Abstract

We demonstrate a method to measure and actively reduce the coupling of vibrations to the phase noise of a cavity-stabilized laser. This method uses the vibration noise of the laboratory environment rather than active drive to perturb the optical cavity. The laser phase noise is measured via a beat note with a second unperturbed ultra-stable laser while the vibrations are measured by accelerometers positioned around the cavity. A Wiener filter algorithm extracts the frequency and direction dependence of the cavity response function. Once the cavity response function is known, real-time noise cancellation can be implemented by use of the accelerometer measurements to predict and then cancel the laser phase fluctuations. We present real-time noise cancellation that results in a 25 dB reduction of the laser phase noise power spectral density.

© 2010 Optical Society of America

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  1. B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, "Visible Lasers with Subhertz Linewidths," Phys. Rev. Lett. 82, 3799-3802 (1999).
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    [CrossRef]
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    [CrossRef]
  4. M. Notcutt, L. S. Ma, J. Ye, and J. L. Hall, "Simple and compact 1-Hz laser system via an improved mounting configuration of a reference cavity," Opt. Lett. 30, 1815-1817 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  8. T. Nazarova, F. Riehle, and U. Sterr, "Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser," Appl. Phys. B 83, 531-536 (2006).
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2010 (1)

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, "Frequency Comparison of Two High-Accuracy Al+ Optical Clocks," Phys. Rev. Lett. 104, 070802 (2010).
[CrossRef] [PubMed]

2008 (4)

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

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," Science 28, 1808-1812 (2008).
[CrossRef]

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

A. Hati, C. W. Nelson, J. Taylor, N. Ashby, and D. A. Howe, "Cancellation of Vibration-Induced Phase Noise in Optical Fibers," IEEE Photon. Technol. Lett. 20, 1842-1844 (2008).
[CrossRef]

2006 (3)

T. M. Fortier, A. Bartels, and S. A. Diddams, "Octave-spanning Ti:sapphire laser with a repetition rate >1 GHz for optical frequency measurements and comparisons," Opt. Lett. 31, 1011-1013 (2006).
[CrossRef] [PubMed]

Z. W. Barber, C. W. Hoyt, C. W. Oates, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, "Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice," Phys. Rev. Lett. 96, 083002 (2006).
[CrossRef] [PubMed]

T. Nazarova, F. Riehle, and U. Sterr, "Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser," Appl. Phys. B 83, 531-536 (2006).
[CrossRef]

2005 (1)

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, 3799-3802 (1999).
[CrossRef]

1994 (1)

1983 (1)

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

1959 (1)

J. Volder, "The CORDIC Trigonometric Computing Technique," IRE Trans. Electron. Comput. EC-8, 330-334 (1959).
[CrossRef]

Ashby, N.

A. Hati, C. W. Nelson, J. Taylor, N. Ashby, and D. A. Howe, "Cancellation of Vibration-Induced Phase Noise in Optical Fibers," IEEE Photon. Technol. Lett. 20, 1842-1844 (2008).
[CrossRef]

Barber, Z. W.

Z. W. Barber, C. W. Hoyt, C. W. Oates, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, "Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice," Phys. Rev. Lett. 96, 083002 (2006).
[CrossRef] [PubMed]

Bartels, A.

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," Science 28, 1808-1812 (2008).
[CrossRef]

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, "Visible Lasers with Subhertz Linewidths," Phys. Rev. Lett. 82, 3799-3802 (1999).
[CrossRef]

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," Science 28, 1808-1812 (2008).
[CrossRef]

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]

Chou, C. W.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, "Frequency Comparison of Two High-Accuracy Al+ Optical Clocks," Phys. Rev. Lett. 104, 070802 (2010).
[CrossRef] [PubMed]

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," Science 28, 1808-1812 (2008).
[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, 3799-3802 (1999).
[CrossRef]

Danzmann, K.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[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," Science 28, 1808-1812 (2008).
[CrossRef]

T. M. Fortier, A. Bartels, and S. A. Diddams, "Octave-spanning Ti:sapphire laser with a repetition rate >1 GHz for optical frequency measurements and comparisons," Opt. Lett. 31, 1011-1013 (2006).
[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, 97-105 (1983).
[CrossRef]

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," Science 28, 1808-1812 (2008).
[CrossRef]

Ford, G. M.

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

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," Science 28, 1808-1812 (2008).
[CrossRef]

T. M. Fortier, A. Bartels, and S. A. Diddams, "Octave-spanning Ti:sapphire laser with a repetition rate >1 GHz for optical frequency measurements and comparisons," Opt. Lett. 31, 1011-1013 (2006).
[CrossRef] [PubMed]

Frede, M.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

Gill, P.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Hall, J. L.

Hati, A.

A. Hati, C. W. Nelson, J. Taylor, N. Ashby, and D. A. Howe, "Cancellation of Vibration-Induced Phase Noise in Optical Fibers," IEEE Photon. Technol. Lett. 20, 1842-1844 (2008).
[CrossRef]

Hollberg, L.

Z. W. Barber, C. W. Hoyt, C. W. Oates, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, "Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice," Phys. Rev. Lett. 96, 083002 (2006).
[CrossRef] [PubMed]

Hough, J.

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

Howe, D. A.

A. Hati, C. W. Nelson, J. Taylor, N. Ashby, and D. A. Howe, "Cancellation of Vibration-Induced Phase Noise in Optical Fibers," IEEE Photon. Technol. Lett. 20, 1842-1844 (2008).
[CrossRef]

Hoyt, C. W.

Z. W. Barber, C. W. Hoyt, C. W. Oates, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, "Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice," Phys. Rev. Lett. 96, 083002 (2006).
[CrossRef] [PubMed]

Hume, D. B.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, "Frequency Comparison of Two High-Accuracy Al+ Optical Clocks," Phys. Rev. Lett. 104, 070802 (2010).
[CrossRef] [PubMed]

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," Science 28, 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," Science 28, 1808-1812 (2008).
[CrossRef]

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, "Visible Lasers with Subhertz Linewidths," Phys. Rev. Lett. 82, 3799-3802 (1999).
[CrossRef]

Junger, P.

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).
[CrossRef]

King, P.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

Koelemeij, J. C. J.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, "Frequency Comparison of Two High-Accuracy Al+ Optical Clocks," Phys. Rev. Lett. 104, 070802 (2010).
[CrossRef] [PubMed]

Kowalski, F. V.

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

Kracht, D.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

Kwee, P.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (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," Science 28, 1808-1812 (2008).
[CrossRef]

Ma, L. S.

Millo, J.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Munley, A. J.

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

Nazarova, T.

T. Nazarova, F. Riehle, and U. Sterr, "Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser," Appl. Phys. B 83, 531-536 (2006).
[CrossRef]

Nelson, C. W.

A. Hati, C. W. Nelson, J. Taylor, N. Ashby, and D. A. Howe, "Cancellation of Vibration-Induced Phase Noise in Optical Fibers," IEEE Photon. Technol. Lett. 20, 1842-1844 (2008).
[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," Science 28, 1808-1812 (2008).
[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.

Z. W. Barber, C. W. Hoyt, C. W. Oates, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, "Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice," Phys. Rev. Lett. 96, 083002 (2006).
[CrossRef] [PubMed]

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," Science 28, 1808-1812 (2008).
[CrossRef]

Oxborrow, M.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Pugla, S.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Puncken, O.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

Riehle, F.

T. Nazarova, F. Riehle, and U. Sterr, "Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser," Appl. Phys. B 83, 531-536 (2006).
[CrossRef]

Rosenband, T.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, "Frequency Comparison of Two High-Accuracy Al+ Optical Clocks," Phys. Rev. Lett. 104, 070802 (2010).
[CrossRef] [PubMed]

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," Science 28, 1808-1812 (2008).
[CrossRef]

Savage, R. L.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

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," Science 28, 1808-1812 (2008).
[CrossRef]

Schulz, B.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

Seifert, F.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

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," Science 28, 1808-1812 (2008).
[CrossRef]

Sterr, U.

T. Nazarova, F. Riehle, and U. Sterr, "Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser," Appl. Phys. B 83, 531-536 (2006).
[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," Science 28, 1808-1812 (2008).
[CrossRef]

Taichenachev, A. V.

Z. W. Barber, C. W. Hoyt, C. W. Oates, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, "Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice," Phys. Rev. Lett. 96, 083002 (2006).
[CrossRef] [PubMed]

Taylor, J.

A. Hati, C. W. Nelson, J. Taylor, N. Ashby, and D. A. Howe, "Cancellation of Vibration-Induced Phase Noise in Optical Fibers," IEEE Photon. Technol. Lett. 20, 1842-1844 (2008).
[CrossRef]

Veltkamp, C.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

Volder, J.

J. Volder, "The CORDIC Trigonometric Computing Technique," IRE Trans. Electron. Comput. EC-8, 330-334 (1959).
[CrossRef]

Wagner, S.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

Ward, H.

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

Webster, S. A.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Weßels, P.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

Willke, B.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

Wineland, D. J.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, "Frequency Comparison of Two High-Accuracy Al+ Optical Clocks," Phys. Rev. Lett. 104, 070802 (2010).
[CrossRef] [PubMed]

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," Science 28, 1808-1812 (2008).
[CrossRef]

Winkelmann, L.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

Ye, J.

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, 3799-3802 (1999).
[CrossRef]

Yudin, V. I.

Z. W. Barber, C. W. Hoyt, C. W. Oates, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, "Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice," Phys. Rev. Lett. 96, 083002 (2006).
[CrossRef] [PubMed]

Appl. Phys. B (2)

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

T. Nazarova, F. Riehle, and U. Sterr, "Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser," Appl. Phys. B 83, 531-536 (2006).
[CrossRef]

Class. Quantum Gravity (1)

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, "Stabilized lasers for advanced gravitational wave detectors," Class. Quantum Gravity 25, 114040 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Hati, C. W. Nelson, J. Taylor, N. Ashby, and D. A. Howe, "Cancellation of Vibration-Induced Phase Noise in Optical Fibers," IEEE Photon. Technol. Lett. 20, 1842-1844 (2008).
[CrossRef]

IRE Trans. Electron. Comput. (1)

J. Volder, "The CORDIC Trigonometric Computing Technique," IRE Trans. Electron. Comput. EC-8, 330-334 (1959).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Phys. Rev. Lett. (4)

Z. W. Barber, C. W. Hoyt, C. W. Oates, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, "Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice," Phys. Rev. Lett. 96, 083002 (2006).
[CrossRef] [PubMed]

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, "Frequency Comparison of Two High-Accuracy Al+ Optical Clocks," Phys. Rev. Lett. 104, 070802 (2010).
[CrossRef] [PubMed]

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]

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, "Visible Lasers with Subhertz Linewidths," Phys. Rev. Lett. 82, 3799-3802 (1999).
[CrossRef]

Science (1)

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," Science 28, 1808-1812 (2008).
[CrossRef]

Other (6)

J. Millo, S. Dawkins, R. Chicireanu, D. V. Magalhaes, C. Mandache, D. Holleville, M. Lours, S. Bize, P. Lemonde, and G. Santarelli, "Ultra-stable optical cavities: Design and experiments at LNE-SYRTE," Proc. IEEE Freq. Control Symp.(IEEE, 2008), pp. 110-114.
[CrossRef]

S. Haykin, "The LMS filter algorithm," in Least-Mean-Square Adaptive Filters, S. Haykin and B. Widrow eds. (Wiley, 2003), pp. xi-xiii.

A. Hati, C. W. Nelson, D. A. Howe, N. Ashby, J. Taylor, K. M. Hudek, C. Hay, D. Seidel, and D. Eliyahu, "Vibration sensitivity of microwave components," Proc. 2007 Joint Mtg. IEEE Int. Freq. Control Symp. and EFTF Conf. (IEEE, 2007), pp. 541-546.

N. Wiener, "Extrapolation, Interpolation, and Smoothing of Stationary Time Series," (The MIT Press, 1949).

J. C. Bergquist, W. M. Itano, and D. J. Wineland, "Laser Stabilization to a Single Ion," in Frontiers in Laser Spectroscopy, proc. International School of Physics "Enrico Fermi", T. W. Hänsch and M. Inguscio eds. (North-Holland, Amsterdam, 2004), pp. 359-376.

D. L. Jones, "Discrete-Time, Causal Wiener Filter," http://cnx.org/content/m11825/latest/.

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Figures (4)

Fig. 1.
Fig. 1.

The setup used to measure the cavity response functions and perform real-time noise cancellation. Six accelerometers (labeled 1-6) are positioned on the table such that (1,3,5) measure accelerations in the vertical (z) direction while (2,4,6) measure accelerations in the horizontal (x,y) plane. This combination of signals allows the measurement of all six motional degrees of freedom. The test light is transmitted to the frequency comb through a noise-cancelled optical fiber [14,15], and the heterodyne beat note (mixed to approximately 4 MHz) measured at the frequency comb returns through a coaxial cable.

Fig. 2.
Fig. 2.

(a) The time domain performance of the Wiener filter algorithm. The measured laser phase (blue), predicted phase (green) and residual error (black) show that the Wiener filter reduces the RMS phase fluctuations by more than an order of magnitude. The inset on the lower left shows the first 0.5 seconds of the time trace. Here, the error is initially large due to the lack of accelerometer information for times t < 0 s. By t = 0.2 s there is a sufficient history of accelerometer measurements to substantially reduce the phase error. The inset on the lower right shows the Wiener filter suppressing the RMS phase fluctuations of the laser by more than a factor of 10. (b) The phase noise power spectral density (PSD) of the measured phase, predicted phase and residual phase error showing more than 30 dB of noise cancellation at 12 Hz. The dashed traces show the velocity PSD measured by the accelerometers.

Fig. 3.
Fig. 3.

(a) The fractional sensitivity of the cavity reference frequency to accelerations for the three translational (x,y,z) degrees of freedom in the 5–30 Hz spectral region. Three independent measurements were performed for each direction (markers) and the solid lines show the average values. (b) The measured SNR of the phase and acceleration measurements show that outside of the 5–30 Hz region, there is insufficient SNR to calculate the cavity acceleration sensitivity.

Fig. 4.
Fig. 4.

(a) The laser phase PSD for three operating conditions: (1) the cavity table resting on the floor with the filter turned off (blue), (2) the cavity table resting on the floor with the filter turned on (green), and (3) the cavity table suspended by vibration isolating rubber bands (black). A real-time noise cancellation of 25 dB is achieved at 12 Hz compared to the free running case, but still several dB more than the vibration isolated case. The direction-averaged velocity PSD shows the effect of the rubber band suspension system in isolating the cavity from laboratory vibration noise. (b) The Allan deviation for the test laser in the three cases shown in (a). Without the LMS filter, the laser frequency instability increases by more than an order of magnitude at τ = 0.1 s and by a factor of 4 at τ = 1 s compared to the vibration isolated case (black). When the LMS filter is on, the test laser instability is within a factor of 2 compared to the vibration-isolated case for all time-scales. The points above and below each Allan deviation curve show the 90% confidence interval for the measurement.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ϕ ̂ [ n ] = m = 1 6 k = 0 N 1 h m , k a m [ n k ] .
e 2 = n = ( ϕ [ n ] ϕ ̂ [ n ] ) 2 ,
n = ϕ [ n ] a i [ n j ] = n = m = 1 6 k = 0 N 1 h m , k a m [ n k ] a j [ n i ] ,
R ϕ , a i [ j ] = m = 1 6 k = 0 N 1 h m , k R a i , a m [ j k ] ,
ϕ ( ω ) = m = 1 6 H m ( ω ) a m ( ω ) .
e [ n ] 2 h i , j = 2 e [ n ] a i ( n j ) = 0 ,
h i , j n + 1 = h i , j n μ e [ n ] 2 h i , j = h i , j n + 2 μe [ n ] a i ( n j ) .

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