Abstract

Squeezed states of light are an important tool for optical measurements below the shot noise limit and for optical realizations of quantum information systems. Recently, squeezed vacuum states were deployed to enhance the shot noise limited performance of gravitational wave detectors. In most practical implementations of squeezing enhancement, relative fluctuations between the squeezed quadrature angle and the measured quadrature (sometimes called squeezing angle jitter or phase noise) are one limit to the noise reduction that can be achieved. We present calculations of several effects that lead to quadrature fluctuations, and use these estimates to account for the observed quadrature fluctuations in a LIGO gravitational wave detector. We discuss the implications of this work for quantum enhanced advanced detectors and even more sensitive third generation detectors.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. The LIGO Scientific Collaboration, , “LIGO: The laser interferometer gravitational-wave observatory,” Rep. Prog. Phys.72, 076901 (2009).
  2. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D23, 1693 (1981).
    [CrossRef]
  3. R. Schnabel, N. Mavalvala, D.E. McClelland, and P.K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.1, 121. (2010).
    [CrossRef] [PubMed]
  4. D.E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser and Photonics Rev.5, 677–696 (2011).
  5. LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nature Photon. doi:(2013).
    [CrossRef]
  6. LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nature Phys.7(12) 962–965 (2011).
  7. H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett.110, 181101 (2013).
    [CrossRef]
  8. K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A27, 2003–2007 (1983).
    [CrossRef]
  9. D. D. Crouch and S. L. Braunstein, “Limitations to squeezing in a parametric amplifier due to pump quantum fluctuations,” Phys. Rev. A38, 4696–4711 (1988).
    [CrossRef] [PubMed]
  10. 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 a below threshold optical parametric oscillator,” J. Opt. B: Quantum S. O.1, 469–474 (1999).
    [CrossRef]
  11. M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
    [CrossRef]
  12. T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett.104, 25, 251102 (2010).
    [CrossRef] [PubMed]
  13. T. Aoki, G. Takahashi, and A. Furasawa, “Squeezing at 946 nm with periodically poled KTiOPO4,” Opt. Express14(15), 6930–6935 (2006).
    [CrossRef] [PubMed]
  14. Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, “Observation of −9 dB quadrature squeezing with improvement of phase stability in homodyne measurement,” Opt. Express15, 4321–4327 (2007).
    [CrossRef] [PubMed]
  15. A. Franzen, B. Hage, J. DiGuglielmo, J. Fiurásek, and R. Schnabel, “Experimental demonstration of continuous variable purification of squeezed states,” Phys. Rev. Lett.97, 150505 (2006).
    [CrossRef] [PubMed]
  16. S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”
  17. T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
    [CrossRef]
  18. S. Chua, M. Stefszky, C. Mow-Lowry, B. Buchler, S. Dwyer, D. Shaddock, P. K. Lam, and D. McClelland, “Backscatter tolerant squeezed light source for advanced gravitational-wave detectors,” Opt. Lett.36(23) 4680–4682 (2011).
    [CrossRef] [PubMed]
  19. S. Chelkowski, H. Vahlbruch, K. Danzmann, and R. Schnabel, “Coherent control of broadband vacuum squeezing,” Phys. Rev. A75, 043814 (2007).
    [CrossRef]
  20. 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]
  21. 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]
  22. K. McKenzie, “Squeezing in the audio gravitational wave detection band,” Ph.D. thesis, Australian National University (2008).
  23. J. Gea-Banacloche and M. S. Zubairy, “Influence of pump-phase fluctuations on the squeezing in a degenerate parametric oscillator,” Phys. Rev. A42, 1742–1751 (1990).
    [CrossRef] [PubMed]
  24. M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A30, 1386–1391 (1984).
    [CrossRef]
  25. C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A31, 3761–3774 (1985).
    [CrossRef] [PubMed]
  26. K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Nonlinear phase matching locking via optical readout,” Opt. Express14, 11256–11264 (2006).
    [CrossRef] [PubMed]
  27. A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav.29, 075001 (2012).
    [CrossRef]
  28. K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A72, 043819 (2005).
    [CrossRef]
  29. G. M. Harry, (for the LIGO Scientific Collaboration), “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quant. Grav.27, 084006 (2010).
    [CrossRef]
  30. A Khalaidovski, “Beyond the quantum limit: A squeezed light laser in GEO600,” Ph.D. thesis, Gottfried Wilhelm Leibniz Universität Hannover (2011).
  31. Einstein gravitational wave telescope conceptual design study. https://tds.ego-gw.it/ql/?c=7954
  32. K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O.7, S421 (2005).
    [CrossRef]
  33. C. M. Caves and B. L. Schumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A31, 3068–3092 (1985).
    [CrossRef] [PubMed]
  34. B. Buchler, “Electro-optic control of quantum measurements,” Ph.D. thesis, Australian National University (2001).

2013

LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nature Photon. doi:(2013).
[CrossRef]

H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett.110, 181101 (2013).
[CrossRef]

2012

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
[CrossRef]

A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav.29, 075001 (2012).
[CrossRef]

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

2011

S. Chua, M. Stefszky, C. Mow-Lowry, B. Buchler, S. Dwyer, D. Shaddock, P. K. Lam, and D. McClelland, “Backscatter tolerant squeezed light source for advanced gravitational-wave detectors,” Opt. Lett.36(23) 4680–4682 (2011).
[CrossRef] [PubMed]

LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nature Phys.7(12) 962–965 (2011).

D.E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser and Photonics Rev.5, 677–696 (2011).

2010

R. Schnabel, N. Mavalvala, D.E. McClelland, and P.K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.1, 121. (2010).
[CrossRef] [PubMed]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett.104, 25, 251102 (2010).
[CrossRef] [PubMed]

G. M. Harry, (for the LIGO Scientific Collaboration), “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quant. Grav.27, 084006 (2010).
[CrossRef]

2009

The LIGO Scientific Collaboration, , “LIGO: The laser interferometer gravitational-wave observatory,” Rep. Prog. Phys.72, 076901 (2009).

2007

2006

T. Aoki, G. Takahashi, and A. Furasawa, “Squeezing at 946 nm with periodically poled KTiOPO4,” Opt. Express14(15), 6930–6935 (2006).
[CrossRef] [PubMed]

K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Nonlinear phase matching locking via optical readout,” Opt. Express14, 11256–11264 (2006).
[CrossRef] [PubMed]

A. Franzen, B. Hage, J. DiGuglielmo, J. Fiurásek, and R. Schnabel, “Experimental demonstration of continuous variable purification of squeezed states,” Phys. Rev. Lett.97, 150505 (2006).
[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]

2005

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A72, 043819 (2005).
[CrossRef]

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O.7, S421 (2005).
[CrossRef]

2004

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]

1999

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 a below threshold optical parametric oscillator,” J. Opt. B: Quantum S. O.1, 469–474 (1999).
[CrossRef]

1990

J. Gea-Banacloche and M. S. Zubairy, “Influence of pump-phase fluctuations on the squeezing in a degenerate parametric oscillator,” Phys. Rev. A42, 1742–1751 (1990).
[CrossRef] [PubMed]

1988

D. D. Crouch and S. L. Braunstein, “Limitations to squeezing in a parametric amplifier due to pump quantum fluctuations,” Phys. Rev. A38, 4696–4711 (1988).
[CrossRef] [PubMed]

1985

C. M. Caves and B. L. Schumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A31, 3068–3092 (1985).
[CrossRef] [PubMed]

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A31, 3761–3774 (1985).
[CrossRef] [PubMed]

1984

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A30, 1386–1391 (1984).
[CrossRef]

1983

K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A27, 2003–2007 (1983).
[CrossRef]

1981

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D23, 1693 (1981).
[CrossRef]

Abbott, R.

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

Adhikari, R.

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

Aoki, T.

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 a below threshold optical parametric oscillator,” J. Opt. B: Quantum S. O.1, 469–474 (1999).
[CrossRef]

Barsotti, L.

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Bauchrowitz, J.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett.104, 25, 251102 (2010).
[CrossRef] [PubMed]

Bowen, W. P.

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]

Braunstein, S. L.

D. D. Crouch and S. L. Braunstein, “Limitations to squeezing in a parametric amplifier due to pump quantum fluctuations,” Phys. Rev. A38, 4696–4711 (1988).
[CrossRef] [PubMed]

Buchler, B.

Buchler, B. C.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
[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 a below threshold optical parametric oscillator,” J. Opt. B: Quantum S. O.1, 469–474 (1999).
[CrossRef]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Caves, C. M.

C. M. Caves and B. L. Schumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A31, 3068–3092 (1985).
[CrossRef] [PubMed]

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D23, 1693 (1981).
[CrossRef]

Chelkowski, S.

S. Chelkowski, H. Vahlbruch, K. Danzmann, and R. Schnabel, “Coherent control of broadband vacuum squeezing,” Phys. Rev. A75, 043814 (2007).
[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]

Chen, Y.

D.E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser and Photonics Rev.5, 677–696 (2011).

Chua, S.

Chua, S. S. Y.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
[CrossRef]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Collett, M. J.

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A31, 3761–3774 (1985).
[CrossRef] [PubMed]

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A30, 1386–1391 (1984).
[CrossRef]

Crouch, D. D.

D. D. Crouch and S. L. Braunstein, “Limitations to squeezing in a parametric amplifier due to pump quantum fluctuations,” Phys. Rev. A38, 4696–4711 (1988).
[CrossRef] [PubMed]

Danzmann, K

H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett.110, 181101 (2013).
[CrossRef]

Danzmann, K.

A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav.29, 075001 (2012).
[CrossRef]

S. Chelkowski, H. Vahlbruch, K. Danzmann, and R. Schnabel, “Coherent control of broadband vacuum squeezing,” Phys. Rev. A75, 043814 (2007).
[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]

DiGuglielmo, J.

A. Franzen, B. Hage, J. DiGuglielmo, J. Fiurásek, and R. Schnabel, “Experimental demonstration of continuous variable purification of squeezed states,” Phys. Rev. Lett.97, 150505 (2006).
[CrossRef] [PubMed]

Dooley, K

H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett.110, 181101 (2013).
[CrossRef]

Dooley, K. L.

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

Dwyer, S.

S. Chua, M. Stefszky, C. Mow-Lowry, B. Buchler, S. Dwyer, D. Shaddock, P. K. Lam, and D. McClelland, “Backscatter tolerant squeezed light source for advanced gravitational-wave detectors,” Opt. Lett.36(23) 4680–4682 (2011).
[CrossRef] [PubMed]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Eberle, T.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett.104, 25, 251102 (2010).
[CrossRef] [PubMed]

Evans, M.

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Factourovich, M.

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Fiurásek, J.

A. Franzen, B. Hage, J. DiGuglielmo, J. Fiurásek, and R. Schnabel, “Experimental demonstration of continuous variable purification of squeezed states,” Phys. Rev. Lett.97, 150505 (2006).
[CrossRef] [PubMed]

Franzen, A.

A. Franzen, B. Hage, J. DiGuglielmo, J. Fiurásek, and R. Schnabel, “Experimental demonstration of continuous variable purification of squeezed states,” Phys. Rev. Lett.97, 150505 (2006).
[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]

Fricke, T. T.

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

Fritschel, P.

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

Frolov, V. V.

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Furasawa, A.

Furusawa, A.

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 a below threshold optical parametric oscillator,” J. Opt. B: Quantum S. O.1, 469–474 (1999).
[CrossRef]

Gardiner, C. W.

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A31, 3761–3774 (1985).
[CrossRef] [PubMed]

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A30, 1386–1391 (1984).
[CrossRef]

Gea-Banacloche, J.

J. Gea-Banacloche and M. S. Zubairy, “Influence of pump-phase fluctuations on the squeezing in a degenerate parametric oscillator,” Phys. Rev. A42, 1742–1751 (1990).
[CrossRef] [PubMed]

Goda, K.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O.7, S421 (2005).
[CrossRef]

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A72, 043819 (2005).
[CrossRef]

Gräf, C.

A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav.29, 075001 (2012).
[CrossRef]

Gray, M. B.

K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Nonlinear phase matching locking via optical readout,” Opt. Express14, 11256–11264 (2006).
[CrossRef] [PubMed]

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O.7, S421 (2005).
[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]

Grosse, N.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O.7, S421 (2005).
[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]

Grote, H

H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett.110, 181101 (2013).
[CrossRef]

Grote, H.

A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav.29, 075001 (2012).
[CrossRef]

Gustafson, R.

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

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]

A. Franzen, B. Hage, J. DiGuglielmo, J. Fiurásek, and R. Schnabel, “Experimental demonstration of continuous variable purification of squeezed states,” Phys. Rev. Lett.97, 150505 (2006).
[CrossRef] [PubMed]

Händchen, V.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett.104, 25, 251102 (2010).
[CrossRef] [PubMed]

Harry, G. M.

G. M. Harry, (for the LIGO Scientific Collaboration), “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quant. Grav.27, 084006 (2010).
[CrossRef]

Kawabe, K.

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Khalaidovski, A

A Khalaidovski, “Beyond the quantum limit: A squeezed light laser in GEO600,” Ph.D. thesis, Gottfried Wilhelm Leibniz Universität Hannover (2011).

Khalaidovski, A.

A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav.29, 075001 (2012).
[CrossRef]

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
[CrossRef]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Kissel, J. S.

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

Lam, P. K.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
[CrossRef]

S. Chua, M. Stefszky, C. Mow-Lowry, B. Buchler, S. Dwyer, D. Shaddock, P. K. Lam, and D. McClelland, “Backscatter tolerant squeezed light source for advanced gravitational-wave detectors,” Opt. Lett.36(23) 4680–4682 (2011).
[CrossRef] [PubMed]

K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Nonlinear phase matching locking via optical readout,” Opt. Express14, 11256–11264 (2006).
[CrossRef] [PubMed]

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A72, 043819 (2005).
[CrossRef]

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O.7, S421 (2005).
[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 a below threshold optical parametric oscillator,” J. Opt. B: Quantum S. O.1, 469–474 (1999).
[CrossRef]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Lam, P.K.

R. Schnabel, N. Mavalvala, D.E. McClelland, and P.K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.1, 121. (2010).
[CrossRef] [PubMed]

Landry, M.

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Lastzka, N.

A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav.29, 075001 (2012).
[CrossRef]

Mavalvala, N.

D.E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser and Photonics Rev.5, 677–696 (2011).

R. Schnabel, N. Mavalvala, D.E. McClelland, and P.K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.1, 121. (2010).
[CrossRef] [PubMed]

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A72, 043819 (2005).
[CrossRef]

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O.7, S421 (2005).
[CrossRef]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

McClelland, D.

McClelland, D. E.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
[CrossRef]

K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Nonlinear phase matching locking via optical readout,” Opt. Express14, 11256–11264 (2006).
[CrossRef] [PubMed]

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A72, 043819 (2005).
[CrossRef]

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O.7, S421 (2005).
[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 a below threshold optical parametric oscillator,” J. Opt. B: Quantum S. O.1, 469–474 (1999).
[CrossRef]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

McClelland, D.E.

D.E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser and Photonics Rev.5, 677–696 (2011).

R. Schnabel, N. Mavalvala, D.E. McClelland, and P.K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.1, 121. (2010).
[CrossRef] [PubMed]

McKenzie, K.

K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Nonlinear phase matching locking via optical readout,” Opt. Express14, 11256–11264 (2006).
[CrossRef] [PubMed]

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A72, 043819 (2005).
[CrossRef]

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O.7, S421 (2005).
[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]

K. McKenzie, “Squeezing in the audio gravitational wave detection band,” Ph.D. thesis, Australian National University (2008).

Meadors, G. D.

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Mehment, M.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett.104, 25, 251102 (2010).
[CrossRef] [PubMed]

Mikhailov, E. E.

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A72, 043819 (2005).
[CrossRef]

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O.7, S421 (2005).
[CrossRef]

Mow-Lowry, C.

Mow-Lowry, C. M.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
[CrossRef]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Müller-Ebhardt, H.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett.104, 25, 251102 (2010).
[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 a below threshold optical parametric oscillator,” J. Opt. B: Quantum S. O.1, 469–474 (1999).
[CrossRef]

Schnabel, R

H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett.110, 181101 (2013).
[CrossRef]

Schnabel, R.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
[CrossRef]

A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav.29, 075001 (2012).
[CrossRef]

D.E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser and Photonics Rev.5, 677–696 (2011).

R. Schnabel, N. Mavalvala, D.E. McClelland, and P.K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.1, 121. (2010).
[CrossRef] [PubMed]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett.104, 25, 251102 (2010).
[CrossRef] [PubMed]

S. Chelkowski, H. Vahlbruch, K. Danzmann, and R. Schnabel, “Coherent control of broadband vacuum squeezing,” Phys. Rev. A75, 043814 (2007).
[CrossRef]

A. Franzen, B. Hage, J. DiGuglielmo, J. Fiurásek, and R. Schnabel, “Experimental demonstration of continuous variable purification of squeezed states,” Phys. Rev. Lett.97, 150505 (2006).
[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]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Schofield, R. M. S.

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Schumaker, B. L.

C. M. Caves and B. L. Schumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A31, 3068–3092 (1985).
[CrossRef] [PubMed]

Shaddock, D.

Shaddock, D. A.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
[CrossRef]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Sigg, D.

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Slagmolen, B. J. J.

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

Slutzky, J

H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett.110, 181101 (2013).
[CrossRef]

Smith-Lefebvre, N. D.

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

Stefszky, M.

Stefszky, M. S.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
[CrossRef]

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Steinlechner, S.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett.104, 25, 251102 (2010).
[CrossRef] [PubMed]

Takahashi, G.

Takeno, Y.

Vahlbruch, H

H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett.110, 181101 (2013).
[CrossRef]

Vahlbruch, H.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
[CrossRef]

A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav.29, 075001 (2012).
[CrossRef]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett.104, 25, 251102 (2010).
[CrossRef] [PubMed]

S. Chelkowski, H. Vahlbruch, K. Danzmann, and R. Schnabel, “Coherent control of broadband vacuum squeezing,” Phys. Rev. A75, 043814 (2007).
[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]

Vorvick, C.

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

Waldman, S. J.

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[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]

Wódkiewicz, K.

K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A27, 2003–2007 (1983).
[CrossRef]

Yonezawa, H.

Yukawa, M.

Zubairy, M. S.

J. Gea-Banacloche and M. S. Zubairy, “Influence of pump-phase fluctuations on the squeezing in a degenerate parametric oscillator,” Phys. Rev. A42, 1742–1751 (1990).
[CrossRef] [PubMed]

K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A27, 2003–2007 (1983).
[CrossRef]

Class. and Quant. Grav.

A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav.29, 075001 (2012).
[CrossRef]

T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012).
[CrossRef]

Class. Quant. Grav.

G. M. Harry, (for the LIGO Scientific Collaboration), “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quant. Grav.27, 084006 (2010).
[CrossRef]

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quant. Grav.29, 145015–145029. (2012).
[CrossRef]

J. Opt. B: Quantum S. O.

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 a below threshold optical parametric oscillator,” J. Opt. B: Quantum S. O.1, 469–474 (1999).
[CrossRef]

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O.7, S421 (2005).
[CrossRef]

Laser and Photonics Rev.

D.E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser and Photonics Rev.5, 677–696 (2011).

Nat. Commun.

R. Schnabel, N. Mavalvala, D.E. McClelland, and P.K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.1, 121. (2010).
[CrossRef] [PubMed]

Nature Photon.

LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nature Photon. doi:(2013).
[CrossRef]

Nature Phys.

LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nature Phys.7(12) 962–965 (2011).

Opt. Express

Opt. Lett.

Phys. Rev. A

C. M. Caves and B. L. Schumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A31, 3068–3092 (1985).
[CrossRef] [PubMed]

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A72, 043819 (2005).
[CrossRef]

J. Gea-Banacloche and M. S. Zubairy, “Influence of pump-phase fluctuations on the squeezing in a degenerate parametric oscillator,” Phys. Rev. A42, 1742–1751 (1990).
[CrossRef] [PubMed]

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A30, 1386–1391 (1984).
[CrossRef]

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A31, 3761–3774 (1985).
[CrossRef] [PubMed]

K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A27, 2003–2007 (1983).
[CrossRef]

D. D. Crouch and S. L. Braunstein, “Limitations to squeezing in a parametric amplifier due to pump quantum fluctuations,” Phys. Rev. A38, 4696–4711 (1988).
[CrossRef] [PubMed]

S. Chelkowski, H. Vahlbruch, K. Danzmann, and R. Schnabel, “Coherent control of broadband vacuum squeezing,” Phys. Rev. A75, 043814 (2007).
[CrossRef]

Phys. Rev. D

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D23, 1693 (1981).
[CrossRef]

Phys. Rev. Lett.

H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett.110, 181101 (2013).
[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]

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]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett.104, 25, 251102 (2010).
[CrossRef] [PubMed]

A. Franzen, B. Hage, J. DiGuglielmo, J. Fiurásek, and R. Schnabel, “Experimental demonstration of continuous variable purification of squeezed states,” Phys. Rev. Lett.97, 150505 (2006).
[CrossRef] [PubMed]

Rep. Prog. Phys.

The LIGO Scientific Collaboration, , “LIGO: The laser interferometer gravitational-wave observatory,” Rep. Prog. Phys.72, 076901 (2009).

Other

K. McKenzie, “Squeezing in the audio gravitational wave detection band,” Ph.D. thesis, Australian National University (2008).

S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

B. Buchler, “Electro-optic control of quantum measurements,” Ph.D. thesis, Australian National University (2001).

A Khalaidovski, “Beyond the quantum limit: A squeezed light laser in GEO600,” Ph.D. thesis, Gottfried Wilhelm Leibniz Universität Hannover (2011).

Einstein gravitational wave telescope conceptual design study. https://tds.ego-gw.it/ql/?c=7954

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 (6)

Fig. 1
Fig. 1

Possible squeezing as a function of the total effective losses 100 × (1 − η) and total squeezed quadrature fluctuations, in the absence of technical noise. Here pump power is optimized for best squeezing given the level of quadrature fluctuations. Squeezing levels in decibels relative to shot noise are negative for an improvement in sensitivity.

Fig. 2
Fig. 2

The LIGO interferometer with a squeezed vacuum source. The pump laser, locked to the LIGO main laser frequency through an optical fiber, pumps the second harmonic generator (SHG) [19] and the optical parametric oscillator (OPO) [18]. The control laser – for the quadrature control scheme – is offset locked 29.5 MHz above the pump laser frequency, and injected into the OPO where the nonlinear interaction generates a symmetric sideband 29.5 MHz below the pump with, under ideal conditions, a phase determined by the phase of the circulating pump [19, 20]. The phase of the control laser is then locked relative to the phase of the circulating pump by the coherent field photo-detector (CF PD). The squeezed field, with coherent control sidebands, reflects off the interferometer after which the quadrature control photo-detector senses the phase between the interferometer beam and the coherent sidebands. This error signal is used to adjust the pump laser phase and control the quadrature angle. The output mode cleaner (OMC) reflects the coherent sidebands and transmits the carrier towards the gravitational wave readout photo-detectors (GW PD) where the squeezing is measured.

Fig. 3
Fig. 3

Variance (in dB relative to vacuum fluctuations) in one quadrature of the OPO output field as a function of the phase of the incident second harmonic pump. With no detuning and ideal phase matching (red trace), the minimum variance occurs at θB = π, and the pump phase alone determines the squeezed quadrature θsqz = θB/2. However small changes in the cavity length or crystal temperature shift the location of the minimum variance, introducing a relative shift between the squeezed quadrature angle and the pump phase. The green trace shows the variance with the cavity length shifted 6 nm away from resonance, while the blue trace shows the variance produced when the temperature deviates by 0.01 K from the phase matching temperature. These predictions assume Ω γ a tot, | x | = 1 / 2, ηesc = 0.96, γ a tot = 2 π × 12 MHz, and γ b tot = 2 π × 30 MHz.

Fig. 4
Fig. 4

Expected variances of the squeezed (solid lines) and anti-squeezed (dashed lines) quadratures as a function of nonlinear gain, based on Eq. (1). The level of anti-squeezing is sensitive to the total losses, while at high gains the level of squeezing is sensitive to the quadrature fluctuations. Left panel: θ̃ =50 mrad and η= 90% (blue) 70% (green) and 50% (red). Right panel: η=70%, and θ̃ =30 (blue), 50 (green), and 100 (red) mrad. Blue and green dashed lines are below the red dashed line in the right panel.

Fig. 5
Fig. 5

Characterization of Enhanced LIGO interferometer as a squeezing detector. Red points show measured squeezing and anti squeezing between 1.9 kHz and 3.7 kHz. Blue trace is a fit to the red points with η = 38 ± 3% and θ̃ = 81 ± 6 mrad. Control bandwidths were consistent for measurements at different nonlinear gains. The black and green points were measured at a later date with η = 42 ± 7%. After measurement of the black point (θ̃ = 109 ± 9 mrad), the interferometer alignment was adjusted slightly and the squeezing angle lock point adjusted, reducing the quadrature fluctuations to (θ̃ = 37 ± 6 mrad) as shown by the green point.

Fig. 6
Fig. 6

Squeezing targets for gravitational wave detectors, in decibels relative to shot noise. This experiment measured −2.1 dB of squeezing in Enhanced LIGO, with 55% losses and at least 37 ± 6 mrad squeezing angle fluctuations. For Advanced LIGO we would like to be able to measure at least −6 dB of squeezing in an initial implementation. Since the total losses are expected to be 20–28%, planning for 15 mrad or less of phase noise would allow for −6 dB of squeezing. Designs for third generation detectors call for even higher levels of squeezing [31], which will place very stringent limits on the total quadrature fluctuations and losses.

Tables (1)

Tables Icon

Table 1 Summary of contributions to total relative quadrature fluctuations (mrad RMS) and independent measurements made at high nonlinear gains.

Equations (21)

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

V sqz = 1 + 4 η x [ ( sin θ ˜ ) 2 ( 1 x ) 2 + 4 ( Ω / γ a tot ) 2 ( cos θ ˜ ) 2 ( 1 + x ) 2 + 4 ( Ω / γ a tot ) 2 ] ,
d θ sqz d δ L = 1 2 d V / d δ L d V / d θ b | θ B = π / 2 , δ L = 0 = ω L ¯ ( 1 γ b tot + 1 γ a tot ( 1 + x 2 ) ) .
ε = ε 0 e i κ ( T T 0 ) sinc ( κ ( T T 0 ) ) .
Δ a = κ ( T T 0 ) / τ ,
d θ sqz d T = 1 2 d V / d T d V / d θ b | θ B = π / 2 , T = T 0 = κ ( 1 γ a tot τ ( 1 + x 2 ) + 1 2 ) .
θ ˜ RF = T SB P sig ( 2 P ¯ SB P CD P sig + d P SB 2 8 P ¯ SB ) ,
Δ θ alignment = i j γ i j ifo γ i j clf sin ϕ i j 1 i j γ i j ifo γ i j clf cos ϕ i j ,
H = 2 ω b b + ω a a + i 2 ( ε a 2 b + ε * a 2 b )
b = 2 γ b f | B in | γ b t o t e i θ B 1 i Δ b / γ b tot
δ a ˙ = γ a tot M δ a + 2 γ a l δ A l , in + 2 γ a f δ A f , in
δ a = ( δ a δ a ) , M = ( 1 + i Δ a γ a tot x e i θ B 1 i Δ b / γ b tot x * e i θ B 1 + i Δ b / γ b tot 1 i Δ a γ a tot ) , x = 2 γ b f | B in | γ b tot ε γ a tot
δ a ˜ ( Ω ) = ( Ω γ a tot M ) l [ 2 γ a l δ A ˜ l , in ( Ω ) + 2 γ a f δ A ˜ f , in ( Ω ) ]
δ A f , out ( Ω ) = 2 γ a f δ a ˜ ( Ω ) δ A ˜ f , in ( Ω ) = ( 2 γ a f ( i Ω I γ a tot M ) 1 I ) δ A f , in ( Ω ) + 2 γ a l γ a f ( i Ω I γ a tot M ) 1 δ A l , in
δ X ˜ f , out ( Ω ) = ( δ X ˜ 1 ( Ω ) δ X ˜ 2 ( Ω ) ) = ( 1 1 i i ) δ A ˜ f , out ( Ω ) = R δ A ˜ f , out ( Ω )
V 1 ( θ b , Ω ) = V + ( Ω ) cos 2 ( θ b / 2 ) + V ( Ω ) sin 2 ( θ b / 2 ) V ± = 1 ± 4 η esc x ( 1 x ) 2 + ( Ω / γ a tot ) 2
a ˙ s = ( i Δ s γ a tot ) a s + ε b a i + 2 γ a c A s , in
a ˙ i = ( i Δ i γ a tot ) a i + ε b a s
A s , r = 2 γ a c a s A s , in A i , r = 2 γ a c a i
A s , t = 2 γ a f a s A i , t = 2 γ a f a i
E r = Re [ A s , r A i , r ] sin ϕ dm 1 + Im [ A s , r A i , r ] cos ϕ dm 1
E t = Re [ A s , t A LO + A i , t A LO ] sin ϕ dm 2 + Im [ A s , t A LO + A i , t A LO ] cos ϕ dm 1

Metrics