Abstract

Balanced homodyne detection is typically used to measure quantum-noise-limited optical beams, including squeezed states of light, at audio-band frequencies. Current designs of advanced gravitational wave interferometers use some type of homodyne readout for signal detection, in part because of its compatibility with the use of squeezed light. The readout scheme used in Advanced LIGO, called DC readout, is however not a balanced detection scheme. Instead, the local oscillator field, generated from a dark fringe offset, co-propagates with the signal field at the anti-symmetric output of the beam splitter. This article examines the alternative of a true balanced homodyne detection for the readout of gravitational wave detectors such as Advanced LIGO. Several practical advantages of the balanced detection scheme are described.

© 2014 Optical Society of America

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References

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2013 (2)

LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics 7, 613–619 (2013).
[CrossRef]

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

2012 (2)

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, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 065005 (2012).
[CrossRef]

2011 (5)

W. Chaibi, F. Bondu, “Optomechanical issues in the gravitational wave detector Advanced VIRGO,” C. R. Phys. 12(9–10), 888–897 (2011).
[CrossRef]

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

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

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011).
[CrossRef]

N. Smith-Lefebvre, S. Ballmer, M. Evans, S. J. Waldman, K. Kawabe, V. Frolov, N. Mavalvala, “Optimal alignment sensing of a readout mode cleaner cavity,” Opt. Lett. 36(22), 4365–4367 (2011).
[CrossRef] [PubMed]

2010 (2)

R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1(8), 121 (2010).
[CrossRef] [PubMed]

G. M. Harry, and The LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wave detectors,” Classical Quantum Gravity 27(8), 084006 (2010).
[CrossRef]

2009 (2)

LIGO Scientific Collaboration, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Rep. Prog. Phys. 72(7), 076901 (2009).
[CrossRef]

The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A 80(4), 043802 (2009).
[CrossRef]

2007 (1)

2003 (2)

A. Buonanno, Y. Chen, N. Mavalvala, “Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme,” Phys. Rev. D 67(12), 122005 (2003).
[CrossRef]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, R. Schnabel, “Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors,” Phys. Rev. D 68(4), 042001 (2003).
[CrossRef]

2002 (1)

P. Purdue, Y. Chen, “Practical speed meter designs for quantum nondemolition gravitational-wave interferometers,” Phys. Rev. D 66(12), 122004 (2002).
[CrossRef]

2001 (3)

H. Kimble, Y. Levin, A. Matsko, K. Thorne, S. Vyatchanin, “Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics,” Phys. Rev. D 65(2), 022002 (2001).
[CrossRef]

A. Buonanno, Y. Chen, “Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors,” Phys. Rev. D 64(4), 042006 (2001).
[CrossRef]

Suitable RF sidebands are already present in all modern interferometric gravitational wave detectors: P. Fritschel, R. Bork, G. Gonzalez, N. Mavalvala, D. Ouimette, H. Rong, D. Sigg, M. Zucker, “Readout and control of a power-recycled interferometric gravitational-wave antenna,” Appl. Opt. 40(28), 4988–4998 (2001).
[CrossRef]

1997 (1)

1991 (1)

B. J. Meers, K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44(7), 4693 (1991).
[CrossRef] [PubMed]

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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 065005 (2012).
[CrossRef]

Ballmer, S.

Bondu, F.

W. Chaibi, F. Bondu, “Optomechanical issues in the gravitational wave detector Advanced VIRGO,” C. R. Phys. 12(9–10), 888–897 (2011).
[CrossRef]

Bork, R.

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, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (2012).
[CrossRef]

Buonanno, A.

A. Buonanno, Y. Chen, N. Mavalvala, “Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme,” Phys. Rev. D 67(12), 122005 (2003).
[CrossRef]

A. Buonanno, Y. Chen, “Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors,” Phys. Rev. D 64(4), 042006 (2001).
[CrossRef]

Chaibi, W.

W. Chaibi, F. Bondu, “Optomechanical issues in the gravitational wave detector Advanced VIRGO,” C. R. Phys. 12(9–10), 888–897 (2011).
[CrossRef]

Chelkowski, S.

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, R. Schnabel, “Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors,” Phys. Rev. D 68(4), 042001 (2003).
[CrossRef]

Chen, Y

The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A 80(4), 043802 (2009).
[CrossRef]

Chen, Y.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011).
[CrossRef]

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

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, R. Schnabel, “Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors,” Phys. Rev. D 68(4), 042001 (2003).
[CrossRef]

A. Buonanno, Y. Chen, N. Mavalvala, “Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme,” Phys. Rev. D 67(12), 122005 (2003).
[CrossRef]

P. Purdue, Y. Chen, “Practical speed meter designs for quantum nondemolition gravitational-wave interferometers,” Phys. Rev. D 66(12), 122004 (2002).
[CrossRef]

A. Buonanno, Y. Chen, “Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors,” Phys. Rev. D 64(4), 042006 (2001).
[CrossRef]

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, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (2012).
[CrossRef]

Danilishin, S.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011).
[CrossRef]

Danzmann, K.

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

The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A 80(4), 043802 (2009).
[CrossRef]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, R. Schnabel, “Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors,” Phys. Rev. D 68(4), 042001 (2003).
[CrossRef]

Dooley, K. L.

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

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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 065005 (2012).
[CrossRef]

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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 065005 (2012).
[CrossRef]

N. Smith-Lefebvre, S. Ballmer, M. Evans, S. J. Waldman, K. Kawabe, V. Frolov, N. Mavalvala, “Optimal alignment sensing of a readout mode cleaner cavity,” Opt. Lett. 36(22), 4365–4367 (2011).
[CrossRef] [PubMed]

Franzen, A.

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, R. Schnabel, “Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors,” Phys. Rev. D 68(4), 042001 (2003).
[CrossRef]

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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 065005 (2012).
[CrossRef]

Suitable RF sidebands are already present in all modern interferometric gravitational wave detectors: P. Fritschel, R. Bork, G. Gonzalez, N. Mavalvala, D. Ouimette, H. Rong, D. Sigg, M. Zucker, “Readout and control of a power-recycled interferometric gravitational-wave antenna,” Appl. Opt. 40(28), 4988–4998 (2001).
[CrossRef]

Frolov, V.

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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 065005 (2012).
[CrossRef]

Gonzalez, G.

Gray, M. B.

Grote, H.

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

Harms, J.

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, R. Schnabel, “Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors,” Phys. Rev. D 68(4), 042001 (2003).
[CrossRef]

Harry, G. M.

G. M. Harry, and The LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wave detectors,” Classical Quantum Gravity 27(8), 084006 (2010).
[CrossRef]

Hobbs, P. C. D.

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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 065005 (2012).
[CrossRef]

N. Smith-Lefebvre, S. Ballmer, M. Evans, S. J. Waldman, K. Kawabe, V. Frolov, N. Mavalvala, “Optimal alignment sensing of a readout mode cleaner cavity,” Opt. Lett. 36(22), 4365–4367 (2011).
[CrossRef] [PubMed]

Khalaidovski, 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, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (2012).
[CrossRef]

Khalili, F.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011).
[CrossRef]

Kimble, H.

H. Kimble, Y. Levin, A. Matsko, K. Thorne, S. Vyatchanin, “Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics,” Phys. Rev. D 65(2), 022002 (2001).
[CrossRef]

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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 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, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (2012).
[CrossRef]

R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1(8), 121 (2010).
[CrossRef] [PubMed]

K. McKenzie, M. B. Gray, P. K. Lam, D. E. McClelland, “Technical limitations to homodyne detection at audio frequencies,” Appl. Opt. 46, 3389–3395 (2007).
[CrossRef] [PubMed]

Levin, Y.

H. Kimble, Y. Levin, A. Matsko, K. Thorne, S. Vyatchanin, “Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics,” Phys. Rev. D 65(2), 022002 (2001).
[CrossRef]

Li, C.

The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A 80(4), 043802 (2009).
[CrossRef]

Matsko, A.

H. Kimble, Y. Levin, A. Matsko, K. Thorne, S. Vyatchanin, “Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics,” Phys. Rev. D 65(2), 022002 (2001).
[CrossRef]

Mavalvala, N.

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

N. Smith-Lefebvre, S. Ballmer, M. Evans, S. J. Waldman, K. Kawabe, V. Frolov, N. Mavalvala, “Optimal alignment sensing of a readout mode cleaner cavity,” Opt. Lett. 36(22), 4365–4367 (2011).
[CrossRef] [PubMed]

R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1(8), 121 (2010).
[CrossRef] [PubMed]

A. Buonanno, Y. Chen, N. Mavalvala, “Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme,” Phys. Rev. D 67(12), 122005 (2003).
[CrossRef]

Suitable RF sidebands are already present in all modern interferometric gravitational wave detectors: P. Fritschel, R. Bork, G. Gonzalez, N. Mavalvala, D. Ouimette, H. Rong, D. Sigg, M. Zucker, “Readout and control of a power-recycled interferometric gravitational-wave antenna,” Appl. Opt. 40(28), 4988–4998 (2001).
[CrossRef]

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, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (2012).
[CrossRef]

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

R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1(8), 121 (2010).
[CrossRef] [PubMed]

K. McKenzie, M. B. Gray, P. K. Lam, D. E. McClelland, “Technical limitations to homodyne detection at audio frequencies,” Appl. Opt. 46, 3389–3395 (2007).
[CrossRef] [PubMed]

McKenzie, K.

Meers, B. J.

B. J. Meers, K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44(7), 4693 (1991).
[CrossRef] [PubMed]

Miao, H.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011).
[CrossRef]

Mino, Y.

The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A 80(4), 043802 (2009).
[CrossRef]

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, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (2012).
[CrossRef]

Müller-Ebhardt, H.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011).
[CrossRef]

The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A 80(4), 043802 (2009).
[CrossRef]

Ouimette, D.

Purdue, P.

P. Purdue, Y. Chen, “Practical speed meter designs for quantum nondemolition gravitational-wave interferometers,” Phys. Rev. D 66(12), 122004 (2002).
[CrossRef]

Rehbein, H.

The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A 80(4), 043802 (2009).
[CrossRef]

Rong, H.

Schnabel, R.

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

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, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (2012).
[CrossRef]

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

R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1(8), 121 (2010).
[CrossRef] [PubMed]

The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A 80(4), 043802 (2009).
[CrossRef]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, R. Schnabel, “Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors,” Phys. Rev. D 68(4), 042001 (2003).
[CrossRef]

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, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (2012).
[CrossRef]

Sigg, D.

Slagmolen, B. 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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 065005 (2012).
[CrossRef]

Slutsky, J.

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

Smith-Lefebvre, N.

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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 065005 (2012).
[CrossRef]

Somiya, K.

The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A 80(4), 043802 (2009).
[CrossRef]

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, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (2012).
[CrossRef]

Strain, K. A.

B. J. Meers, K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44(7), 4693 (1991).
[CrossRef] [PubMed]

Thorne, K.

H. Kimble, Y. Levin, A. Matsko, K. Thorne, S. Vyatchanin, “Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics,” Phys. Rev. D 65(2), 022002 (2001).
[CrossRef]

Vahlbruch, H.

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

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, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (2012).
[CrossRef]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, R. Schnabel, “Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors,” Phys. Rev. D 68(4), 042001 (2003).
[CrossRef]

Vyatchanin, S.

H. Kimble, Y. Levin, A. Matsko, K. Thorne, S. Vyatchanin, “Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics,” Phys. Rev. D 65(2), 022002 (2001).
[CrossRef]

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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 065005 (2012).
[CrossRef]

N. Smith-Lefebvre, S. Ballmer, M. Evans, S. J. Waldman, K. Kawabe, V. Frolov, N. Mavalvala, “Optimal alignment sensing of a readout mode cleaner cavity,” Opt. Lett. 36(22), 4365–4367 (2011).
[CrossRef] [PubMed]

Zhao, C.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011).
[CrossRef]

Zucker, M.

Appl. Opt. (3)

C. R. Phys. (1)

W. Chaibi, F. Bondu, “Optomechanical issues in the gravitational wave detector Advanced VIRGO,” C. R. Phys. 12(9–10), 888–897 (2011).
[CrossRef]

Classical Quantum Gravity (3)

G. M. Harry, and The LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wave detectors,” Classical Quantum Gravity 27(8), 084006 (2010).
[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. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 065005 (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, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (2012).
[CrossRef]

Laser Photonics Rev. (1)

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

Nat. Commun. (1)

R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1(8), 121 (2010).
[CrossRef] [PubMed]

Nat. Photonics (1)

LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics 7, 613–619 (2013).
[CrossRef]

Nat. Phys. (1)

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

Opt. Lett. (1)

Phys. Rev. A (2)

The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A 80(4), 043802 (2009).
[CrossRef]

B. J. Meers, K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44(7), 4693 (1991).
[CrossRef] [PubMed]

Phys. Rev. D (6)

H. Kimble, Y. Levin, A. Matsko, K. Thorne, S. Vyatchanin, “Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics,” Phys. Rev. D 65(2), 022002 (2001).
[CrossRef]

A. Buonanno, Y. Chen, “Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors,” Phys. Rev. D 64(4), 042006 (2001).
[CrossRef]

P. Purdue, Y. Chen, “Practical speed meter designs for quantum nondemolition gravitational-wave interferometers,” Phys. Rev. D 66(12), 122004 (2002).
[CrossRef]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, R. Schnabel, “Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors,” Phys. Rev. D 68(4), 042001 (2003).
[CrossRef]

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011).
[CrossRef]

A. Buonanno, Y. Chen, N. Mavalvala, “Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme,” Phys. Rev. D 67(12), 122005 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

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

Rep. Prog. Phys. (1)

LIGO Scientific Collaboration, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Rep. Prog. Phys. 72(7), 076901 (2009).
[CrossRef]

Other (5)

Gravitational Wave International Committee (GWIC) Roadmap, 2010, https://gwic.ligo.org/roadmap/

LIGO Laboratory, LIGO web site: http://www.ligo.caltech.edu/

Virgo Collaboration, Virgo web site: http://wwwcascina.virgo.infn.it/

GEO600, GEO web site: http://geo600.aei.mpg.de/

KAGRA, KAGRA web site: http://gwcenter.icrr.u-tokyo.ac.jp/en

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Figures (3)

Fig. 1
Fig. 1

A simplified interferometer with DC readout.

Fig. 2
Fig. 2

A simplified interferometer with balanced homodyne readout.

Fig. 3
Fig. 3

An interferometer with signal mirror (SRM) for recycling or signal extraction, combined with balanced homodyne readout. The BHR scheme includes an output mode cleaner (OMC) and a similar LO mode cleaner (LMC) which pass the gravitational wave signal and LO fields respectively, while rejecting unwanted light in other spatial modes. The OMC and LMC are shown associated with the readout beam splitter (BS2) and photodiodes (PD A and B, in the blue shaded area) to indicated that these parts may be rigidly mounted together to ensure optimal overlap between the LO and signal field. The SRM in this figure can be replaced with a variety of QND readout schemes, such as variational readout [17] and speed meters [19], which depend on being able to choose the homodyne readout angle independent of the DC response of the interferometer.

Equations (12)

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

A A S = r B S e i ϕ X A E X t B S e i ϕ Y A E Y = A I N 2 ( e i ϕ X e i ϕ Y )
A G W = A I N 2 ( e i ϕ G W e i ϕ G W ) i ϕ G W A I N
A A S i ( ϕ D C + ϕ G W ) A I N = A D C + A G W .
P A S = | A D C | 2 + A D C * A G W + A D C A G W * = | A D C | 2 + 2 e ( A D C A G W * )
P A S = P ¯ A S + 2 e ( A ¯ D C ( A G W + ε A ¯ D C ) * )
A P O = ( 1 + ε ) A ¯ P O and P ¯ P O = A ¯ P O 2
P A = P ¯ P O / 2 + e ( e i ϕ A ¯ P O ( A G W + ε e i ϕ A ¯ P O ) * )
P B = P ¯ P O / 2 + e ( e i ϕ A ¯ P O ( A G W + ε e i ϕ A ¯ P O ) * )
P A + P B = P ¯ P O ( 1 + 2 ε )
P A P B = 2 e ( e i ϕ A ¯ P O A G W * )
ν n = 2 k B T R ε R 2 h ν P A S / ( α F S Q Z )
V D C = ε R P A S = 2 k B T ε h ν F S Q Z 2 5 V F S Q Z 2 .

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