Abstract

We propose a new interferometer technique for high-precision phase measurements such as those in gravitational wave detection. The technique utilizes a pair of optically coupled resonators that provide identical resonance conditions for the upper as well the lower phase modulation signal sidebands. This symmetry significantly reduces the noise spectral density in a wide frequency band compared with single-sideband recycling topologies of current and planned gravitational wave detectors. Furthermore, the application of squeezed states of light becomes less demanding.

© 2007 Optical Society of America

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  1. D. Sigg (for the LIGO Science Collaboration), Class. Quantum Grav. 23, S51 (2006).
    [CrossRef]
  2. M. Ando, Phys. Rev. Lett. 86, 3950 (2001).
    [CrossRef] [PubMed]
  3. F. Acernese, Class. Quantum Grav. 23, S635 (2006).
    [CrossRef]
  4. S. Hild (for the LIGO Scientific Collaboration), Class. Quantum Grav. 23, S643 (2006).
    [CrossRef]
  5. G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
    [CrossRef]
  6. A. Weinstein, Class. Quantum Grav. 19, 1575-1584 (2002).
    [CrossRef]
  7. C. M. Caves, Phys. Rev. D 23, 1693 (1981).
    [CrossRef]
  8. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 97, 011101 (2006).
    [CrossRef] [PubMed]
  9. J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, Phys. Rev. D 68, 042001 (2003).
    [CrossRef]
  10. H. J. Kimble, Y. Levin, A. B. Matsko, K. S. Thorne, and S. P. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
    [CrossRef]
  11. R. Schnabel, J. Harms, K. A. Strain, and K. Danzmann, Class. Quantum Grav. 21, S1045 (2004).
    [CrossRef]
  12. This feature has previously been noticed by B. J. Meers and R. W. P. Drever in a draft titled "Doubly resonant signal recycling for interferometric gravitational wave detectors."
  13. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 95, 211102 (2005).
    [CrossRef] [PubMed]
  14. G. de Vine, M. Gray, D. E. McClelland, Y. Chen, and S. Whitcomb, Phys. Lett. A 316, 17 (2003).
    [CrossRef]
  15. A. Thüring, H. Lück, and K. Danzmann, Phys. Rev. E 72, 066615 (2005).
    [CrossRef]
  16. A. Buonanno and Y. Chen, Phys. Rev. D 65, 042001 (2002).
    [CrossRef]
  17. V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, Phys. Lett. A 264, 1 (1999).
    [CrossRef]

2006 (4)

D. Sigg (for the LIGO Science Collaboration), Class. Quantum Grav. 23, S51 (2006).
[CrossRef]

F. Acernese, Class. Quantum Grav. 23, S635 (2006).
[CrossRef]

S. Hild (for the LIGO Scientific Collaboration), Class. Quantum Grav. 23, S643 (2006).
[CrossRef]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

2005 (2)

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 95, 211102 (2005).
[CrossRef] [PubMed]

A. Thüring, H. Lück, and K. Danzmann, Phys. Rev. E 72, 066615 (2005).
[CrossRef]

2004 (1)

R. Schnabel, J. Harms, K. A. Strain, and K. Danzmann, Class. Quantum Grav. 21, S1045 (2004).
[CrossRef]

2003 (2)

G. de Vine, M. Gray, D. E. McClelland, Y. Chen, and S. Whitcomb, Phys. Lett. A 316, 17 (2003).
[CrossRef]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, Phys. Rev. D 68, 042001 (2003).
[CrossRef]

2002 (2)

A. Weinstein, Class. Quantum Grav. 19, 1575-1584 (2002).
[CrossRef]

A. Buonanno and Y. Chen, Phys. Rev. D 65, 042001 (2002).
[CrossRef]

2001 (2)

H. J. Kimble, Y. Levin, A. B. Matsko, K. S. Thorne, and S. P. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[CrossRef]

M. Ando, Phys. Rev. Lett. 86, 3950 (2001).
[CrossRef] [PubMed]

1999 (1)

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, Phys. Lett. A 264, 1 (1999).
[CrossRef]

1998 (1)

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

1981 (1)

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

Acernese, F.

F. Acernese, Class. Quantum Grav. 23, S635 (2006).
[CrossRef]

Ando, M.

M. Ando, Phys. Rev. Lett. 86, 3950 (2001).
[CrossRef] [PubMed]

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, Phys. Lett. A 264, 1 (1999).
[CrossRef]

Buonanno, A.

A. Buonanno and Y. Chen, Phys. Rev. D 65, 042001 (2002).
[CrossRef]

Caves, C. M.

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

Chelkowski, S.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 95, 211102 (2005).
[CrossRef] [PubMed]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, Phys. Rev. D 68, 042001 (2003).
[CrossRef]

Chen, Y.

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, Phys. Rev. D 68, 042001 (2003).
[CrossRef]

G. de Vine, M. Gray, D. E. McClelland, Y. Chen, and S. Whitcomb, Phys. Lett. A 316, 17 (2003).
[CrossRef]

A. Buonanno and Y. Chen, Phys. Rev. D 65, 042001 (2002).
[CrossRef]

Danzmann, K.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

A. Thüring, H. Lück, and K. Danzmann, Phys. Rev. E 72, 066615 (2005).
[CrossRef]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 95, 211102 (2005).
[CrossRef] [PubMed]

R. Schnabel, J. Harms, K. A. Strain, and K. Danzmann, Class. Quantum Grav. 21, S1045 (2004).
[CrossRef]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, Phys. Rev. D 68, 042001 (2003).
[CrossRef]

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

de Vine, G.

G. de Vine, M. Gray, D. E. McClelland, Y. Chen, and S. Whitcomb, Phys. Lett. A 316, 17 (2003).
[CrossRef]

Drever, R. W. P.

This feature has previously been noticed by B. J. Meers and R. W. P. Drever in a draft titled "Doubly resonant signal recycling for interferometric gravitational wave detectors."

Franzen, A.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 95, 211102 (2005).
[CrossRef] [PubMed]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, Phys. Rev. D 68, 042001 (2003).
[CrossRef]

Gorodetsky, M. L.

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, Phys. Lett. A 264, 1 (1999).
[CrossRef]

Gray, M.

G. de Vine, M. Gray, D. E. McClelland, Y. Chen, and S. Whitcomb, Phys. Lett. A 316, 17 (2003).
[CrossRef]

Hage, B.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 95, 211102 (2005).
[CrossRef] [PubMed]

Harms, J.

R. Schnabel, J. Harms, K. A. Strain, and K. Danzmann, Class. Quantum Grav. 21, S1045 (2004).
[CrossRef]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, Phys. Rev. D 68, 042001 (2003).
[CrossRef]

Heinzel, G.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Hild, S.

S. Hild (for the LIGO Scientific Collaboration), Class. Quantum Grav. 23, S643 (2006).
[CrossRef]

Kimble, H. J.

H. J. Kimble, Y. Levin, A. B. Matsko, K. S. Thorne, and S. P. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[CrossRef]

Levin, Y.

H. J. Kimble, Y. Levin, A. B. Matsko, K. S. Thorne, and S. P. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[CrossRef]

Lück, H.

A. Thüring, H. Lück, and K. Danzmann, Phys. Rev. E 72, 066615 (2005).
[CrossRef]

Matsko, A. B.

H. J. Kimble, Y. Levin, A. B. Matsko, K. S. Thorne, and S. P. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[CrossRef]

McClelland, D. E.

G. de Vine, M. Gray, D. E. McClelland, Y. Chen, and S. Whitcomb, Phys. Lett. A 316, 17 (2003).
[CrossRef]

Meers, B. J.

This feature has previously been noticed by B. J. Meers and R. W. P. Drever in a draft titled "Doubly resonant signal recycling for interferometric gravitational wave detectors."

Mizuno, J.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Rüdiger, A.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Schilling, R.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Schnabel, R.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 95, 211102 (2005).
[CrossRef] [PubMed]

R. Schnabel, J. Harms, K. A. Strain, and K. Danzmann, Class. Quantum Grav. 21, S1045 (2004).
[CrossRef]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, Phys. Rev. D 68, 042001 (2003).
[CrossRef]

Sigg, D.

D. Sigg (for the LIGO Science Collaboration), Class. Quantum Grav. 23, S51 (2006).
[CrossRef]

Skeldon, K. D.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Strain, K. A.

R. Schnabel, J. Harms, K. A. Strain, and K. Danzmann, Class. Quantum Grav. 21, S1045 (2004).
[CrossRef]

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Thorne, K. S.

H. J. Kimble, Y. Levin, A. B. Matsko, K. S. Thorne, and S. P. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[CrossRef]

Thüring, A.

A. Thüring, H. Lück, and K. Danzmann, Phys. Rev. E 72, 066615 (2005).
[CrossRef]

Vahlbruch, H.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 95, 211102 (2005).
[CrossRef] [PubMed]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, Phys. Rev. D 68, 042001 (2003).
[CrossRef]

Vyatchanin, S. P.

H. J. Kimble, Y. Levin, A. B. Matsko, K. S. Thorne, and S. P. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, Phys. Lett. A 264, 1 (1999).
[CrossRef]

Weinstein, A.

A. Weinstein, Class. Quantum Grav. 19, 1575-1584 (2002).
[CrossRef]

Whitcomb, S.

G. de Vine, M. Gray, D. E. McClelland, Y. Chen, and S. Whitcomb, Phys. Lett. A 316, 17 (2003).
[CrossRef]

Willke, B.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Winkler, W.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Class. Quantum Grav. (5)

D. Sigg (for the LIGO Science Collaboration), Class. Quantum Grav. 23, S51 (2006).
[CrossRef]

F. Acernese, Class. Quantum Grav. 23, S635 (2006).
[CrossRef]

S. Hild (for the LIGO Scientific Collaboration), Class. Quantum Grav. 23, S643 (2006).
[CrossRef]

A. Weinstein, Class. Quantum Grav. 19, 1575-1584 (2002).
[CrossRef]

R. Schnabel, J. Harms, K. A. Strain, and K. Danzmann, Class. Quantum Grav. 21, S1045 (2004).
[CrossRef]

Phys. Lett. A (2)

G. de Vine, M. Gray, D. E. McClelland, Y. Chen, and S. Whitcomb, Phys. Lett. A 316, 17 (2003).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, Phys. Lett. A 264, 1 (1999).
[CrossRef]

Phys. Rev. D (4)

A. Buonanno and Y. Chen, Phys. Rev. D 65, 042001 (2002).
[CrossRef]

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, Phys. Rev. D 68, 042001 (2003).
[CrossRef]

H. J. Kimble, Y. Levin, A. B. Matsko, K. S. Thorne, and S. P. Vyatchanin, Phys. Rev. D 65, 022002 (2001).
[CrossRef]

Phys. Rev. E (1)

A. Thüring, H. Lück, and K. Danzmann, Phys. Rev. E 72, 066615 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 95, 211102 (2005).
[CrossRef] [PubMed]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

M. Ando, Phys. Rev. Lett. 86, 3950 (2001).
[CrossRef] [PubMed]

Other (1)

This feature has previously been noticed by B. J. Meers and R. W. P. Drever in a draft titled "Doubly resonant signal recycling for interferometric gravitational wave detectors."

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Figures (3)

Fig. 1
Fig. 1

Top left (shaded), topology of the current GW detector GEO 600. The mirror PRM in the laser input port realizes so-called power recycling. The SR mirror (SRM) in the output port establishes a carrier light detuned single-sideband SR cavity. Bottom left, extension for a broadband shot-noise reduction utilizing squeezed states. Right, topology, proposed here. Two optically coupled cavities are formed with the help of an additional mirror TSRM. Their resonance doublet enables detuned TSR, resulting in lower shot noise. Squeezed states can be used without an additional filter cavity.

Fig. 2
Fig. 2

Resonance doublet of two optically coupled Fabry–Perot resonators. The frequency splitting f sp = ± 1 kHz is related to the carrier frequency f 0 , here set to zero.

Fig. 3
Fig. 3

Comparison of linear noise spectral densities (NSD) of TSR (solid curves) with detuned single-sideband SR (a) without squeezed input and (b) with squeezed input ( r = 1 ) . The dashed-dotted curves represent SR of the upper sideband; the dotted curves represent SR of the lower sideband. In both cases the TSR topology yields a lower noise spectral density, by up to a factor of two, at sideband frequencies above 40 Hz . For a detailed description refer to the text.

Equations (3)

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

1 2 arg [ ρ 23 ( ω sp L SR 2 c ) ] = L SR 1 L SR 2 ω sp L SR 2 c ,
T c = 1 4 cos 2 ( 2 ω sp L SR 1 c ) ρ end 2 ( 1 + ρ end 2 ) 2 .
T c = 1 cos 2 ( 2 ω sp L SR 1 c ) .

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