Abstract

We propose and demonstrate a pump-phase locking technique that makes use of weak pump depletion (WPD) – an unavoidable effect that is usually neglected – in a sub-threshold optical parametric oscillator (OPO). We show that the phase difference between seed and pump beam is imprinted on both light fields by the non-linear interaction in the crystal and can be read out without disturbing the squeezed output. In our experimental setup we observe squeezing levels of 1.96 ± 0.01 dB, with an anti-squeezing level of 3.78 ± 0.02 dB (for a 0.55 mW seed beam at 1064 nm and 67.8 mW of pump light at 532 nm). Our new locking technique allows for the first experimental realization of a pump-phase lock by reading out the pre-existing phase information in the pump field. There is no degradation of the detected squeezed states required to implement this scheme.

© 2015 Optical Society of America

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References

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  1. E. Schrödinger, “Der stetige Übergang von der Mikro-zur Makromechanik,” Naturwissenschaften 14, 664–666 (1926).
    [Crossref]
  2. E. Kennard, “Zur Quantenmechanik einfacher Bewegungstypen,” Zeitschrift für Physik 44, 326–352 (1927).
    [Crossref]
  3. C. Darwin, “Free motion in the wave mechanics,” Proc. Royal Soc. London Ser. A 117, 258–293 (1927).
    [Crossref]
  4. D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proc. Royal Soc. London A 400, 97–117 (1985).
    [Crossref]
  5. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 56, 788 (1986).
    [Crossref]
  6. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
    [Crossref]
  7. H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Classical Quant. Grav. 27, 084027 (2010).
    [Crossref]
  8. H. Vahlbruch, S. Chelkowski, K. Danzmann, and R. Schnabel, “Quantum engineering of squeezed states for quantum communication and metrology,” New J. Phys. 9, 371 (2007).
    [Crossref]
  9. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
    [Crossref] [PubMed]
  10. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
    [Crossref] [PubMed]
  11. L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
    [Crossref] [PubMed]
  12. T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
    [Crossref] [PubMed]
  13. R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [Crossref]
  14. N. P. Robins, B. J. J. Slagmolen, D. A. Shaddock, J. D. Close, and M. B. Gray, “Interferometric, modulation-free laser stabilization,” Opt. Lett. 27, 1905–1907 (2002).
    [Crossref]
  15. T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
    [Crossref]
  16. M. Heurs, I. R. Petersen, M. R. James, and E. H. Huntington, “Homodyne locking of a squeezer,” Opt. Lett. 34, 2465–2467 (2009).
    [Crossref] [PubMed]
  17. K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S421 (2005).
    [Crossref]
  18. N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
    [Crossref] [PubMed]
  19. D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 2007).
  20. H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004).
  21. O. Svelto and D. C. Hanna, Principles of Lasers (Springer, 1998).
    [Crossref]
  22. A. Hemmerich, D. McIntyre, D. Schropp, D. Meschede, and T. Hänsch, “Optically stabilized narrow linewidth semiconductor laser for high resolution spectroscopy,” Opt. Commun. 75, 118–122 (1990).
    [Crossref]

2010 (2)

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

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

2009 (1)

2007 (1)

H. Vahlbruch, S. Chelkowski, K. Danzmann, and R. Schnabel, “Quantum engineering of squeezed states for quantum communication and metrology,” New J. Phys. 9, 371 (2007).
[Crossref]

2006 (1)

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
[Crossref] [PubMed]

2005 (1)

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

2002 (1)

2001 (1)

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[Crossref] [PubMed]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

1990 (1)

A. Hemmerich, D. McIntyre, D. Schropp, D. Meschede, and T. Hänsch, “Optically stabilized narrow linewidth semiconductor laser for high resolution spectroscopy,” Opt. Commun. 75, 118–122 (1990).
[Crossref]

1986 (1)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 56, 788 (1986).
[Crossref]

1985 (1)

D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proc. Royal Soc. London A 400, 97–117 (1985).
[Crossref]

1983 (1)

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

1981 (1)

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

1980 (1)

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

1927 (2)

E. Kennard, “Zur Quantenmechanik einfacher Bewegungstypen,” Zeitschrift für Physik 44, 326–352 (1927).
[Crossref]

C. Darwin, “Free motion in the wave mechanics,” Proc. Royal Soc. London Ser. A 117, 258–293 (1927).
[Crossref]

1926 (1)

E. Schrödinger, “Der stetige Übergang von der Mikro-zur Makromechanik,” Naturwissenschaften 14, 664–666 (1926).
[Crossref]

Bachor, H.-A.

H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004).

Bauchrowitz, J.

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

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Bowen, W. P.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
[Crossref] [PubMed]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

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, K. Danzmann, and R. Schnabel, “Quantum engineering of squeezed states for quantum communication and metrology,” New J. Phys. 9, 371 (2007).
[Crossref]

Cirac, J. I.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[Crossref] [PubMed]

Close, J. D.

Couillaud, B.

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

Crépeau, C.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Danzmann, K.

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

H. Vahlbruch, S. Chelkowski, K. Danzmann, and R. Schnabel, “Quantum engineering of squeezed states for quantum communication and metrology,” New J. Phys. 9, 371 (2007).
[Crossref]

Darwin, C.

C. Darwin, “Free motion in the wave mechanics,” Proc. Royal Soc. London Ser. A 117, 258–293 (1927).
[Crossref]

Deutsch, D.

D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proc. Royal Soc. London A 400, 97–117 (1985).
[Crossref]

Drever, R.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Duan, L. M.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[Crossref] [PubMed]

Eberle, T.

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

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

Ford, G.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Goda, K.

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

Gräf, C.

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

Gray, M. B.

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

N. P. Robins, B. J. J. Slagmolen, D. A. Shaddock, J. D. Close, and M. B. Gray, “Interferometric, modulation-free laser stabilization,” Opt. Lett. 27, 1905–1907 (2002).
[Crossref]

Grosse, N.

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

Grosse, N. B.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
[Crossref] [PubMed]

Hall, J.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Händchen, V.

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

Hanna, D. C.

O. Svelto and D. C. Hanna, Principles of Lasers (Springer, 1998).
[Crossref]

Hansch, T.

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

Hänsch, T.

A. Hemmerich, D. McIntyre, D. Schropp, D. Meschede, and T. Hänsch, “Optically stabilized narrow linewidth semiconductor laser for high resolution spectroscopy,” Opt. Commun. 75, 118–122 (1990).
[Crossref]

Hemmerich, A.

A. Hemmerich, D. McIntyre, D. Schropp, D. Meschede, and T. Hänsch, “Optically stabilized narrow linewidth semiconductor laser for high resolution spectroscopy,” Opt. Commun. 75, 118–122 (1990).
[Crossref]

Heurs, M.

Hollberg, L. W.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 56, 788 (1986).
[Crossref]

Hough, J.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Huntington, E. H.

James, M. R.

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Kennard, E.

E. Kennard, “Zur Quantenmechanik einfacher Bewegungstypen,” Zeitschrift für Physik 44, 326–352 (1927).
[Crossref]

Khalaidovski, A.

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

Kowalski, F.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Lam, P. K.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
[Crossref] [PubMed]

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

Lastzka, N.

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

Lukin, M. D.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[Crossref] [PubMed]

Mavalvala, N.

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

McClelland, D. E.

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

McIntyre, D.

A. Hemmerich, D. McIntyre, D. Schropp, D. Meschede, and T. Hänsch, “Optically stabilized narrow linewidth semiconductor laser for high resolution spectroscopy,” Opt. Commun. 75, 118–122 (1990).
[Crossref]

McKenzie, K.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
[Crossref] [PubMed]

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

Mehmet, M.

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

Mertz, J. C.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 56, 788 (1986).
[Crossref]

Meschede, D.

A. Hemmerich, D. McIntyre, D. Schropp, D. Meschede, and T. Hänsch, “Optically stabilized narrow linewidth semiconductor laser for high resolution spectroscopy,” Opt. Commun. 75, 118–122 (1990).
[Crossref]

Mikhailov, E. E.

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

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 2007).

Müller-Ebhardt, H.

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

Munley, A.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Peres, A.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Petersen, I. R.

Ralph, T. C.

H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004).

Robins, N. P.

Schnabel, R.

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

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

H. Vahlbruch, S. Chelkowski, K. Danzmann, and R. Schnabel, “Quantum engineering of squeezed states for quantum communication and metrology,” New J. Phys. 9, 371 (2007).
[Crossref]

Schrödinger, E.

E. Schrödinger, “Der stetige Übergang von der Mikro-zur Makromechanik,” Naturwissenschaften 14, 664–666 (1926).
[Crossref]

Schropp, D.

A. Hemmerich, D. McIntyre, D. Schropp, D. Meschede, and T. Hänsch, “Optically stabilized narrow linewidth semiconductor laser for high resolution spectroscopy,” Opt. Commun. 75, 118–122 (1990).
[Crossref]

Shaddock, D. A.

Slagmolen, B. J. J.

Slusher, R. E.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 56, 788 (1986).
[Crossref]

Steinlechner, S.

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

Svelto, O.

O. Svelto and D. C. Hanna, Principles of Lasers (Springer, 1998).
[Crossref]

Vahlbruch, H.

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

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

H. Vahlbruch, S. Chelkowski, K. Danzmann, and R. Schnabel, “Quantum engineering of squeezed states for quantum communication and metrology,” New J. Phys. 9, 371 (2007).
[Crossref]

Valley, J. F.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 56, 788 (1986).
[Crossref]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 2007).

Ward, H.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Yurke, B.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 56, 788 (1986).
[Crossref]

Zoller, P.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[Crossref] [PubMed]

Appl. Phys. B (1)

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Classical Quant. Grav. (1)

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

J. Opt. B (1)

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

Nature (1)

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
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H. Vahlbruch, S. Chelkowski, K. Danzmann, and R. Schnabel, “Quantum engineering of squeezed states for quantum communication and metrology,” New J. Phys. 9, 371 (2007).
[Crossref]

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[Crossref]

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

Phys. Rev. Lett. (5)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 56, 788 (1986).
[Crossref]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
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D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 2007).

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Figures (7)

Fig. 1
Fig. 1 Plot of detected variance (Eq. (10)) as a function of total loss ηtot with the initial squeezing value V init ± = ± 5.82   dB.

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Fig. 2
Fig. 2 Schematic overview of the experimental setup. The infrared light is sent through a mode cleaner for spatial mode filtering and power stabilization and then frequency doubled in a linear SHG cavity. The generated green pump light is prepared with a similar mode cleaning cavity and sent to the bow-tie OPO cavity. For locking purposes the infrared light is coupled into the OPO cavity as well. The homodyne detector OPO is responsible for locking the OPO and simultaneously detecting the phase quadrature variance whereas the homodyne detector WPD generates the error signal for locking the green pump phase to the OPO cavity.

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Fig. 3
Fig. 3 Error signal of the transmitted pump light for WPD (black) and transmitted cavity field (red) with swept pump phase versus time. The slight phase offset gives a strong enough signal for pump phase stabilization. For purposes of presentation the scaling of the two signals differs. The tiny effect of WPD on the pump phase is lowpass filtered and amplified by the homodyne photodetector electronic.

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Fig. 4
Fig. 4 Zero span measurements of the shot noise levels for the two different locking schemes (Left: OPO stabilization via dither locking. Right: OPO stabilization via WPD locking.). The shot noise level without pump is shown in black (with scanned pump phase grey), pump phase locked to anti-squeezed phase quadrature in green, pump phase locked to squeezed phase quadrature in red. The blue line illustrates the behaviour of switching the scanned pump phase to in-lock.

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Fig. 5
Fig. 5 Squeezing spectrum around 197.4 MHz with squeezing level (red) and anti-squeezing level (green) versus scanned frequency. Left: OPO stabilization via dither locking. Right: OPO stabilization via WPD locking. The spectrum analyzer settings were: 1.5 MHz resolution bandwidth and 91 Hz video bandwidth with a sweep time of 1.8 s and an internal attenuation of 6 dB. Averaging factor is 10. The noise levels were normalized to shot noise (black).

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Fig. 6
Fig. 6 Plot of pump power dependences of the (anti-)squeezing levels by calculating the outcoupled (anti-)squeezing V A out ± (see Eqs. (7) and (8)) and taking the loss factor of ηpropηhηqe = 0.59 into account (Eq. (10)).

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Fig. 7
Fig. 7 Transfer functions for dither- (blue) and WPD-lock (red). The larger amplitude of the resonance frequencies at 1.7 and 2.2 kHz is based on the high sensitivity of the photodiodes in the homodyne detector for the WPD-lock.

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Tables (1)

Tables Icon

Table 1 Overview of all parameters characterizing the OPO. The calculation of the parameter χ is described in subsection 2.3.

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Equations (16)

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H ^ = − i ℏ ε c ( b ^ † a ^ 2 − a ^ † 2 b ^ ) ,
a ^ ˙ = − 2 ε c a ^ † b ^ − ( κ a + i Δ a ) a ^ + 2 κ A A ^ in + 2 κ l , A A ^ l ,
b ^ ˙ = ε c a ^ 2 − ( κ b + i Δ b ) b ^ + 2 κ B B ^ in + 2 κ l , B B ^ l ,
α = 2 κ A α in κ a − 2 κ A α in | χ | κ a 2
β = 2 κ B | β in | κ B + κ A α in 2 | χ | 2 κ B | β in | κ a 2 e − i θ b
X α out + = 2 α in ( 2 κ a κ A − ( κ a 2 − | χ | 2 ) ) κ a 2 − | χ | 2 − 4 α in κ A | χ | κ a 2 − | χ | 2 cos ( θ b )
X α out − = 4 κ A α in | χ | κ a 2 − | χ | 2 sin ( θ b )
X β out + = | β in |     ( − 2 + 4 κ B κ b ) + 2 α in κ A | χ | | β in | κ a 2 cos ( θ b )
X β out − = 2 α in 2 | χ | κ A | β in | κ a 2 sin ( θ b )
I lock = 2 | χ | κ A α in 2 κ a 2 | β in | | β p , in | sin ( θ b + γ ) ,
V A out + ( θ b = 0 ) = V A in + ( | χ | + κ a − 2 κ A ) 2 ( κ a + | χ | ) 2 + V B in + 4 α in 2 κ A 2 | χ | 2 | β in | 2 κ a 2 ( κ a + | χ | ) 2 + V A l + 4 κ l , A κ A ( κ a + | χ | ) 2 = V A out − ( θ b = π / 2 )
V A out − ( θ b = 0 ) = V A in − ( | χ | − κ a + 2 κ A ) 2 ( κ a − | χ | ) 2 + V B in − 4 α in 2 κ A 2 | χ | 2 | β in | 2 κ a 2 ( κ a − | χ | ) 2 + V A l − 4 κ l , A κ A ( κ a − | χ | ) 2 = V A out + ( θ b = π / 2 )
V init ± = V A in ± ( | χ | ∓ κ a ) 2 ( κ a ± | χ | ) 2
V det ± = η tot V init ± + ( 1 − η tot )
V init − = − V init + = V det − − 1 V det + − 1
V init ± → η esc V A out ± → η prop η h η qe V det ± .

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