Abstract

Homodyne detection relies on the beat between a relatively strong local oscillator (LO) field at the carrier frequency and a signal beam with sidebands centered around the carrier frequency. This type of signal detection, or signal readout, is widely used in quantum optics applications and is expected to be used in advanced interferometric gravitational wave detectors. We investigate experimentally the limitations to making such measurements in a laboratory environment at audio frequencies. We find that beam jitter noise, electronic noise of the photodetectors, and the LO intensity noise can limit the homodyne detection in this frequency band, and we discuss potential solutions.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, "Optimization and transfer of vacuum squeezing from an optical parametric oscillator," J. Opt. B 1, 469-474 (1999).
    [CrossRef]
  2. M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, "Optimal optical measurement of small displacements," J. Opt. B 6, 495-501 (2004).
    [CrossRef]
  3. A. Buonanno, Y. Chen, and N. Mavalvala, "Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme," Phys. Rev. D 67, 122005 (2003).
    [CrossRef]
  4. D. Shoemaker, "Ground-based interferometric gravitational-wave detectors in the LISA epoch," Class. Quantum Grav. 20, S11-S22 (2003).
    [CrossRef]
  5. H. Yuen and V. Chan, "Noise in homodyne and heterodyne detection," Opt. Lett. 8, 177-179 (1983).
    [CrossRef] [PubMed]
  6. Excess QN due to nonstationary shot noise can be avoided if the demodulation signal is the reciprocal waveform of the inverse of the modulation signal or can be reduced by using an approximation of the reciprocal . Because minimum QN heterodyne schemes are technically challenging, homodyne detection is usually chosen.
  7. B. J. Meers and K. A. Strain, "Modulation, signal, and quantum noise in interferometers," Phys. Rev. A 44, 4693-4703 (1991).
    [CrossRef] [PubMed]
  8. T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, "Nonstationary shot noise and its effect on the sensitivity of interferometers," Phys. Rev. A 43, 5022-5029 (1991).
    [CrossRef] [PubMed]
  9. M. B. Gray, A. J. Stevenson, H.-A. Bachor, and D. E. McClelland, "Harmonic demodulation of nonstationary shot noise," Opt. Lett. 18, 759 (1993).
    [CrossRef] [PubMed]
  10. K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, "Squeezing in the audio gravitational-wave detection band," Phys. Rev. Lett. 93, 161105 (2004).
    [CrossRef] [PubMed]
  11. K. McKenzie, M. B. Gray, S. Goßler, P. K. Lam, and D. E. McClelland, "Squeezed state generation for interferometric gravitational-wave detection," Class. Quantum Grav. 23, S245-S250 (2006).
    [CrossRef]
  12. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
    [CrossRef] [PubMed]
  13. It has been brought to our attention that scattered light noise may also limit homodyne detector sensitivity at low frequencies . We have not characterized this noise source experimentally.
  14. H. Vahlbruch, Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institute), Callinstrasse 38, 30167, Hannover, Germany (personal communication, 2006).
  15. A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, and K. Maischberger, "A mode selector to suppress fluctuations in laser beam geometry," Opt. Acta 28, 641-658 (1981).
    [CrossRef]
  16. 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]
  17. M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
    [CrossRef]
  18. B. Lantz, D. Shoemaker, and J. Kerman, "Spatial uniformity of silicon photodiodes," LIGO document T952007 (1999), http://www.ligo.caltech.edu/docs/T/T952014-00.pdf.
  19. P. Csatorday, A. Marin, and M. Zucker, "Photodiodes for Initial and Advanced LIGO," LIGO document (1998) G980022-00-D, http://www.ligo.caltech.edu/docs/G980022-00-D.
  20. L. G. Gouy, "Sur une propriété nouvelle des ondes lumineuses," C. R. Acad. Sci. Paris 110, 1251 (1890).
  21. This fit was normalized to maximum value of the experimental data.
  22. If the distances were not matched, the QPD might measure the beam when it has a Guoy phase different from that at the homodyne photodetectors and therefore might measure a different contribution of tilt and offset.
  23. Subtracting the electronic noise below 10 Hz may be misleading, since electronic noise becomes the dominant noise source here.

2006 (2)

K. McKenzie, M. B. Gray, S. Goßler, P. K. Lam, and D. E. McClelland, "Squeezed state generation for interferometric gravitational-wave detection," Class. Quantum Grav. 23, S245-S250 (2006).
[CrossRef]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

2004 (2)

K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, "Squeezing in the audio gravitational-wave detection band," Phys. Rev. Lett. 93, 161105 (2004).
[CrossRef] [PubMed]

M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, "Optimal optical measurement of small displacements," J. Opt. B 6, 495-501 (2004).
[CrossRef]

2003 (2)

A. Buonanno, Y. Chen, and N. Mavalvala, "Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme," Phys. Rev. D 67, 122005 (2003).
[CrossRef]

D. Shoemaker, "Ground-based interferometric gravitational-wave detectors in the LISA epoch," Class. Quantum Grav. 20, S11-S22 (2003).
[CrossRef]

1999 (1)

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, "Optimization and transfer of vacuum squeezing from an optical parametric oscillator," J. Opt. B 1, 469-474 (1999).
[CrossRef]

1998 (1)

M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

1993 (1)

M. B. Gray, A. J. Stevenson, H.-A. Bachor, and D. E. McClelland, "Harmonic demodulation of nonstationary shot noise," Opt. Lett. 18, 759 (1993).
[CrossRef] [PubMed]

1991 (2)

B. J. Meers and K. A. Strain, "Modulation, signal, and quantum noise in interferometers," Phys. Rev. A 44, 4693-4703 (1991).
[CrossRef] [PubMed]

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, "Nonstationary shot noise and its effect on the sensitivity of interferometers," Phys. Rev. A 43, 5022-5029 (1991).
[CrossRef] [PubMed]

1983 (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]

H. Yuen and V. Chan, "Noise in homodyne and heterodyne detection," Opt. Lett. 8, 177-179 (1983).
[CrossRef] [PubMed]

1981 (1)

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, and K. Maischberger, "A mode selector to suppress fluctuations in laser beam geometry," Opt. Acta 28, 641-658 (1981).
[CrossRef]

1890 (1)

L. G. Gouy, "Sur une propriété nouvelle des ondes lumineuses," C. R. Acad. Sci. Paris 110, 1251 (1890).

Bachor, H.-A.

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, "Optimization and transfer of vacuum squeezing from an optical parametric oscillator," J. Opt. B 1, 469-474 (1999).
[CrossRef]

M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

M. B. Gray, A. J. Stevenson, H.-A. Bachor, and D. E. McClelland, "Harmonic demodulation of nonstationary shot noise," Opt. Lett. 18, 759 (1993).
[CrossRef] [PubMed]

Billing, H.

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, and K. Maischberger, "A mode selector to suppress fluctuations in laser beam geometry," Opt. Acta 28, 641-658 (1981).
[CrossRef]

Bowen, W. P.

M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, "Optimal optical measurement of small displacements," J. Opt. B 6, 495-501 (2004).
[CrossRef]

K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, "Squeezing in the audio gravitational-wave detection band," Phys. Rev. Lett. 93, 161105 (2004).
[CrossRef] [PubMed]

Buchler, B. C.

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, "Optimization and transfer of vacuum squeezing from an optical parametric oscillator," J. Opt. B 1, 469-474 (1999).
[CrossRef]

Buonanno, A.

A. Buonanno, Y. Chen, and N. Mavalvala, "Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme," Phys. Rev. D 67, 122005 (2003).
[CrossRef]

Chan, V.

Chelkowski, S.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

Chen, Y.

A. Buonanno, Y. Chen, and N. Mavalvala, "Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme," Phys. Rev. D 67, 122005 (2003).
[CrossRef]

Csatorday, P.

P. Csatorday, A. Marin, and M. Zucker, "Photodiodes for Initial and Advanced LIGO," LIGO document (1998) G980022-00-D, http://www.ligo.caltech.edu/docs/G980022-00-D.

Danzmann, K.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, "Nonstationary shot noise and its effect on the sensitivity of interferometers," Phys. Rev. A 43, 5022-5029 (1991).
[CrossRef] [PubMed]

Delaubert, V.

M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, "Optimal optical measurement of small displacements," J. Opt. B 6, 495-501 (2004).
[CrossRef]

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]

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]

Franzen, A.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

Gao, J.

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, "Optimization and transfer of vacuum squeezing from an optical parametric oscillator," J. Opt. B 1, 469-474 (1999).
[CrossRef]

Goßler, S.

K. McKenzie, M. B. Gray, S. Goßler, P. K. Lam, and D. E. McClelland, "Squeezed state generation for interferometric gravitational-wave detection," Class. Quantum Grav. 23, S245-S250 (2006).
[CrossRef]

Gouy, L. G.

L. G. Gouy, "Sur une propriété nouvelle des ondes lumineuses," C. R. Acad. Sci. Paris 110, 1251 (1890).

Gray, M. B.

K. McKenzie, M. B. Gray, S. Goßler, P. K. Lam, and D. E. McClelland, "Squeezed state generation for interferometric gravitational-wave detection," Class. Quantum Grav. 23, S245-S250 (2006).
[CrossRef]

K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, "Squeezing in the audio gravitational-wave detection band," Phys. Rev. Lett. 93, 161105 (2004).
[CrossRef] [PubMed]

M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

M. B. Gray, A. J. Stevenson, H.-A. Bachor, and D. E. McClelland, "Harmonic demodulation of nonstationary shot noise," Opt. Lett. 18, 759 (1993).
[CrossRef] [PubMed]

Grosse, N.

K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, "Squeezing in the audio gravitational-wave detection band," Phys. Rev. Lett. 93, 161105 (2004).
[CrossRef] [PubMed]

Hage, B.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

Hall, J. L.

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]

Harb, C. C.

M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

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]

Hsu, M. T. L.

M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, "Optimal optical measurement of small displacements," J. Opt. B 6, 495-501 (2004).
[CrossRef]

Kerman, J.

B. Lantz, D. Shoemaker, and J. Kerman, "Spatial uniformity of silicon photodiodes," LIGO document T952007 (1999), http://www.ligo.caltech.edu/docs/T/T952014-00.pdf.

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]

Lam, P. K.

K. McKenzie, M. B. Gray, S. Goßler, P. K. Lam, and D. E. McClelland, "Squeezed state generation for interferometric gravitational-wave detection," Class. Quantum Grav. 23, S245-S250 (2006).
[CrossRef]

K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, "Squeezing in the audio gravitational-wave detection band," Phys. Rev. Lett. 93, 161105 (2004).
[CrossRef] [PubMed]

M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, "Optimal optical measurement of small displacements," J. Opt. B 6, 495-501 (2004).
[CrossRef]

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, "Optimization and transfer of vacuum squeezing from an optical parametric oscillator," J. Opt. B 1, 469-474 (1999).
[CrossRef]

Lantz, B.

B. Lantz, D. Shoemaker, and J. Kerman, "Spatial uniformity of silicon photodiodes," LIGO document T952007 (1999), http://www.ligo.caltech.edu/docs/T/T952014-00.pdf.

Maischberger, K.

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, and K. Maischberger, "A mode selector to suppress fluctuations in laser beam geometry," Opt. Acta 28, 641-658 (1981).
[CrossRef]

Marin, A.

P. Csatorday, A. Marin, and M. Zucker, "Photodiodes for Initial and Advanced LIGO," LIGO document (1998) G980022-00-D, http://www.ligo.caltech.edu/docs/G980022-00-D.

Mavalvala, N.

A. Buonanno, Y. Chen, and N. Mavalvala, "Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme," Phys. Rev. D 67, 122005 (2003).
[CrossRef]

McClelland, D. E.

K. McKenzie, M. B. Gray, S. Goßler, P. K. Lam, and D. E. McClelland, "Squeezed state generation for interferometric gravitational-wave detection," Class. Quantum Grav. 23, S245-S250 (2006).
[CrossRef]

K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, "Squeezing in the audio gravitational-wave detection band," Phys. Rev. Lett. 93, 161105 (2004).
[CrossRef] [PubMed]

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, "Optimization and transfer of vacuum squeezing from an optical parametric oscillator," J. Opt. B 1, 469-474 (1999).
[CrossRef]

M. B. Gray, A. J. Stevenson, H.-A. Bachor, and D. E. McClelland, "Harmonic demodulation of nonstationary shot noise," Opt. Lett. 18, 759 (1993).
[CrossRef] [PubMed]

McKenzie, K.

K. McKenzie, M. B. Gray, S. Goßler, P. K. Lam, and D. E. McClelland, "Squeezed state generation for interferometric gravitational-wave detection," Class. Quantum Grav. 23, S245-S250 (2006).
[CrossRef]

K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, "Squeezing in the audio gravitational-wave detection band," Phys. Rev. Lett. 93, 161105 (2004).
[CrossRef] [PubMed]

Meers, B. J.

B. J. Meers and K. A. Strain, "Modulation, signal, and quantum noise in interferometers," Phys. Rev. A 44, 4693-4703 (1991).
[CrossRef] [PubMed]

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]

Niebauer, T. M.

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, "Nonstationary shot noise and its effect on the sensitivity of interferometers," Phys. Rev. A 43, 5022-5029 (1991).
[CrossRef] [PubMed]

Ralph, T. C.

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, "Optimization and transfer of vacuum squeezing from an optical parametric oscillator," J. Opt. B 1, 469-474 (1999).
[CrossRef]

Rüdiger, A.

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, "Nonstationary shot noise and its effect on the sensitivity of interferometers," Phys. Rev. A 43, 5022-5029 (1991).
[CrossRef] [PubMed]

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, and K. Maischberger, "A mode selector to suppress fluctuations in laser beam geometry," Opt. Acta 28, 641-658 (1981).
[CrossRef]

Schilling, R.

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, "Nonstationary shot noise and its effect on the sensitivity of interferometers," Phys. Rev. A 43, 5022-5029 (1991).
[CrossRef] [PubMed]

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, and K. Maischberger, "A mode selector to suppress fluctuations in laser beam geometry," Opt. Acta 28, 641-658 (1981).
[CrossRef]

Schnabel, R.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

Schnupp, L.

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, and K. Maischberger, "A mode selector to suppress fluctuations in laser beam geometry," Opt. Acta 28, 641-658 (1981).
[CrossRef]

Shaddock, D. A.

M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

Shoemaker, D.

D. Shoemaker, "Ground-based interferometric gravitational-wave detectors in the LISA epoch," Class. Quantum Grav. 20, S11-S22 (2003).
[CrossRef]

B. Lantz, D. Shoemaker, and J. Kerman, "Spatial uniformity of silicon photodiodes," LIGO document T952007 (1999), http://www.ligo.caltech.edu/docs/T/T952014-00.pdf.

Stevenson, A. J.

M. B. Gray, A. J. Stevenson, H.-A. Bachor, and D. E. McClelland, "Harmonic demodulation of nonstationary shot noise," Opt. Lett. 18, 759 (1993).
[CrossRef] [PubMed]

Strain, K. A.

B. J. Meers and K. A. Strain, "Modulation, signal, and quantum noise in interferometers," Phys. Rev. A 44, 4693-4703 (1991).
[CrossRef] [PubMed]

Vahlbruch, H.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

H. Vahlbruch, Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institute), Callinstrasse 38, 30167, Hannover, Germany (personal communication, 2006).

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]

Whitcomb, S. E.

K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, "Squeezing in the audio gravitational-wave detection band," Phys. Rev. Lett. 93, 161105 (2004).
[CrossRef] [PubMed]

Winkler, W.

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, "Nonstationary shot noise and its effect on the sensitivity of interferometers," Phys. Rev. A 43, 5022-5029 (1991).
[CrossRef] [PubMed]

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, and K. Maischberger, "A mode selector to suppress fluctuations in laser beam geometry," Opt. Acta 28, 641-658 (1981).
[CrossRef]

Yuen, H.

Zucker, M.

P. Csatorday, A. Marin, and M. Zucker, "Photodiodes for Initial and Advanced LIGO," LIGO document (1998) G980022-00-D, http://www.ligo.caltech.edu/docs/G980022-00-D.

Appl. Phys. B (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]

C. R. Acad. Sci. Paris (1)

L. G. Gouy, "Sur une propriété nouvelle des ondes lumineuses," C. R. Acad. Sci. Paris 110, 1251 (1890).

Class. Quantum Grav. (2)

K. McKenzie, M. B. Gray, S. Goßler, P. K. Lam, and D. E. McClelland, "Squeezed state generation for interferometric gravitational-wave detection," Class. Quantum Grav. 23, S245-S250 (2006).
[CrossRef]

D. Shoemaker, "Ground-based interferometric gravitational-wave detectors in the LISA epoch," Class. Quantum Grav. 20, S11-S22 (2003).
[CrossRef]

J. Opt. B (2)

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, "Optimization and transfer of vacuum squeezing from an optical parametric oscillator," J. Opt. B 1, 469-474 (1999).
[CrossRef]

M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, "Optimal optical measurement of small displacements," J. Opt. B 6, 495-501 (2004).
[CrossRef]

Opt. Acta (1)

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, and K. Maischberger, "A mode selector to suppress fluctuations in laser beam geometry," Opt. Acta 28, 641-658 (1981).
[CrossRef]

Opt. Lett. (2)

H. Yuen and V. Chan, "Noise in homodyne and heterodyne detection," Opt. Lett. 8, 177-179 (1983).
[CrossRef] [PubMed]

M. B. Gray, A. J. Stevenson, H.-A. Bachor, and D. E. McClelland, "Harmonic demodulation of nonstationary shot noise," Opt. Lett. 18, 759 (1993).
[CrossRef] [PubMed]

Phys. Rev. A (2)

B. J. Meers and K. A. Strain, "Modulation, signal, and quantum noise in interferometers," Phys. Rev. A 44, 4693-4703 (1991).
[CrossRef] [PubMed]

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, "Nonstationary shot noise and its effect on the sensitivity of interferometers," Phys. Rev. A 43, 5022-5029 (1991).
[CrossRef] [PubMed]

Phys. Rev. D (1)

A. Buonanno, Y. Chen, and N. Mavalvala, "Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme," Phys. Rev. D 67, 122005 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, "Squeezing in the audio gravitational-wave detection band," Phys. Rev. Lett. 93, 161105 (2004).
[CrossRef] [PubMed]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

Other (8)

B. Lantz, D. Shoemaker, and J. Kerman, "Spatial uniformity of silicon photodiodes," LIGO document T952007 (1999), http://www.ligo.caltech.edu/docs/T/T952014-00.pdf.

P. Csatorday, A. Marin, and M. Zucker, "Photodiodes for Initial and Advanced LIGO," LIGO document (1998) G980022-00-D, http://www.ligo.caltech.edu/docs/G980022-00-D.

This fit was normalized to maximum value of the experimental data.

If the distances were not matched, the QPD might measure the beam when it has a Guoy phase different from that at the homodyne photodetectors and therefore might measure a different contribution of tilt and offset.

Subtracting the electronic noise below 10 Hz may be misleading, since electronic noise becomes the dominant noise source here.

It has been brought to our attention that scattered light noise may also limit homodyne detector sensitivity at low frequencies . We have not characterized this noise source experimentally.

H. Vahlbruch, Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institute), Callinstrasse 38, 30167, Hannover, Germany (personal communication, 2006).

Excess QN due to nonstationary shot noise can be avoided if the demodulation signal is the reciprocal waveform of the inverse of the modulation signal or can be reduced by using an approximation of the reciprocal . Because minimum QN heterodyne schemes are technically challenging, homodyne detection is usually chosen.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

(Color online) Schematic of the experimental setup for the homodyne detection system. The laser field is passed though a phase modulator (PM), a broadband amplitude modulator (BBAM), and a mode-cleaner cavity (MC) and is incident on the fast steering mirror (FSM). (PD), photodetector; QPD, quadrant photodetector; PZT, piezoelectric transducer; g, gain. The signal beam in this case is vacuum fluctuations.

Fig. 2
Fig. 2

Common mode rejection (CMR) of the homodyne detector as a function of frequency measured via a transfer function measurement (solid curve) and fitted curve (dashed). The variable electronic gain was set to optimize the CMR at low frequencies.

Fig. 3
Fig. 3

Trace (a), intensity noise spectrum of the laser relative to the SNL measured from 10 to 100   Hz . Trace (b) intensity noise contribution to the homodyne detector spectrum inferred from trace (a) and the CMR shown in Fig. 2.

Fig. 4
Fig. 4

(Color online) Electronic noise spectrum of the homodyne detector. The peaks at 50 Hz and higher harmonics are pickup from the power supply mains.

Fig. 5
Fig. 5

(Color online) Beam jitter measurements for the (a) vertical axis and (b) horizontal axis using the QPD.

Fig. 6
Fig. 6

(Color online) RIN of the low-frequency homodyne spectrum taken with AC on, trace (a), and the estimated RIN BJ noise contribution of beam jitter to the homodyne spectrum, trace (b). Trace (c) is the calculated for RIN SNL for P opt = 380   μm and ρ = 0.7 A∕W.

Fig. 7
Fig. 7

Induced displacement signal measured on the homodyne detector (at 10 Hz) as a function of LO power. Triangles, experimental data; solid line, linear fit.

Fig. 8
Fig. 8

(Color online) Measured homodyne spectrum with and without active beam jitter suppression. Homodyne spectrum with the FSM in the beam path and the control loop open, trace (a). With the active suppression of beam jitter, trace (b). Calculated shot noise for LO power 140 μW, trace (c). Electronic noise of the homodyne detector, trace (d). Sum of shot and electronic noise, trace (e).

Fig. 9
Fig. 9

(Color online) Homodyne spectrum with electronic noise subtracted, taken with the laboratory AC on, trace (a), AC off, trace (b), and with active beam jitter suppression, trace (c). Note that traces (a) and (b) were taken without the FSM actuator in the optical path.

Fig. 10
Fig. 10

(Color online) Homodyne spectrum with and without AC on and inferred noise budget. Beam jitter noise and electronic noise limit the spectrum at frequencies below 200   Hz . Above 200   Hz the homodyne spectrum is QN dominated.

Equations (5)

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

V H = | i H ( t ) | 2 .
V H = C V LO + ,
RIN SNL = 2 e / ρ P opt ,
NEP = P e L dc 2 e ρ P l P e ,
RIN BJ = A Δ x ( f ) ,

Metrics