are shown for reference.

Equations (2)

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θ 532 = 2 θ 1064 π / 2 Δ k L / 2 ,
θ 532 A θ 532 B = 2 ( θ 1064 A θ 1064 B ) ( Δ k A Δ k B ) L / 2 .

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