Abstract

Low-frequency (Hz~kHz) squeezing is very important in many schemes of quantum precision measurement. But it is more difficult than that at megahertz-frequency because of the introduction of laser low-frequency technical noise. In this paper, we propose a scheme to obtain a low-frequency signal beyond the quantum limit from the frequency comb in a non-degenerate frequency and degenerate polarization optical parametric amplifier (NOPA) operating below threshold with type I phase matching by frequency-shift detection. Low-frequency squeezing immune to laser technical noise is obtained by a detection system with a local beam of two-frequency intense laser. Furthermore, the low-frequency squeezing can be used for phase measurement in Mach-Zehnder interferometer, and the signal-to-noise ratio (SNR) can be enhanced greatly.

© 2015 Optical Society of America

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    [Crossref] [PubMed]
  2. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled Michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
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    [Crossref] [PubMed]
  5. A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92(17), 177903 (2004).
    [Crossref] [PubMed]
  6. V. Josse, M. Sabuncu, N. J. Cerf, G. Leuchs, and U. L. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96(16), 163602 (2006).
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  9. R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1(8), 121 (2010).
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    [Crossref]
  11. R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun. 240(1-3), 185–190 (2004).
    [Crossref]
  12. J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, “Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies,” Phys. Rev. A 70(4), 042315 (2004).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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  18. H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
    [Crossref]
  19. K. Wodkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A 27(4), 2003–2007 (1983).
    [Crossref]
  20. D. D. Crouch and S. L. Braunstein, “Limitations to squeezing in a parametric amplifier due to pump quantum fluctuations,” Phys. Rev. A 38(9), 4696–4711 (1988).
    [Crossref] [PubMed]
  21. J. Gea-Banacloche and M. S. Zubairy, “Influence of pump-phase fluctuations on the squeezing in a degenerate parametric oscillator,” Phys. Rev. A 42(3), 1742–1751 (1990).
    [Crossref] [PubMed]
  22. P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B Quantum Semiclassical Opt. 1(4), 469–474 (1999).
    [Crossref]
  23. 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(16), 161105 (2004).
    [Crossref] [PubMed]
  24. K. Goda, K. McKenzie, E. Mikhailov, P. K. Lam, D. McClelland, and N. Mavalvala, “Photo thermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerateoptical parametric oscillator,” Phys. Rev. A 72(4), 043819 (2005).
    [Crossref]
  25. J. Gea-Banacloche and G. Leuchs, “Squeezed states for interferometric gravitational-wave detectors,” J. Mod. Opt. 34(6-7), 793–811 (1987).
    [Crossref]
  26. B. Yurke, P. Grangier, and R. E. Slusher, “Squeezed-state enhanced two-frequency interferometry,” J. Opt. Soc. Am. B 4(10), 1677–1682 (1987).
    [Crossref]
  27. Z. Zhai and J. Gao, “Low-frequency phase measurement with high-frequency squeezing,” Opt. Express 20(16), 18173–18179 (2012).
    [Crossref] [PubMed]
  28. A. E. Dunlop, E. H. Huntington, C. C. Harb, and T. C. Ralph, “Generation of a frequency comb of squeezing in an optical parametric oscillator,” Phys. Rev. A 73(1), 013817 (2006).
    [Crossref]
  29. R. J. Senior, G. N. Milford, J. Janousek, A. E. Dunlop, K. Wagner, H.-A. Bachor, T. C. Ralph, E. H. Huntington, and C. C. Harb, “Observation of a comb of optical squeezing over many gigahertz of bandwidth,” Opt. Express 15(9), 5310–5317 (2007).
    [Crossref] [PubMed]
  30. R. Yang, J. Zhang, S. Zhai, K. Liu, J. Zhang, and J. Gao, “Generating multiplexed entanglement frequency comb in a nondegenerate optical parametric amplifier,” J. Opt. Soc. Am. B 30(2), 314–318 (2013).
    [Crossref]
  31. M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
    [Crossref]
  32. M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
    [Crossref] [PubMed]

2013 (2)

R. Yang, J. Zhang, S. Zhai, K. Liu, J. Zhang, and J. Gao, “Generating multiplexed entanglement frequency comb in a nondegenerate optical parametric amplifier,” J. Opt. Soc. Am. B 30(2), 314–318 (2013).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

2012 (2)

Z. Zhai and J. Gao, “Low-frequency phase measurement with high-frequency squeezing,” Opt. Express 20(16), 18173–18179 (2012).
[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, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quantum Gravity 29(14), 145015 (2012).
[Crossref]

2011 (1)

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

2010 (3)

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

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

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Graf, K. Danzmann, and R. Schnabel, “The GEO600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

2008 (3)

2007 (1)

2006 (2)

A. E. Dunlop, E. H. Huntington, C. C. Harb, and T. C. Ralph, “Generation of a frequency comb of squeezing in an optical parametric oscillator,” Phys. Rev. A 73(1), 013817 (2006).
[Crossref]

V. Josse, M. Sabuncu, N. J. Cerf, G. Leuchs, and U. L. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96(16), 163602 (2006).
[Crossref] [PubMed]

2005 (3)

S. L. Braunstein and P. V. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77(2), 513–577 (2005).
[Crossref]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled Michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref] [PubMed]

K. Goda, K. McKenzie, E. Mikhailov, P. K. Lam, D. McClelland, and N. Mavalvala, “Photo thermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerateoptical parametric oscillator,” Phys. Rev. A 72(4), 043819 (2005).
[Crossref]

2004 (5)

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(16), 161105 (2004).
[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(16), 161105 (2004).
[Crossref] [PubMed]

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92(17), 177903 (2004).
[Crossref] [PubMed]

R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun. 240(1-3), 185–190 (2004).
[Crossref]

J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, “Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies,” Phys. Rev. A 70(4), 042315 (2004).
[Crossref]

2003 (1)

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90(16), 167903 (2003).
[Crossref] [PubMed]

2002 (1)

W. P. Bowen, R. Schnabel, N. Treps, H.-A. Bachor, and P. K. Lam, “Recovery of continuous wave squeezing at low frequencies,” J. Opt. B Quantum Semiclassical Opt. 4(6), 421–424 (2002).
[Crossref]

1999 (1)

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B Quantum Semiclassical Opt. 1(4), 469–474 (1999).
[Crossref]

1998 (1)

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

1990 (1)

J. Gea-Banacloche and M. S. Zubairy, “Influence of pump-phase fluctuations on the squeezing in a degenerate parametric oscillator,” Phys. Rev. A 42(3), 1742–1751 (1990).
[Crossref] [PubMed]

1988 (1)

D. D. Crouch and S. L. Braunstein, “Limitations to squeezing in a parametric amplifier due to pump quantum fluctuations,” Phys. Rev. A 38(9), 4696–4711 (1988).
[Crossref] [PubMed]

1987 (3)

J. Gea-Banacloche and G. Leuchs, “Squeezed states for interferometric gravitational-wave detectors,” J. Mod. Opt. 34(6-7), 793–811 (1987).
[Crossref]

B. Yurke, P. Grangier, and R. E. Slusher, “Squeezed-state enhanced two-frequency interferometry,” J. Opt. Soc. Am. B 4(10), 1677–1682 (1987).
[Crossref]

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref] [PubMed]

1983 (1)

K. Wodkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A 27(4), 2003–2007 (1983).
[Crossref]

Andersen, U. L.

V. Josse, M. Sabuncu, N. J. Cerf, G. Leuchs, and U. L. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96(16), 163602 (2006).
[Crossref] [PubMed]

Bachor, H.-A.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

R. J. Senior, G. N. Milford, J. Janousek, A. E. Dunlop, K. Wagner, H.-A. Bachor, T. C. Ralph, E. H. Huntington, and C. C. Harb, “Observation of a comb of optical squeezing over many gigahertz of bandwidth,” Opt. Express 15(9), 5310–5317 (2007).
[Crossref] [PubMed]

R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun. 240(1-3), 185–190 (2004).
[Crossref]

W. P. Bowen, R. Schnabel, N. Treps, H.-A. Bachor, and P. K. Lam, “Recovery of continuous wave squeezing at low frequencies,” J. Opt. B Quantum Semiclassical Opt. 4(6), 421–424 (2002).
[Crossref]

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B Quantum Semiclassical Opt. 1(4), 469–474 (1999).
[Crossref]

Bowen, W. P.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[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(16), 161105 (2004).
[Crossref] [PubMed]

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92(17), 177903 (2004).
[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(16), 161105 (2004).
[Crossref] [PubMed]

R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun. 240(1-3), 185–190 (2004).
[Crossref]

W. P. Bowen, R. Schnabel, N. Treps, H.-A. Bachor, and P. K. Lam, “Recovery of continuous wave squeezing at low frequencies,” J. Opt. B Quantum Semiclassical Opt. 4(6), 421–424 (2002).
[Crossref]

Braunstein, S. L.

S. L. Braunstein and P. V. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77(2), 513–577 (2005).
[Crossref]

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

D. D. Crouch and S. L. Braunstein, “Limitations to squeezing in a parametric amplifier due to pump quantum fluctuations,” Phys. Rev. A 38(9), 4696–4711 (1988).
[Crossref] [PubMed]

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. Quantum Gravity 29(14), 145015 (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 an optical parametric oscillator,” J. Opt. B Quantum Semiclassical Opt. 1(4), 469–474 (1999).
[Crossref]

Cerf, N. J.

V. Josse, M. Sabuncu, N. J. Cerf, G. Leuchs, and U. L. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96(16), 163602 (2006).
[Crossref] [PubMed]

Chelkowski, S.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled Michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref] [PubMed]

R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun. 240(1-3), 185–190 (2004).
[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, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quantum Gravity 29(14), 145015 (2012).
[Crossref]

Coudreau, T.

J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, “Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies,” Phys. Rev. A 70(4), 042315 (2004).
[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. A 38(9), 4696–4711 (1988).
[Crossref] [PubMed]

Danzmann, K.

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Graf, K. Danzmann, and R. Schnabel, “The GEO600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled Michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref] [PubMed]

R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun. 240(1-3), 185–190 (2004).
[Crossref]

Daria, V.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Dunlop, A. E.

Fabre, C.

J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, “Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies,” Phys. Rev. A 70(4), 042315 (2004).
[Crossref]

Franzen, A.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled Michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref] [PubMed]

R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun. 240(1-3), 185–190 (2004).
[Crossref]

Fuchs, C. A.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

Furusawa, A.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

Gao, J.

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. A 42(3), 1742–1751 (1990).
[Crossref] [PubMed]

J. Gea-Banacloche and G. Leuchs, “Squeezed states for interferometric gravitational-wave detectors,” J. Mod. Opt. 34(6-7), 793–811 (1987).
[Crossref]

Goda, K.

K. Goda, E. E. Mikhailov, O. Miyakawa, S. Saraf, S. Vass, A. Weinstein, and N. Mavalvala, “Generation of a stable low-frequency squeezed vacuum field with periodically poled KTiOPO4 at 1064 nm,” Opt. Lett. 33(2), 92–94 (2008).
[Crossref] [PubMed]

K. Goda, K. McKenzie, E. Mikhailov, P. K. Lam, D. McClelland, and N. Mavalvala, “Photo thermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerateoptical parametric oscillator,” Phys. Rev. A 72(4), 043819 (2005).
[Crossref]

Graf, C.

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Graf, K. Danzmann, and R. Schnabel, “The GEO600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

Gräf, C.

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

Grangier, P.

Gray, M. B.

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(16), 161105 (2004).
[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(16), 161105 (2004).
[Crossref] [PubMed]

Grosse, N.

K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, “Squeezing in the audio gravitational-wave detection band,” Phys. Rev. Lett. 93(16), 161105 (2004).
[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(16), 161105 (2004).
[Crossref] [PubMed]

R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun. 240(1-3), 185–190 (2004).
[Crossref]

Guo, H. B.

G. Q. He, S. W. Zhu, H. B. Guo, and G. H. Zeng, “Security of quantum key distribution using two-mode squeezed states against optimal beam splitter attack,” Chin. Phys. B 17(4), 1263–1268 (2008).
[Crossref]

Hage, B.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled Michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref] [PubMed]

Harb, C. C.

He, G. Q.

G. Q. He, S. W. Zhu, H. B. Guo, and G. H. Zeng, “Security of quantum key distribution using two-mode squeezed states against optimal beam splitter attack,” Chin. Phys. B 17(4), 1263–1268 (2008).
[Crossref]

Huntington, E. H.

Janousek, J.

Jing, J.

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90(16), 167903 (2003).
[Crossref] [PubMed]

Josse, V.

V. Josse, M. Sabuncu, N. J. Cerf, G. Leuchs, and U. L. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96(16), 163602 (2006).
[Crossref] [PubMed]

Keller, G.

J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, “Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies,” Phys. Rev. A 70(4), 042315 (2004).
[Crossref]

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

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Graf, K. Danzmann, and R. Schnabel, “The GEO600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

Kimble, H. J.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref] [PubMed]

Knittel, J.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[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. Quantum Gravity 29(14), 145015 (2012).
[Crossref]

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

K. Goda, K. McKenzie, E. Mikhailov, P. K. Lam, D. McClelland, and N. Mavalvala, “Photo thermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerateoptical parametric oscillator,” Phys. Rev. A 72(4), 043819 (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(16), 161105 (2004).
[Crossref] [PubMed]

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92(17), 177903 (2004).
[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(16), 161105 (2004).
[Crossref] [PubMed]

R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun. 240(1-3), 185–190 (2004).
[Crossref]

W. P. Bowen, R. Schnabel, N. Treps, H.-A. Bachor, and P. K. Lam, “Recovery of continuous wave squeezing at low frequencies,” J. Opt. B Quantum Semiclassical Opt. 4(6), 421–424 (2002).
[Crossref]

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B Quantum Semiclassical Opt. 1(4), 469–474 (1999).
[Crossref]

Lance, A. M.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92(17), 177903 (2004).
[Crossref] [PubMed]

Lastzka, N.

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Graf, K. Danzmann, and R. Schnabel, “The GEO600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

Laurat, J.

J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, “Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies,” Phys. Rev. A 70(4), 042315 (2004).
[Crossref]

Leuchs, G.

V. Josse, M. Sabuncu, N. J. Cerf, G. Leuchs, and U. L. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96(16), 163602 (2006).
[Crossref] [PubMed]

J. Gea-Banacloche and G. Leuchs, “Squeezed states for interferometric gravitational-wave detectors,” J. Mod. Opt. 34(6-7), 793–811 (1987).
[Crossref]

Liu, K.

Loock, P. V.

S. L. Braunstein and P. V. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77(2), 513–577 (2005).
[Crossref]

Mavalvala, N.

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

K. Goda, E. E. Mikhailov, O. Miyakawa, S. Saraf, S. Vass, A. Weinstein, and N. Mavalvala, “Generation of a stable low-frequency squeezed vacuum field with periodically poled KTiOPO4 at 1064 nm,” Opt. Lett. 33(2), 92–94 (2008).
[Crossref] [PubMed]

K. Goda, K. McKenzie, E. Mikhailov, P. K. Lam, D. McClelland, and N. Mavalvala, “Photo thermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerateoptical parametric oscillator,” Phys. Rev. A 72(4), 043819 (2005).
[Crossref]

McClelland, D.

K. Goda, K. McKenzie, E. Mikhailov, P. K. Lam, D. McClelland, and N. Mavalvala, “Photo thermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerateoptical parametric oscillator,” Phys. Rev. A 72(4), 043819 (2005).
[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, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Class. Quantum Gravity 29(14), 145015 (2012).
[Crossref]

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1(8), 121 (2010).
[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(16), 161105 (2004).
[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(16), 161105 (2004).
[Crossref] [PubMed]

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B Quantum Semiclassical Opt. 1(4), 469–474 (1999).
[Crossref]

McKenzie, K.

K. Goda, K. McKenzie, E. Mikhailov, P. K. Lam, D. McClelland, and N. Mavalvala, “Photo thermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerateoptical parametric oscillator,” Phys. Rev. A 72(4), 043819 (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(16), 161105 (2004).
[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(16), 161105 (2004).
[Crossref] [PubMed]

Mikhailov, E.

K. Goda, K. McKenzie, E. Mikhailov, P. K. Lam, D. McClelland, and N. Mavalvala, “Photo thermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerateoptical parametric oscillator,” Phys. Rev. A 72(4), 043819 (2005).
[Crossref]

Mikhailov, E. E.

Milford, G. N.

Miyakawa, O.

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. Quantum Gravity 29(14), 145015 (2012).
[Crossref]

Novikova, I.

Peng, K.

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90(16), 167903 (2003).
[Crossref] [PubMed]

Polzik, E. S.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

Ralph, T. C.

R. J. Senior, G. N. Milford, J. Janousek, A. E. Dunlop, K. Wagner, H.-A. Bachor, T. C. Ralph, E. H. Huntington, and C. C. Harb, “Observation of a comb of optical squeezing over many gigahertz of bandwidth,” Opt. Express 15(9), 5310–5317 (2007).
[Crossref] [PubMed]

A. E. Dunlop, E. H. Huntington, C. C. Harb, and T. C. Ralph, “Generation of a frequency comb of squeezing in an optical parametric oscillator,” Phys. Rev. A 73(1), 013817 (2006).
[Crossref]

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B Quantum Semiclassical Opt. 1(4), 469–474 (1999).
[Crossref]

Sabuncu, M.

V. Josse, M. Sabuncu, N. J. Cerf, G. Leuchs, and U. L. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96(16), 163602 (2006).
[Crossref] [PubMed]

Sanders, B. C.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92(17), 177903 (2004).
[Crossref] [PubMed]

Saraf, S.

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. Quantum Gravity 29(14), 145015 (2012).
[Crossref]

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Graf, K. Danzmann, and R. Schnabel, “The GEO600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1(8), 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 Gravity 27(8), 084027 (2010).
[Crossref]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled Michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref] [PubMed]

R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun. 240(1-3), 185–190 (2004).
[Crossref]

W. P. Bowen, R. Schnabel, N. Treps, H.-A. Bachor, and P. K. Lam, “Recovery of continuous wave squeezing at low frequencies,” J. Opt. B Quantum Semiclassical Opt. 4(6), 421–424 (2002).
[Crossref]

Senior, R. J.

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. Quantum Gravity 29(14), 145015 (2012).
[Crossref]

Slusher, R. E.

Sorensen, J. L.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref] [PubMed]

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. Quantum Gravity 29(14), 145015 (2012).
[Crossref]

Symul, T.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92(17), 177903 (2004).
[Crossref] [PubMed]

Taylor, M. A.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Treps, N.

J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, “Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies,” Phys. Rev. A 70(4), 042315 (2004).
[Crossref]

W. P. Bowen, R. Schnabel, N. Treps, H.-A. Bachor, and P. K. Lam, “Recovery of continuous wave squeezing at low frequencies,” J. Opt. B Quantum Semiclassical Opt. 4(6), 421–424 (2002).
[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. Quantum Gravity 29(14), 145015 (2012).
[Crossref]

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Graf, K. Danzmann, and R. Schnabel, “The GEO600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled Michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref] [PubMed]

R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun. 240(1-3), 185–190 (2004).
[Crossref]

Vass, S.

Wagner, K.

Weinstein, A.

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(16), 161105 (2004).
[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(16), 161105 (2004).
[Crossref] [PubMed]

Wodkiewicz, K.

K. Wodkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A 27(4), 2003–2007 (1983).
[Crossref]

Wu, L. A.

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref] [PubMed]

Xiao, M.

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref] [PubMed]

Xie, C.

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90(16), 167903 (2003).
[Crossref] [PubMed]

Yan, Y.

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90(16), 167903 (2003).
[Crossref] [PubMed]

Yang, R.

Yurke, B.

Zeng, G. H.

G. Q. He, S. W. Zhu, H. B. Guo, and G. H. Zeng, “Security of quantum key distribution using two-mode squeezed states against optimal beam splitter attack,” Chin. Phys. B 17(4), 1263–1268 (2008).
[Crossref]

Zhai, S.

Zhai, Z.

Zhang, J.

Zhao, F.

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90(16), 167903 (2003).
[Crossref] [PubMed]

Zhu, S. W.

G. Q. He, S. W. Zhu, H. B. Guo, and G. H. Zeng, “Security of quantum key distribution using two-mode squeezed states against optimal beam splitter attack,” Chin. Phys. B 17(4), 1263–1268 (2008).
[Crossref]

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. A 42(3), 1742–1751 (1990).
[Crossref] [PubMed]

K. Wodkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A 27(4), 2003–2007 (1983).
[Crossref]

Chin. Phys. B (1)

G. Q. He, S. W. Zhu, H. B. Guo, and G. H. Zeng, “Security of quantum key distribution using two-mode squeezed states against optimal beam splitter attack,” Chin. Phys. B 17(4), 1263–1268 (2008).
[Crossref]

Class. Quantum Gravity (3)

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Graf, K. Danzmann, and R. Schnabel, “The GEO600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (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. Quantum Gravity 29(14), 145015 (2012).
[Crossref]

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010).
[Crossref]

J. Mod. Opt. (1)

J. Gea-Banacloche and G. Leuchs, “Squeezed states for interferometric gravitational-wave detectors,” J. Mod. Opt. 34(6-7), 793–811 (1987).
[Crossref]

J. Opt. B Quantum Semiclassical Opt. (2)

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B Quantum Semiclassical Opt. 1(4), 469–474 (1999).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 The scheme of a low-frequency squeezing generated from squeezed frequency comb of NOPA. χ ( 2 ) : Nonlinear crystal, BS: Beam splitter, D: Photo-detector, SA: Spectrum analyzer.
Fig. 2
Fig. 2 The squeezed comb noise spectra vs the side-band frequency, Inset shows the detail of a comb tooth.
Fig. 3
Fig. 3 Phase quadrature noise spectra of output versus side-band frequency. Inset shows the detail of the squeezing level of the zero-order tooth.
Fig. 4
Fig. 4 Noise spectra with Δ = 0.3 2 π MHz (dot line), Δ = 0 (solid line). (a) Squeezing of the zero-order tooth. (b) Squeezing of the first order tooth
Fig. 5
Fig. 5 Low-frequency squeezing by two-frequency local beam ω L ± ω 1 , ω 1 = 2 2 π MHz and ω L ± ω 2 , ω 2 = 800 2 π MHz , respectively.
Fig. 6
Fig. 6 The noise spectra in low frequency domain. Two curves correspond to two kinds of two-frequency laser: curve i, ω L ± 2 2 π MHz ; curve ii, ω L ± 800 2 π MHz .
Fig. 7
Fig. 7 Application of low-frequency squeezing for phase measurement in Mach-Zehnder interferometer. EOM: Electro optic modulator, C: Cavity, BS1, BS2: Beam splitter, D: Photo-detector, SA: Spectrum analyzer.
Fig. 8
Fig. 8 SNR vs frequency for low-frequency phase measurement in Mach-Zehnder interferometer with two kinds of two-frequency laser, curve i, ω L ± 2 2 π MHz ; curve ii, ω L ± 800 2 π MHz .

Equations (16)

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H = i χ ( 2 ) ( a ^ 0 a ^ + a ^ a ^ 0 a ^ + a ^ ) .
a ^ + ( t+ τ ) = e i τ [ χ τ a ^ ( t ) + ( 1 k τ ) a ^ + ( t ) + 2 k τ b ^ + i n ( t ) + 2 γ τ c ^ + ( t ) ] ,
a ^ ( t+ τ ) = e i τ [ χ τ a ^ + ( t ) + ( 1 k τ ) a ^ ( t ) + 2 k τ b ^ i n ( t ) + 2 γ τ c ^ ( t ) ] .
δ a ^ + ( ω ) [ e i ω τ ( 1 k τ ) ] = χ τ δ a ^ ( ω ) + 2 k τ δ b ^ + i n ( ω ) + 2 γ τ δ c ^ + ( ω ) ,
δ a ^ ( ω ) [ e i ω τ ( 1 k τ ) ] = χ τ δ a ^ + ( ω ) + 2 k τ δ b ^ i n ( ω ) + 2 γ τ δ c ^ ( ω ) .
δ a ^ + ( ω ) = [ 2 k τ δ b ^ + i n ( ω ) + 2 γ τ δ c ^ + ( ω ) ] [ e i ω τ ( 1 k τ ) ] [ e i ω τ ( 1 k τ ) ] 2 χ 2 τ 2 χ τ 2 [ 2 k δ b ^ i n ( ω ) + 2 γ δ c ^ ( ω ) ] [ e i ω τ ( 1 k τ ) ] 2 χ 2 τ 2 ,
δ a ^ ( ω ) = [ 2 k τ δ b ^ i n ( ω ) + 2 γ τ δ b c ^ ( ω ) ] [ e i ω τ ( 1 k τ ) ] [ e i ω τ ( 1 k τ ) ] 2 χ 2 τ 2 χ τ 2 [ 2 k δ b ^ + i n ( ω ) + 2 γ δ c ^ + ( ω ) ] [ e i ω τ ( 1 k τ ) ] 2 χ 2 τ 2 ,
V + x , y ( ω ) = | k 2 + χ 2 ( 1 e i ω τ τ ) 2 ( k 1 e i ω τ τ ) 2 χ 2 | 2 V + i n x , y + | 2 k χ ( k 1 e i ω τ τ ) 2 χ 2 | 2 V i n x , y + | 2 k γ ( k 1 e i ω τ τ ) ( k 1 e i ω τ τ ) 2 χ 2 | 2 V + c x , y + | 2 χ k γ ( k 1 e i ω τ τ ) 2 χ 2 | 2 V c x , y ,
V x , y ( ω ) = | k 2 + χ 2 ( 1 e i ω τ τ ) 2 ( k 1 e i ω τ τ ) 2 χ 2 | 2 V i n x , y + | 2 k χ ( k 1 e i ω τ τ ) 2 χ 2 | 2 V + i n x , y + | 2 k γ ( k 1 e i ω τ τ ) ( k 1 e i ω τ τ ) 2 χ 2 | 2 V c x , y + | 2 χ k γ ( k 1 e i ω τ τ ) 2 χ 2 | 2 V + c x , y .
δ X ^ ± ( ω ) = δ A ^ ± o u t ( ω ) + δ A ^ ± o u t ( ω ) , δ Y ^ ± ( ω ) = i [ δ A ^ ± o u t ( ω ) δ A ^ ± o u t ( ω ) ] δ X ^ ± i n ( ω ) = δ b ^ ± i n ( ω ) + δ b ^ ± i n ( ω ) , δ Y ^ ± i n ( ω ) = i [ δ b ^ ± i n ( ω ) δ b ^ ± i n ( ω ) ] . δ X ^ ± c ( ω ) = δ c ^ ± i n ( ω ) + δ c ^ ± i n ( ω ) , δ Y ^ ± c ( ω ) = i [ δ c ^ ± i n ( ω ) δ c ^ ± i n ( ω ) ]
V ± x ( ω ) = | δ X ^ ± | 2 , V ± y ( ω ) = | δ Y ^ ± | 2 , V ± i n x ( ω ) = | δ X ^ ± i n | 2 , V ± i n y ( ω ) = | δ Y ^ ± i n | 2 , V ± c x ( ω ) = | δ X ^ ± c | 2 , V ± c y ( ω ) = | δ Y ^ ± c | 2
V + , x ( ω ) = | ( k χ ) 2 ( 1 e i ω τ τ ) 2 ( k 1 e i ω τ τ ) 2 χ 2 | 2 V + i n x + | ( k χ ) 2 ( 1 e i ω τ τ ) 2 ( k 1 e i ω τ τ ) 2 χ 2 | 2 V i n x + | 2 k γ ( k 1 e i ω τ τ χ ) ( k 1 e i ω τ τ ) 2 χ 2 | 2 V + c x + | 2 k γ ( k 1 e i ω τ τ χ ) ( k 1 e i ω τ τ ) 2 χ 2 | 2 V c x ,
V + , y ( ω ) = | ( k χ ) 2 ( 1 e i ω τ τ ) 2 ( k 1 e i ω τ τ ) 2 χ 2 | 2 V + i n y + | ( k χ ) 2 ( 1 e i ω τ τ ) 2 ( k 1 e i ω τ τ ) 2 χ 2 | 2 V i n y + | 2 k γ ( k 1 e i ω τ τ χ ) ( k 1 e i ω τ τ ) 2 χ 2 | 2 V + c y + | 2 k γ ( χ k + 1 e i ω τ τ ) ( k 1 e i ω τ τ ) 2 χ 2 | 2 V c y .
V + , x ( ω ) = | [ ( k 1 e i ( ω + ) τ τ ) ( k + 1 e i ( ω ) τ τ ) + χ 2 2 k χ ( k 1 e i ( ω + ) τ τ ) ( k 1 e i ( ω ) τ τ ) χ 2 | 2 V + i n x + | [ ( k 1 e i ( ω + ) τ τ ) ( k + 1 e i ( ω ) τ τ ) + χ 2 2 k χ ( k 1 e i ( ω + ) τ τ ) ( k 1 e i ( ω ) τ τ ) χ 2 | 2 V i n x , + | 2 k γ ( k 1 e i ( ω + ) τ τ χ ) ( k 1 e i ( ω + ) τ τ ) ( k 1 e i ( ω ) τ τ ) χ 2 | 2 V + c x + | 2 k γ ( k 1 e i ( ω + ) τ τ χ ) ( k 1 e i ( ω + ) τ τ ) ( k 1 e i ( ω ) τ τ ) χ 2 | 2 V c x
V + , y ( ω ) = | [ ( k 1 e i ( ω + ) τ τ ) ( k + 1 e i ( ω ) τ τ ) + χ 2 2 k χ ( k 1 e i ( ω + ) τ τ ) ( k 1 e i ( ω ) τ τ ) χ 2 | 2 V + i n y + | [ ( k 1 e i ( ω + ) τ τ ) ( k + 1 e i ( ω ) τ τ ) + χ 2 2 k χ ( k 1 e i ( ω + ) τ τ ) ( k 1 e i ( ω ) τ τ ) χ 2 | 2 V i n y . + | 2 k γ ( k 1 e i ( ω + ) τ τ χ ) ( k 1 e i ( ω + ) τ τ ) ( k 1 e i ( ω ) τ τ ) χ 2 | 2 V + c y + | 2 k γ ( χ + 1 e i ( ω + ) τ τ k ) ( k 1 e i ( ω + ) τ τ ) ( k 1 e i ( ω ) τ τ ) χ 2 | 2 V c y
S N R = 2 N T θ Ω 2 V b φ + π / 2 ( Ω + w i ) + V b φ + π / 2 ( Ω w i ) .

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