Abstract

Beam alignment is an important practical aspect of the application of squeezed states of light. Misalignments in the detection of squeezed light result in a reduction of the observable squeezing level. In the case of squeezed vacuum fields that contain only very few photons, special measures must be taken in order to sense and control the alignment of the essentially dark beam. The GEO 600 gravitational wave detector employs a squeezed vacuum source to improve its detection sensitivity beyond the limits set by classical quantum shot noise. Here, we present our design and implementation of an alignment sensing and control scheme that ensures continuous optimal alignment of the squeezed vacuum field at GEO 600 on long time scales in the presence of free-swinging optics. This first demonstration of a squeezed light automatic alignment system will be of particular interest for future long-term applications of squeezed vacuum states of light.

© 2016 Optical Society of America

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References

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  1. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
    [Crossref]
  2. R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1, 121 (2010).
    [Crossref] [PubMed]
  3. The LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. 7, 962–965 (2011).
    [Crossref]
  4. The LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
    [Crossref]
  5. H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110, 181101 (2013).
    [Crossref] [PubMed]
  6. C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
    [Crossref]
  7. In fact, in the case of GEO 600 (and other interferometric gravitational wave detectors) an additional and even more stringent requirement for the alignment is given by the fact that the squeezed light field needs to pass through the output mode cleaner (OMC) cavity. However, since the interferometer beam is actively aligned to the OMC [6, 8], overlap with the interferometer beam ensures overlap with the OMC eigenmode within the bandwidth of those control loops.
  8. M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).
  9. K. L. Dooley, E. Schreiber, H. Vahlbruch, C. Affeldt, J. Leong, H. Wittel, and H. Grote, “Phase control of squeezed vacuum states of light in gravitational wave detectors,” Opt. Express 23, 8235–8245 (2015).
    [Crossref] [PubMed]
  10. E. Oelker, L. Barsotti, S. Dwyer, D. Sigg, and N. Mavalvala, “Squeezed light for advanced gravitational wave detectors and beyond,” Opt. Express 22, 21106–21121 (2014).
    [Crossref] [PubMed]
  11. S. Dwyer, L. Barsotti, S. S. Y. Chua, M. Evans, M. Factourovich, D. Gustafson, T. Isogai, K. Kawabe, A. Khalaidovski, P. K. Lam, M. Landry, N. Mavalvala, D. E. McClelland, G. D. Meadors, C. M. Mow-Lowry, R. Schnabel, R. M. S. Schofield, N. Smith-Lefebvre, M. Stefszky, C. Vorvick, and D. Sigg, “Squeezed quadrature fluctuations in a gravitational wave detector using squeezed light,” Opt. Express 21, 19047–19060 (2013).
    [Crossref] [PubMed]
  12. We used the interferometer simulation software Finesse [13] to calculate for different misalignments the overlap of the squeezed light field with the interferometer beam as given by the OMC’s eigenmode. Effects of HOMs can be neglected in this case because they are suppressed by the OMC.
  13. A. Freise, G. Heinzel, H. Lück, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004). (The program is available at http://www.gwoptics.org/finesse .)
    [Crossref]
  14. E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, “Automatic alignment of optical interferometers,” Appl. Opt. 33, 5041–5049 (1994).
    [Crossref] [PubMed]
  15. While differential wavefront sensing ideally gives a purely relative signal, common movements of the two beams on the quadrant photodiode can introduce small errors. To mitigate this we use active scanners that keep the Michelson sidebands centered on the sensors by detecting the beat of the two sidebands at twice the modulation frequency [16].
  16. H. Grote and the LIGO Scientific Collaboration, “The GEO 600 status,” Class. Quantum Grav. 27, 084003 (2010).
    [Crossref]
  17. 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]
  18. H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Grav. 27, 084027 (2010).
    [Crossref]
  19. The Michelson sidebands at the interferometer output are less contaminated by HOMs than the carrier. Due to their shifted frequency and the interferometer’s Schnupp asymmetry they are further away from the destructive interference condition. Thus more of the fundamental mode leaves the output port, making it the dominant mode contribution.

2015 (1)

2014 (2)

E. Oelker, L. Barsotti, S. Dwyer, D. Sigg, and N. Mavalvala, “Squeezed light for advanced gravitational wave detectors and beyond,” Opt. Express 22, 21106–21121 (2014).
[Crossref] [PubMed]

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

2013 (3)

S. Dwyer, L. Barsotti, S. S. Y. Chua, M. Evans, M. Factourovich, D. Gustafson, T. Isogai, K. Kawabe, A. Khalaidovski, P. K. Lam, M. Landry, N. Mavalvala, D. E. McClelland, G. D. Meadors, C. M. Mow-Lowry, R. Schnabel, R. M. S. Schofield, N. Smith-Lefebvre, M. Stefszky, C. Vorvick, and D. Sigg, “Squeezed quadrature fluctuations in a gravitational wave detector using squeezed light,” Opt. Express 21, 19047–19060 (2013).
[Crossref] [PubMed]

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

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

2011 (1)

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

2010 (4)

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Grav. 27, 084027 (2010).
[Crossref]

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

H. Grote and the LIGO Scientific Collaboration, “The GEO 600 status,” Class. Quantum Grav. 27, 084003 (2010).
[Crossref]

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

2006 (1)

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

2004 (1)

A. Freise, G. Heinzel, H. Lück, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004). (The program is available at http://www.gwoptics.org/finesse .)
[Crossref]

1994 (1)

1981 (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[Crossref]

Affeldt, C.

K. L. Dooley, E. Schreiber, H. Vahlbruch, C. Affeldt, J. Leong, H. Wittel, and H. Grote, “Phase control of squeezed vacuum states of light in gravitational wave detectors,” Opt. Express 23, 8235–8245 (2015).
[Crossref] [PubMed]

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

Barsotti, L.

Caves, C. M.

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[Crossref]

Chelkowski, S.

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

Chua, S. S. Y.

Danzmann, K.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and 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. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Grav. 27, 084027 (2010).
[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]

A. Freise, G. Heinzel, H. Lück, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004). (The program is available at http://www.gwoptics.org/finesse .)
[Crossref]

Degallaix, J.

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

Dooley, K. L.

K. L. Dooley, E. Schreiber, H. Vahlbruch, C. Affeldt, J. Leong, H. Wittel, and H. Grote, “Phase control of squeezed vacuum states of light in gravitational wave detectors,” Opt. Express 23, 8235–8245 (2015).
[Crossref] [PubMed]

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

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

Dwyer, S.

Evans, M.

Factourovich, M.

Franzen, A.

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

Freise, A.

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

A. Freise, G. Heinzel, H. Lück, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004). (The program is available at http://www.gwoptics.org/finesse .)
[Crossref]

Gräf, C.

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Grav. 27, 084027 (2010).
[Crossref]

Grote, H.

K. L. Dooley, E. Schreiber, H. Vahlbruch, C. Affeldt, J. Leong, H. Wittel, and H. Grote, “Phase control of squeezed vacuum states of light in gravitational wave detectors,” Opt. Express 23, 8235–8245 (2015).
[Crossref] [PubMed]

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and 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. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

H. Grote and the LIGO Scientific Collaboration, “The GEO 600 status,” Class. Quantum Grav. 27, 084003 (2010).
[Crossref]

Gustafson, D.

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]

Heinzel, G.

A. Freise, G. Heinzel, H. Lück, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004). (The program is available at http://www.gwoptics.org/finesse .)
[Crossref]

Hewitson, M.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

Hild, S.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

Hough, J.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

Isogai, T.

Kawabe, K.

Khalaidovski, A.

Lam, P. K.

Landry, M.

Lastzka, N.

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Grav. 27, 084027 (2010).
[Crossref]

Leong, J.

K. L. Dooley, E. Schreiber, H. Vahlbruch, C. Affeldt, J. Leong, H. Wittel, and H. Grote, “Phase control of squeezed vacuum states of light in gravitational wave detectors,” Opt. Express 23, 8235–8245 (2015).
[Crossref] [PubMed]

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

Lück, H.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

A. Freise, G. Heinzel, H. Lück, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004). (The program is available at http://www.gwoptics.org/finesse .)
[Crossref]

Mavalvala, N.

McClelland, D. E.

Meadors, G. D.

Meers, B. J.

Morrison, E.

Mow-Lowry, C. M.

Oelker, E.

Prijatelj, M.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

Robertson, D. I.

Rowan, S.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

Rüdiger, A.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

Schilling, R.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

A. Freise, G. Heinzel, H. Lück, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004). (The program is available at http://www.gwoptics.org/finesse .)
[Crossref]

Schnabel, R.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

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

S. Dwyer, L. Barsotti, S. S. Y. Chua, M. Evans, M. Factourovich, D. Gustafson, T. Isogai, K. Kawabe, A. Khalaidovski, P. K. Lam, M. Landry, N. Mavalvala, D. E. McClelland, G. D. Meadors, C. M. Mow-Lowry, R. Schnabel, R. M. S. Schofield, N. Smith-Lefebvre, M. Stefszky, C. Vorvick, and D. Sigg, “Squeezed quadrature fluctuations in a gravitational wave detector using squeezed light,” Opt. Express 21, 19047–19060 (2013).
[Crossref] [PubMed]

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

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Grav. 27, 084027 (2010).
[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]

Schofield, R. M. S.

Schreiber, E.

K. L. Dooley, E. Schreiber, H. Vahlbruch, C. Affeldt, J. Leong, H. Wittel, and H. Grote, “Phase control of squeezed vacuum states of light in gravitational wave detectors,” Opt. Express 23, 8235–8245 (2015).
[Crossref] [PubMed]

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

Sigg, D.

Slutsky, J.

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and 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.

Sorazu, B.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

Stefszky, M.

Strain, K. A.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

Vahlbruch, H.

K. L. Dooley, E. Schreiber, H. Vahlbruch, C. Affeldt, J. Leong, H. Wittel, and H. Grote, “Phase control of squeezed vacuum states of light in gravitational wave detectors,” Opt. Express 23, 8235–8245 (2015).
[Crossref] [PubMed]

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

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

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Grav. 27, 084027 (2010).
[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.

Ward, H.

Willke, B.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

A. Freise, G. Heinzel, H. Lück, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004). (The program is available at http://www.gwoptics.org/finesse .)
[Crossref]

Winkler, W.

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

Wittel, H.

K. L. Dooley, E. Schreiber, H. Vahlbruch, C. Affeldt, J. Leong, H. Wittel, and H. Grote, “Phase control of squeezed vacuum states of light in gravitational wave detectors,” Opt. Express 23, 8235–8245 (2015).
[Crossref] [PubMed]

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

Appl. Opt. (1)

Class. Quantum Grav. (4)

H. Grote and the LIGO Scientific Collaboration, “The GEO 600 status,” Class. Quantum Grav. 27, 084003 (2010).
[Crossref]

C. Affeldt, K. Danzmann, K. L. Dooley, H. Grote, M. Hewitson, S. Hild, J. Hough, J. Leong, H. Lück, M. Prijatelj, S. Rowan, A. Rüdiger, R. Schilling, R. Schnabel, E. Schreiber, B. Sorazu, K. A. Strain, H. Vahlbruch, B. Willke, W. Winkler, and H. Wittel, “Advanced techniques in GEO 600,” Class. Quantum Grav. 31, 224002 (2014).
[Crossref]

A. Freise, G. Heinzel, H. Lück, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004). (The program is available at http://www.gwoptics.org/finesse .)
[Crossref]

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Grav. 27, 084027 (2010).
[Crossref]

JPCS (1)

M. Prijatelj, H. Grote, J. Degallaix, M. Hewitson, S. Hild, C. Affeldt, A. Freise, J. Leong, H. Lück, K. A. Strain, H. Wittel, B. Willke, and K. Danzmann, “Control and automatic alignment of the output mode cleaner of GEO 600,” JPCS 228, 012014 (2010).

Nat. Commun. (1)

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

Nat. Photon. (1)

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

Nat. Phys. (1)

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

Opt. Express (3)

Phys. Rev. D (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[Crossref]

Phys. Rev. Lett. (2)

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

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

Other (4)

We used the interferometer simulation software Finesse [13] to calculate for different misalignments the overlap of the squeezed light field with the interferometer beam as given by the OMC’s eigenmode. Effects of HOMs can be neglected in this case because they are suppressed by the OMC.

While differential wavefront sensing ideally gives a purely relative signal, common movements of the two beams on the quadrant photodiode can introduce small errors. To mitigate this we use active scanners that keep the Michelson sidebands centered on the sensors by detecting the beat of the two sidebands at twice the modulation frequency [16].

In fact, in the case of GEO 600 (and other interferometric gravitational wave detectors) an additional and even more stringent requirement for the alignment is given by the fact that the squeezed light field needs to pass through the output mode cleaner (OMC) cavity. However, since the interferometer beam is actively aligned to the OMC [6, 8], overlap with the interferometer beam ensures overlap with the OMC eigenmode within the bandwidth of those control loops.

The Michelson sidebands at the interferometer output are less contaminated by HOMs than the carrier. Due to their shifted frequency and the interferometer’s Schnupp asymmetry they are further away from the destructive interference condition. Thus more of the fundamental mode leaves the output port, making it the dominant mode contribution.

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Figures (5)

Fig. 1
Fig. 1

The effect of misalignment on the observed squeezing level. Here the squeezed beam is misaligned by rotating one of the mirrors in the input path and the squeezing level is recorded. With 0.4mrad of misalignment, nearly all squeezing is lost. The measurements are compared to a numerical model [12]. The small remaining difference along the x-axis between measurements and model is consistent with the uncertainty of the actuator calibration.

Fig. 2
Fig. 2

Simplified layout of the GEO 600 output optics with squeezing injection. The squeezed vacuum field is injected via a Faraday isolator, enters the interferometer through the output port, and is reflected back. It then travels together with the interferometer output beam through the output mode cleaner (OMC) to the detection photodiode. A pair of 3-axis piezo-actuated mirrors in the in-air path serves to steer the squeezed light field. Sets of differential wavefront sensors (DWSs) at two possible locations can be used for alignment sensing.

Fig. 3
Fig. 3

Squeezing level stability with different alignment signals. The plot shows spectra of the detector’s shot-noise level calculated as a band-limited RMS (BLRMS) in the frequency band from 4 to 5kHz. When locking the alignment of the squeezed beam to the carrier, the contamination of HOMs leads to excess fluctuations within the bandwidth of the alignment loops. When locking to the Michelson sidebands instead, no degradation occurs. There is no measurable improvement with respect to the case without any alignment actuation because alignment fluctuations beyond very slow drifts are currently not a limiting source of squeezing losses. The measurements were done with the alignment well centered on average. Note that there is thus a quadratic relationship between alignment fluctuations and the resulting variations of the shot-noise level.

Fig. 4
Fig. 4

Switching the automatic alignment on. Starting from a situation with significant misalignment, the alignment loops are activated. The loop feedbacks compensate the misalignment, driving the error points to zero, and as a result the observed squeezing level increases.

Fig. 5
Fig. 5

In-loop suppression of the alignment error signals while running the automatic alignment system for two DOFs. Here the signals from one DWS at the pick-off are used and fed back to one of the actuators. The error signals are calibrated to milliradians of angular movement of the steering mirror. The prominent features in the spectra around 1Hz are related to residual pendulum movements and intentional dithers of the interferometer’s output optics. With the current detection electronics the measured error signals are dominated by electronic noise above 6Hz.

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