Abstract

The temperature stability of optical reference cavities is significant in state-of-the-art ultra-stable narrow-linewidth laser systems. In this paper, the thermal time constant and thermal sensitivity of reference cavities are analyzed when reference cavities respond to environmental perturbations via heat transfer of thermal conduction and thermal radiation separately. The analysis as well as simulation results indicate that a reference cavity enclosed in multiple layers of thermal shields with larger mass, higher thermal capacity and lower emissivity is found to have a larger thermal time constant and thus a smaller sensitivity to environmental temperature perturbations. The design of thermal shields for reference cavities may vary according to experimentally achievable temperature stability and the coefficient of thermal expansion of reference cavities. A temperature fluctuation-induced length instability of reference cavities as low as 6 × 10−16 on a day timescale can be achieved if a two-layer thermal shield is inserted between a cavity with the coefficient of thermal expansion of 1 × 10−10 /K and an outer vacuum chamber with temperature fluctuation amplitude of 1 mK and period of 24 hours.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref]

2014 (2)

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(7486), 71–75 (2014).
[Crossref] [PubMed]

C. Hagemann, C. Grebing, C. Lisdat, S. Falke, T. Legero, U. Sterr, F. Riehle, M. J. Martin, and J. Ye, “Ultrastable laser with average fractional frequency drift rate below 5 × 10−19/s,” Opt. Lett. 39(17), 5102–5105 (2014).
[Crossref] [PubMed]

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(6151), 1215–1218 (2013).
[Crossref] [PubMed]

H. Chen, Y. Jiang, S. Fang, Z. Bi, and L. Ma, “Frequency stabilization of Nd:YAG lasers with a most probable linewidth of 0.6 Hz,” J. Opt. Soc. Am. B 30(6), 1546–1550 (2013).
[Crossref]

2012 (3)

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(10), 687–692 (2012).
[Crossref]

B. Argence, E. Prevost, T. Leveque, R. Le Goff, S. Bize, P. Lemonde, and G. Santarelli, “Prototype of an ultra-stable optical cavity for space applications,” Opt. Express 20(23), 25409–25420 (2012)
[Crossref] [PubMed]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, “Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s,” Phys. Rev. Lett. 109(23), 230801 (2012).
[Crossref]

2011 (3)

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

D. R. Leibrandt, M. J. Thorpe, M. Notcutt, R. E. Drullinger, T. Rosenband, and J. C. Bergquist, “Spherical reference cavities for frequency stabilization of lasers in non-laboratory environments,” Opt. Express 19(4), 3471–3482 (2011).
[Crossref] [PubMed]

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(7), 425–429 (2011).
[Crossref]

2009 (3)

S. G. Turyshev, “Experimental tests of general relativity: recent progress and future directions,” Phys. Uspekhi 52(1), 1–27 (2009).
[Crossref]

Y. N. Zhao, J. Zhang, A. Stejskal, T. Liu, V. Elman, Z. H. Lu, and L. J. Wang, “A vibration-insensitive optical cavity and absolute determination of its ultrahigh stability,” Opt. Express 17(11), 8970–8982 (2009).
[Crossref] [PubMed]

P. Dube, A. A. Madej, J. E. Bernard, L. Marmet, and A. D. Shiner, “A narrow linewidth and frequency-stable probe laser source for the 88Sr+ single ion optical frequency standard,” Appl. Phys. B 95(1), 43–54 (2009).
[Crossref]

2008 (1)

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hansch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Perot cavities,” Phys. Rev. A 77, 053809 (2008).
[Crossref]

2007 (2)

A. D. Ludlow, X. Huang, M. Notcutt, T. Zanon-Willette, S. M. Foreman, M. M. Boyd, S. Blatt, and J. Ye, “Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1 × 10−15,” Opt. Lett. 32(6), 641–643 (2007).
[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(7), 070801 (2007).
[Crossref] [PubMed]

2006 (5)

J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78(4), 1279–1295 (2006).
[Crossref]

T. W. Hansch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78(4), 1297–1309 (2006).
[Crossref]

L. Chen, J. L. Hall, J. Ye, T. Yang, E. Zang, and T. Li, “Vibration-induced elastic deformation of Fabry-Perot cavities,” Phys. Rev. A 74(5), 053801 (2006).
[Crossref]

H. Stoehr, F. Mensing, J. Helmcke, and U. Sterr, “Diode laser with 1 Hz linewidth,” Opt. Lett. 31(6), 736–738 (2006).
[Crossref] [PubMed]

M. Notcutt, L. S. Ma, A. D. Ludlow, S. M. Foreman, J. Ye, and J. L. Hall, “Contribution of thermal noise to frequency stability of rigid optical cavity via hertz-linewidth lasers,” Phys. Rev. A 73, 031804(R) (2006).
[Crossref]

2004 (1)

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93, 250602 (2004).
[Crossref]

1999 (1)

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82(19), 3799–3802 (1999).
[Crossref]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Alnis, J.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hansch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Perot cavities,” Phys. Rev. A 77, 053809 (2008).
[Crossref]

Argence, B.

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(7), 070801 (2007).
[Crossref] [PubMed]

Beloy, K.

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(6151), 1215–1218 (2013).
[Crossref] [PubMed]

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(7), 425–429 (2011).
[Crossref]

D. R. Leibrandt, M. J. Thorpe, M. Notcutt, R. E. Drullinger, T. Rosenband, and J. C. Bergquist, “Spherical reference cavities for frequency stabilization of lasers in non-laboratory environments,” Opt. Express 19(4), 3471–3482 (2011).
[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(7), 070801 (2007).
[Crossref] [PubMed]

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82(19), 3799–3802 (1999).
[Crossref]

Bernard, J. E.

P. Dube, A. A. Madej, J. E. Bernard, L. Marmet, and A. D. Shiner, “A narrow linewidth and frequency-stable probe laser source for the 88Sr+ single ion optical frequency standard,” Appl. Phys. B 95(1), 43–54 (2009).
[Crossref]

Bi, Z.

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(7486), 71–75 (2014).
[Crossref] [PubMed]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, “Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s,” Phys. Rev. Lett. 109(23), 230801 (2012).
[Crossref]

Bize, S.

Blatt, S.

Bloom, B. J.

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(7486), 71–75 (2014).
[Crossref] [PubMed]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, “Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s,” Phys. Rev. Lett. 109(23), 230801 (2012).
[Crossref]

Boyd, M. M.

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(7486), 71–75 (2014).
[Crossref] [PubMed]

Camp, J.

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93, 250602 (2004).
[Crossref]

Campbell, 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(7486), 71–75 (2014).
[Crossref] [PubMed]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, “Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s,” Phys. Rev. Lett. 109(23), 230801 (2012).
[Crossref]

Chen, H.

Chen, L.

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(10), 687–692 (2012).
[Crossref]

L. Chen, J. L. Hall, J. Ye, T. Yang, E. Zang, and T. Li, “Vibration-induced elastic deformation of Fabry-Perot cavities,” Phys. Rev. A 74(5), 053801 (2006).
[Crossref]

Cruz, F. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82(19), 3799–3802 (1999).
[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(7), 070801 (2007).
[Crossref] [PubMed]

Diddams, S. A.

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(7), 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(7), 070801 (2007).
[Crossref] [PubMed]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Drullinger, R. E.

Dube, P.

P. Dube, A. A. Madej, J. E. Bernard, L. Marmet, and A. D. Shiner, “A narrow linewidth and frequency-stable probe laser source for the 88Sr+ single ion optical frequency standard,” Appl. Phys. B 95(1), 43–54 (2009).
[Crossref]

Elman, V.

Falke, S.

Fang, S.

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Foreman, S. M.

A. D. Ludlow, X. Huang, M. Notcutt, T. Zanon-Willette, S. M. Foreman, M. M. Boyd, S. Blatt, and J. Ye, “Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1 × 10−15,” Opt. Lett. 32(6), 641–643 (2007).
[Crossref] [PubMed]

M. Notcutt, L. S. Ma, A. D. Ludlow, S. M. Foreman, J. Ye, and J. L. Hall, “Contribution of thermal noise to frequency stability of rigid optical cavity via hertz-linewidth lasers,” Phys. Rev. A 73, 031804(R) (2006).
[Crossref]

Fortier, T. M.

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(7), 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(7), 070801 (2007).
[Crossref] [PubMed]

Fox, R. W.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

Grebing, C.

C. Hagemann, C. Grebing, C. Lisdat, S. Falke, T. Legero, U. Sterr, F. Riehle, M. J. Martin, and J. Ye, “Ultrastable laser with average fractional frequency drift rate below 5 × 10−19/s,” Opt. Lett. 39(17), 5102–5105 (2014).
[Crossref] [PubMed]

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(10), 687–692 (2012).
[Crossref]

Hagemann, C.

C. Hagemann, C. Grebing, C. Lisdat, S. Falke, T. Legero, U. Sterr, F. Riehle, M. J. Martin, and J. Ye, “Ultrastable laser with average fractional frequency drift rate below 5 × 10−19/s,” Opt. Lett. 39(17), 5102–5105 (2014).
[Crossref] [PubMed]

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(10), 687–692 (2012).
[Crossref]

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L. Chen, J. L. Hall, J. Ye, T. Yang, E. Zang, and T. Li, “Vibration-induced elastic deformation of Fabry-Perot cavities,” Phys. Rev. A 74(5), 053801 (2006).
[Crossref]

M. Notcutt, L. S. Ma, A. D. Ludlow, S. M. Foreman, J. Ye, and J. L. Hall, “Contribution of thermal noise to frequency stability of rigid optical cavity via hertz-linewidth lasers,” Phys. Rev. A 73, 031804(R) (2006).
[Crossref]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
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Hansch, T. W.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hansch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Perot cavities,” Phys. Rev. A 77, 053809 (2008).
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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(7), 070801 (2007).
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Hinkley, N.

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(6151), 1215–1218 (2013).
[Crossref] [PubMed]

Hollberg, L.

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(7), 070801 (2007).
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J. G. Knudsen, H. C. Hottel, A. F. Sarofim, P. C. Wankat, and K. S. Knaebel, “Heat and mass transfer,” in Perry’s Chemical Engineers’ Handbook, R. H. Perry and D. W. Green, eds. 8th ed. (Academic, 2007), pp. 25–32.

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
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Huang, X.

Itano, W. M.

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(7), 070801 (2007).
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B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82(19), 3799–3802 (1999).
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Jefferts, S. R.

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(7), 070801 (2007).
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Jiang, Y.

H. Chen, Y. Jiang, S. Fang, Z. Bi, and L. Ma, “Frequency stabilization of Nd:YAG lasers with a most probable linewidth of 0.6 Hz,” J. Opt. Soc. Am. B 30(6), 1546–1550 (2013).
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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(7), 425–429 (2011).
[Crossref]

Jiang, Y. Y.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
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Kemery, A.

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93, 250602 (2004).
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Kessler, T.

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(10), 687–692 (2012).
[Crossref]

Kim, K.

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(7), 070801 (2007).
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Kirchner, M. S.

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(7), 425–429 (2011).
[Crossref]

Knaebel, K. S.

J. G. Knudsen, H. C. Hottel, A. F. Sarofim, P. C. Wankat, and K. S. Knaebel, “Heat and mass transfer,” in Perry’s Chemical Engineers’ Handbook, R. H. Perry and D. W. Green, eds. 8th ed. (Academic, 2007), pp. 25–32.

Knudsen, J. G.

J. G. Knudsen, H. C. Hottel, A. F. Sarofim, P. C. Wankat, and K. S. Knaebel, “Heat and mass transfer,” in Perry’s Chemical Engineers’ Handbook, R. H. Perry and D. W. Green, eds. 8th ed. (Academic, 2007), pp. 25–32.

Kolachevsky, N.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hansch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Perot cavities,” Phys. Rev. A 77, 053809 (2008).
[Crossref]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Le Goff, R.

Legero, T.

C. Hagemann, C. Grebing, C. Lisdat, S. Falke, T. Legero, U. Sterr, F. Riehle, M. J. Martin, and J. Ye, “Ultrastable laser with average fractional frequency drift rate below 5 × 10−19/s,” Opt. Lett. 39(17), 5102–5105 (2014).
[Crossref] [PubMed]

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(10), 687–692 (2012).
[Crossref]

Leibrandt, D. R.

Lemke, N.

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(7), 425–429 (2011).
[Crossref]

Lemke, N. D.

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(6151), 1215–1218 (2013).
[Crossref] [PubMed]

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

Lemonde, P.

Leveque, T.

Levi, F.

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(7), 070801 (2007).
[Crossref] [PubMed]

Li, T.

L. Chen, J. L. Hall, J. Ye, T. Yang, E. Zang, and T. Li, “Vibration-induced elastic deformation of Fabry-Perot cavities,” Phys. Rev. A 74(5), 053801 (2006).
[Crossref]

Lisdat, C.

Liu, T.

Lorini, L.

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(7), 070801 (2007).
[Crossref] [PubMed]

Lu, Z. H.

Ludlow, A.

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(7), 425–429 (2011).
[Crossref]

Ludlow, A. D.

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(6151), 1215–1218 (2013).
[Crossref] [PubMed]

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

A. D. Ludlow, X. Huang, M. Notcutt, T. Zanon-Willette, S. M. Foreman, M. M. Boyd, S. Blatt, and J. Ye, “Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1 × 10−15,” Opt. Lett. 32(6), 641–643 (2007).
[Crossref] [PubMed]

M. Notcutt, L. S. Ma, A. D. Ludlow, S. M. Foreman, J. Ye, and J. L. Hall, “Contribution of thermal noise to frequency stability of rigid optical cavity via hertz-linewidth lasers,” Phys. Rev. A 73, 031804(R) (2006).
[Crossref]

Ma, L.

Ma, L. S.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

M. Notcutt, L. S. Ma, A. D. Ludlow, S. M. Foreman, J. Ye, and J. L. Hall, “Contribution of thermal noise to frequency stability of rigid optical cavity via hertz-linewidth lasers,” Phys. Rev. A 73, 031804(R) (2006).
[Crossref]

Madej, A. A.

P. Dube, A. A. Madej, J. E. Bernard, L. Marmet, and A. D. Shiner, “A narrow linewidth and frequency-stable probe laser source for the 88Sr+ single ion optical frequency standard,” Appl. Phys. B 95(1), 43–54 (2009).
[Crossref]

Marmet, L.

P. Dube, A. A. Madej, J. E. Bernard, L. Marmet, and A. D. Shiner, “A narrow linewidth and frequency-stable probe laser source for the 88Sr+ single ion optical frequency standard,” Appl. Phys. B 95(1), 43–54 (2009).
[Crossref]

Martin, M. J.

C. Hagemann, C. Grebing, C. Lisdat, S. Falke, T. Legero, U. Sterr, F. Riehle, M. J. Martin, and J. Ye, “Ultrastable laser with average fractional frequency drift rate below 5 × 10−19/s,” Opt. Lett. 39(17), 5102–5105 (2014).
[Crossref] [PubMed]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, “Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s,” Phys. Rev. Lett. 109(23), 230801 (2012).
[Crossref]

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(10), 687–692 (2012).
[Crossref]

Matveev, A.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hansch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Perot cavities,” Phys. Rev. A 77, 053809 (2008).
[Crossref]

Mensing, F.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Nicholson, T. 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(7486), 71–75 (2014).
[Crossref] [PubMed]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, “Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s,” Phys. Rev. Lett. 109(23), 230801 (2012).
[Crossref]

Notcutt, M.

Numata, K.

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93, 250602 (2004).
[Crossref]

Oates, C. W.

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(6151), 1215–1218 (2013).
[Crossref] [PubMed]

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(7), 425–429 (2011).
[Crossref]

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

Oskay, W. H.

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(7), 070801 (2007).
[Crossref] [PubMed]

Parker, T. E.

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(7), 070801 (2007).
[Crossref] [PubMed]

Phillips, N. B.

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(6151), 1215–1218 (2013).
[Crossref] [PubMed]

Pizzocaro, M.

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(6151), 1215–1218 (2013).
[Crossref] [PubMed]

Prevost, E.

Quinlan, F.

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(7), 425–429 (2011).
[Crossref]

Riehle, F.

C. Hagemann, C. Grebing, C. Lisdat, S. Falke, T. Legero, U. Sterr, F. Riehle, M. J. Martin, and J. Ye, “Ultrastable laser with average fractional frequency drift rate below 5 × 10−19/s,” Opt. Lett. 39(17), 5102–5105 (2014).
[Crossref] [PubMed]

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(10), 687–692 (2012).
[Crossref]

Rosenband, T.

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(7), 425–429 (2011).
[Crossref]

D. R. Leibrandt, M. J. Thorpe, M. Notcutt, R. E. Drullinger, T. Rosenband, and J. C. Bergquist, “Spherical reference cavities for frequency stabilization of lasers in non-laboratory environments,” Opt. Express 19(4), 3471–3482 (2011).
[Crossref] [PubMed]

Santarelli, G.

Sarofim, A. F.

J. G. Knudsen, H. C. Hottel, A. F. Sarofim, P. C. Wankat, and K. S. Knaebel, “Heat and mass transfer,” in Perry’s Chemical Engineers’ Handbook, R. H. Perry and D. W. Green, eds. 8th ed. (Academic, 2007), pp. 25–32.

Schioppo, M.

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(6151), 1215–1218 (2013).
[Crossref] [PubMed]

Sherman, J. A.

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(6151), 1215–1218 (2013).
[Crossref] [PubMed]

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

Shiner, A. D.

P. Dube, A. A. Madej, J. E. Bernard, L. Marmet, and A. D. Shiner, “A narrow linewidth and frequency-stable probe laser source for the 88Sr+ single ion optical frequency standard,” Appl. Phys. B 95(1), 43–54 (2009).
[Crossref]

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(7), 070801 (2007).
[Crossref] [PubMed]

Stalnaker, J. E.

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(7), 070801 (2007).
[Crossref] [PubMed]

Stejskal, A.

Sterr, U.

Stoehr, H.

Swallows, M. D.

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, “Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s,” Phys. Rev. Lett. 109(23), 230801 (2012).
[Crossref]

Taylor, J.

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(7), 425–429 (2011).
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Thorpe, M. J.

Turyshev, S. G.

S. G. Turyshev, “Experimental tests of general relativity: recent progress and future directions,” Phys. Uspekhi 52(1), 1–27 (2009).
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Udem, Th.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hansch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Perot cavities,” Phys. Rev. A 77, 053809 (2008).
[Crossref]

Wang, L. J.

Wankat, P. C.

J. G. Knudsen, H. C. Hottel, A. F. Sarofim, P. C. Wankat, and K. S. Knaebel, “Heat and mass transfer,” in Perry’s Chemical Engineers’ Handbook, R. H. Perry and D. W. Green, eds. 8th ed. (Academic, 2007), pp. 25–32.

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Williams, J. R.

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(7486), 71–75 (2014).
[Crossref] [PubMed]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, “Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s,” Phys. Rev. Lett. 109(23), 230801 (2012).
[Crossref]

Yang, T.

L. Chen, J. L. Hall, J. Ye, T. Yang, E. Zang, and T. Li, “Vibration-induced elastic deformation of Fabry-Perot cavities,” Phys. Rev. A 74(5), 053801 (2006).
[Crossref]

Ye, J.

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(7486), 71–75 (2014).
[Crossref] [PubMed]

C. Hagemann, C. Grebing, C. Lisdat, S. Falke, T. Legero, U. Sterr, F. Riehle, M. J. Martin, and J. Ye, “Ultrastable laser with average fractional frequency drift rate below 5 × 10−19/s,” Opt. Lett. 39(17), 5102–5105 (2014).
[Crossref] [PubMed]

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(10), 687–692 (2012).
[Crossref]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, “Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s,” Phys. Rev. Lett. 109(23), 230801 (2012).
[Crossref]

A. D. Ludlow, X. Huang, M. Notcutt, T. Zanon-Willette, S. M. Foreman, M. M. Boyd, S. Blatt, and J. Ye, “Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1 × 10−15,” Opt. Lett. 32(6), 641–643 (2007).
[Crossref] [PubMed]

L. Chen, J. L. Hall, J. Ye, T. Yang, E. Zang, and T. Li, “Vibration-induced elastic deformation of Fabry-Perot cavities,” Phys. Rev. A 74(5), 053801 (2006).
[Crossref]

M. Notcutt, L. S. Ma, A. D. Ludlow, S. M. Foreman, J. Ye, and J. L. Hall, “Contribution of thermal noise to frequency stability of rigid optical cavity via hertz-linewidth lasers,” Phys. Rev. A 73, 031804(R) (2006).
[Crossref]

Young, B. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82(19), 3799–3802 (1999).
[Crossref]

Zang, E.

L. Chen, J. L. Hall, J. Ye, T. Yang, E. Zang, and T. Li, “Vibration-induced elastic deformation of Fabry-Perot cavities,” Phys. Rev. A 74(5), 053801 (2006).
[Crossref]

Zanon-Willette, T.

Zhang, J.

Zhang, W.

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(7486), 71–75 (2014).
[Crossref] [PubMed]

Zhang, X.

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(7486), 71–75 (2014).
[Crossref] [PubMed]

Zhao, Y. N.

Appl. Phys. B (2)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

P. Dube, A. A. Madej, J. E. Bernard, L. Marmet, and A. D. Shiner, “A narrow linewidth and frequency-stable probe laser source for the 88Sr+ single ion optical frequency standard,” Appl. Phys. B 95(1), 43–54 (2009).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Photonics (3)

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

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(10), 687–692 (2012).
[Crossref]

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(7), 425–429 (2011).
[Crossref]

Nature (1)

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(7486), 71–75 (2014).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. A (3)

M. Notcutt, L. S. Ma, A. D. Ludlow, S. M. Foreman, J. Ye, and J. L. Hall, “Contribution of thermal noise to frequency stability of rigid optical cavity via hertz-linewidth lasers,” Phys. Rev. A 73, 031804(R) (2006).
[Crossref]

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hansch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Perot cavities,” Phys. Rev. A 77, 053809 (2008).
[Crossref]

L. Chen, J. L. Hall, J. Ye, T. Yang, E. Zang, and T. Li, “Vibration-induced elastic deformation of Fabry-Perot cavities,” Phys. Rev. A 74(5), 053801 (2006).
[Crossref]

Phys. Rev. Lett. (4)

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82(19), 3799–3802 (1999).
[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(7), 070801 (2007).
[Crossref] [PubMed]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, “Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s,” Phys. Rev. Lett. 109(23), 230801 (2012).
[Crossref]

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93, 250602 (2004).
[Crossref]

Phys. Uspekhi (1)

S. G. Turyshev, “Experimental tests of general relativity: recent progress and future directions,” Phys. Uspekhi 52(1), 1–27 (2009).
[Crossref]

Rev. Mod. Phys. (2)

J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78(4), 1279–1295 (2006).
[Crossref]

T. W. Hansch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78(4), 1297–1309 (2006).
[Crossref]

Science (1)

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(6151), 1215–1218 (2013).
[Crossref] [PubMed]

Other (2)

“Table of total emissivity,” www.omega.com/temperature/Z/pdf/z088-089.pdf .

J. G. Knudsen, H. C. Hottel, A. F. Sarofim, P. C. Wankat, and K. S. Knaebel, “Heat and mass transfer,” in Perry’s Chemical Engineers’ Handbook, R. H. Perry and D. W. Green, eds. 8th ed. (Academic, 2007), pp. 25–32.

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Figures (5)

Fig. 1
Fig. 1 Thermal conduction. (a) One-layer thermal conduction. (b) Two-layer thermal conduction. (c) The temperature variation of different layers over time when the temperature of M1 changes from Ti = 300 K to Tf = 350 K at t = 0.
Fig. 2
Fig. 2 Thermal radiation. (a) One-layer thermal radiation. (b) Two-layer thermal radiation. (c) The temperature change of different layers over time when the temperature of P1 changes from Ti = 300 K to Tf = 310 K at t = 0.
Fig. 3
Fig. 3 Thermal sensitivity. (a) The temperature change of M2 when the temperature of M1 fluctuates as T 1 ( t ) = 300 + 10 sin [ 2 π t 5 × 10 5 ]. (b) The sensitivity of thermal conduction as a function of temperature fluctuation period. S (S2) is the sensitivity of one (two)-layer thermal conduction. (c) The sensitivity of thermal radiation as a function of temperature fluctuation period. S (S2) is the sensitivity of one (two)-layer thermal radiation.
Fig. 4
Fig. 4 The simulation model. The outer layer is a vacuum chamber made of aluminum, while the most inner layer is a reference cavity made of ULE glass. There are three layers of thermal shields inserted between the vacuum chamber and the reference cavity, labeled as A, B and C. All are in the shape of cylinder.
Fig. 5
Fig. 5 The simulation results of temperature change for the reference cavity over time when the temperature of outer vacuum chamber is changed from 25 °C to 30 °C if (a) the material of one-layer thermal shield varies and (b) the layer number of thermal shields varies. (c) The simulated and calculated thermal sensitivity of a reference cavity to outer temperature fluctuation when it is enclosed in zero to two layers thermal shields. (d) The simulated time constant of a reference cavity when the aperture size of the three-layer thermal shield varies.

Tables (3)

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Table 1 Parameters of materials.

Tables Icon

Table 2 The thermal time constants when the material of thermal shield varies.

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Table 3 Estimation of temperature fluctuation-induced fractional length instability based on outer temperature variation rate, the CTE and the sensitivity of a reference cavity.

Equations (18)

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d Q d t = k 1 A 1 L 1 ( T f T 2 ) ,
d T 2 = d Q C 2 m 2 .
T 2 ( t ) = T f Δ T 1 · e k 1 A 1 C 2 m 2 L 1 t = T f Δ T 1 · e t τ c 1 .
d T 4 d t = k 3 A 3 C 4 m 4 L 3 ( T f Δ T 1 e t τ c 1 T 4 ) .
T 4 ( t ) = T f Δ T 1 τ c 1 τ c 2 ( τ c 2 e t τ c 1 τ c 2 e t τ c 2 ) ,
d Q d t = σ ( T f 4 T 2 4 ) 1 A 1 ( 1 ε 1 1 ) + 1 A 2 1 ε 2 ,
d T 2 d t = σ ( T f 4 T 2 4 ) C 2 m 2 [ 1 A 1 ( 1 ε 1 1 ) + 1 A 2 1 ε 2 ] = β 12 ( T f 4 T 2 4 ) .
T 2 ( t ) T f Δ T 1 e 4 β 12 T f 3 t = T f Δ T 1 e t τ r 1 ,
d T 3 d t = β 23 [ ( T f Δ T 1 e t τ r 1 ) 4 T 3 4 ] ,
T 3 ( t ) T f Δ T 1 τ r 1 τ r 2 [ τ r 1 e t τ r 1 τ r 2 e t τ r 2 ] ,
d T 2 d t = 1 τ c 1 [ T ¯ + Δ T 1 sin ( 2 π t ξ ) T 2 ] .
T 2 ( t ) = T ¯ + ξ ξ 2 + 4 π 2 τ c 1 2 Δ T 1 sin ( 2 π t ξ ϕ ) + 2 π ξ τ c 1 ξ 2 + 4 π 2 τ c 1 2 Δ T 1 e t τ c 1 .
S = Δ T 2 Δ T 1 = ξ ξ 2 + 4 π 2 τ c 1 2 .
S n = i = 1 n ξ ξ 2 + 4 π 2 τ c i 2 .
d T 2 d t = β 12 [ ( T ¯ + Δ T 1 sin ( 2 π t ξ ) ) 4 T 2 4 ] .
T 2 ( t ) T ¯ + ξ ξ 2 + 4 π 2 τ r 1 2 Δ T 1 sin ( 2 π t ξ ψ ) + 2 π ξ τ r 1 ξ 2 + 4 π 2 τ r 1 2 Δ T 1 e t τ r 1 ,
S = ξ ξ 2 + 4 π 2 τ r 1 2 .
S n = i = 1 n ξ ξ 2 + 4 π 2 τ r i 2 .

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