Abstract

We study the implementation of a correlation measurement technique for the characterization of squeezed light. We show that the sign of the covariance coefficient revealed from the time-resolved correlation data allow us to distinguish among squeezed, coherent, and thermal states. In contrast to the traditional method of characterizing squeezed light, involving measurement of the variation of the difference photocurrent, the correlation measurement method allows one to eliminate the contribution of the electronic noise, which becomes a crucial issue in experiments with dim sources of squeezed light.

© 2008 Optical Society of America

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  1. R. Hanbury Brown and R. Q. Twiss, Nature (London) 178, 1046 (1956).
    [CrossRef]
  2. R. Loudon, The Quantum Theory of Light (Oxford U. Press, 2000).
  3. M. Raymer and M. Beck, in Quantum State Estimation, M.G. A.Paris and J.Rehacek, eds. (Springer-Verlag, 2004), p. 235.
  4. A. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
    [CrossRef] [PubMed]
  5. A. Zavatta, S. Viciani, and M. Bellini, Phys. Rev. A 70, 053821 (2004).
    [CrossRef]
  6. J. Appel, D. Hoffman, E. Figueroa, and A. Lvovsky, Phys. Rev. A 75, 035802 (2007).
    [CrossRef]
  7. A. Van der Ziel, Noise in Solid State Devices and Circuits (Wiley, 1986).
  8. U. Andersen and G. Leuchs, Laser Phys. 15, 129 (2005).
  9. Z. Y. Ou, C. K. Hong, and L. Mandel, Phys. Rev. A 36, 192 (1987).
    [CrossRef] [PubMed]
  10. M. Koashi, K. Kono, T. Hirano, and M. Matsuoka, Phys. Rev. Lett. 71, 1164 (1993).
    [CrossRef] [PubMed]
  11. N. B. Grosse, T. Symul, M. Stobin'ska, T. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
    [CrossRef] [PubMed]
  12. H. Bachor and T. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley, 2004).
    [CrossRef]
  13. J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Opt. Lett. 30, 1192 (2005).
    [CrossRef] [PubMed]
  14. J. Corney, P. Drummond, J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Phys. Rev. Lett. 97, 023606 (2006).
    [CrossRef] [PubMed]

2007

J. Appel, D. Hoffman, E. Figueroa, and A. Lvovsky, Phys. Rev. A 75, 035802 (2007).
[CrossRef]

N. B. Grosse, T. Symul, M. Stobin'ska, T. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef] [PubMed]

2006

J. Corney, P. Drummond, J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Phys. Rev. Lett. 97, 023606 (2006).
[CrossRef] [PubMed]

2005

2004

A. Zavatta, S. Viciani, and M. Bellini, Phys. Rev. A 70, 053821 (2004).
[CrossRef]

2001

A. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

1993

M. Koashi, K. Kono, T. Hirano, and M. Matsuoka, Phys. Rev. Lett. 71, 1164 (1993).
[CrossRef] [PubMed]

1987

Z. Y. Ou, C. K. Hong, and L. Mandel, Phys. Rev. A 36, 192 (1987).
[CrossRef] [PubMed]

1956

R. Hanbury Brown and R. Q. Twiss, Nature (London) 178, 1046 (1956).
[CrossRef]

Aichele, T.

A. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Andersen, U.

U. Andersen and G. Leuchs, Laser Phys. 15, 129 (2005).

Andersen, U. L.

J. Corney, P. Drummond, J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Phys. Rev. Lett. 97, 023606 (2006).
[CrossRef] [PubMed]

J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Opt. Lett. 30, 1192 (2005).
[CrossRef] [PubMed]

Appel, J.

J. Appel, D. Hoffman, E. Figueroa, and A. Lvovsky, Phys. Rev. A 75, 035802 (2007).
[CrossRef]

Bachor, H.

H. Bachor and T. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley, 2004).
[CrossRef]

Beck, M.

M. Raymer and M. Beck, in Quantum State Estimation, M.G. A.Paris and J.Rehacek, eds. (Springer-Verlag, 2004), p. 235.

Bellini, M.

A. Zavatta, S. Viciani, and M. Bellini, Phys. Rev. A 70, 053821 (2004).
[CrossRef]

Benson, O.

A. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Corney, J.

J. Corney, P. Drummond, J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Phys. Rev. Lett. 97, 023606 (2006).
[CrossRef] [PubMed]

Drummond, P.

J. Corney, P. Drummond, J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Phys. Rev. Lett. 97, 023606 (2006).
[CrossRef] [PubMed]

Figueroa, E.

J. Appel, D. Hoffman, E. Figueroa, and A. Lvovsky, Phys. Rev. A 75, 035802 (2007).
[CrossRef]

Grosse, N. B.

N. B. Grosse, T. Symul, M. Stobin'ska, T. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef] [PubMed]

Hanbury Brown, R.

R. Hanbury Brown and R. Q. Twiss, Nature (London) 178, 1046 (1956).
[CrossRef]

Hansen, H.

A. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Heersink, J.

J. Corney, P. Drummond, J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Phys. Rev. Lett. 97, 023606 (2006).
[CrossRef] [PubMed]

J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Opt. Lett. 30, 1192 (2005).
[CrossRef] [PubMed]

Hirano, T.

M. Koashi, K. Kono, T. Hirano, and M. Matsuoka, Phys. Rev. Lett. 71, 1164 (1993).
[CrossRef] [PubMed]

Hoffman, D.

J. Appel, D. Hoffman, E. Figueroa, and A. Lvovsky, Phys. Rev. A 75, 035802 (2007).
[CrossRef]

Hong, C. K.

Z. Y. Ou, C. K. Hong, and L. Mandel, Phys. Rev. A 36, 192 (1987).
[CrossRef] [PubMed]

Josse, V.

J. Corney, P. Drummond, J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Phys. Rev. Lett. 97, 023606 (2006).
[CrossRef] [PubMed]

J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Opt. Lett. 30, 1192 (2005).
[CrossRef] [PubMed]

Koashi, M.

M. Koashi, K. Kono, T. Hirano, and M. Matsuoka, Phys. Rev. Lett. 71, 1164 (1993).
[CrossRef] [PubMed]

Kono, K.

M. Koashi, K. Kono, T. Hirano, and M. Matsuoka, Phys. Rev. Lett. 71, 1164 (1993).
[CrossRef] [PubMed]

Lam, P. K.

N. B. Grosse, T. Symul, M. Stobin'ska, T. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef] [PubMed]

Leuchs, G.

J. Corney, P. Drummond, J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Phys. Rev. Lett. 97, 023606 (2006).
[CrossRef] [PubMed]

J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Opt. Lett. 30, 1192 (2005).
[CrossRef] [PubMed]

U. Andersen and G. Leuchs, Laser Phys. 15, 129 (2005).

Loudon, R.

R. Loudon, The Quantum Theory of Light (Oxford U. Press, 2000).

Lvovsky, A.

J. Appel, D. Hoffman, E. Figueroa, and A. Lvovsky, Phys. Rev. A 75, 035802 (2007).
[CrossRef]

A. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Mandel, L.

Z. Y. Ou, C. K. Hong, and L. Mandel, Phys. Rev. A 36, 192 (1987).
[CrossRef] [PubMed]

Matsuoka, M.

M. Koashi, K. Kono, T. Hirano, and M. Matsuoka, Phys. Rev. Lett. 71, 1164 (1993).
[CrossRef] [PubMed]

Mlynek, J.

A. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Ou, Z. Y.

Z. Y. Ou, C. K. Hong, and L. Mandel, Phys. Rev. A 36, 192 (1987).
[CrossRef] [PubMed]

Ralph, T.

N. B. Grosse, T. Symul, M. Stobin'ska, T. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef] [PubMed]

H. Bachor and T. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley, 2004).
[CrossRef]

Raymer, M.

M. Raymer and M. Beck, in Quantum State Estimation, M.G. A.Paris and J.Rehacek, eds. (Springer-Verlag, 2004), p. 235.

Schiller, S.

A. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Stobin'ska, M.

N. B. Grosse, T. Symul, M. Stobin'ska, T. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef] [PubMed]

Symul, T.

N. B. Grosse, T. Symul, M. Stobin'ska, T. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef] [PubMed]

Twiss, R. Q.

R. Hanbury Brown and R. Q. Twiss, Nature (London) 178, 1046 (1956).
[CrossRef]

Van der Ziel, A.

A. Van der Ziel, Noise in Solid State Devices and Circuits (Wiley, 1986).

Viciani, S.

A. Zavatta, S. Viciani, and M. Bellini, Phys. Rev. A 70, 053821 (2004).
[CrossRef]

Zavatta, A.

A. Zavatta, S. Viciani, and M. Bellini, Phys. Rev. A 70, 053821 (2004).
[CrossRef]

Laser Phys.

U. Andersen and G. Leuchs, Laser Phys. 15, 129 (2005).

Nature (London)

R. Hanbury Brown and R. Q. Twiss, Nature (London) 178, 1046 (1956).
[CrossRef]

Opt. Lett.

Phys. Rev. A

A. Zavatta, S. Viciani, and M. Bellini, Phys. Rev. A 70, 053821 (2004).
[CrossRef]

J. Appel, D. Hoffman, E. Figueroa, and A. Lvovsky, Phys. Rev. A 75, 035802 (2007).
[CrossRef]

Z. Y. Ou, C. K. Hong, and L. Mandel, Phys. Rev. A 36, 192 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett.

M. Koashi, K. Kono, T. Hirano, and M. Matsuoka, Phys. Rev. Lett. 71, 1164 (1993).
[CrossRef] [PubMed]

N. B. Grosse, T. Symul, M. Stobin'ska, T. Ralph, and P. K. Lam, Phys. Rev. Lett. 98, 153603 (2007).
[CrossRef] [PubMed]

J. Corney, P. Drummond, J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, Phys. Rev. Lett. 97, 023606 (2006).
[CrossRef] [PubMed]

A. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Other

H. Bachor and T. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley, 2004).
[CrossRef]

A. Van der Ziel, Noise in Solid State Devices and Circuits (Wiley, 1986).

R. Loudon, The Quantum Theory of Light (Oxford U. Press, 2000).

M. Raymer and M. Beck, in Quantum State Estimation, M.G. A.Paris and J.Rehacek, eds. (Springer-Verlag, 2004), p. 235.

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Figures (3)

Fig. 1
Fig. 1

Scheme of the HD setup. The beam from the squeezing setup is interfering with the LO on a 50 50 beam splitter (BS), ϕ is the phase of the LO, and D1 and D2 are analog photodetectors. Linear attenuation is introduced in both beams by the NDF. The produced photocurrents i 1 and i 2 are further analyzed by the computer.

Fig. 2
Fig. 2

Experimental dependence of the covariance versus the phase of the LO. A is the dependence on the full range of the phase variation, and B is the magnified part of the dependence with the positive covariance. The light-gray shaded region corresponds to the measurement of the squeezed quadrature; the dark-gray shaded region corresponds to the measurement of the quadrature exhibiting excess noise. The curve represents the fit of experimental data.

Fig. 3
Fig. 3

Experimental dependence of the squeezing on the transmission 1 η . A is the subtraction method, and B is the covariance method. The solid curves represent the theoretical dependence without accounting for the EN. The horizontal dashed lines at zero define a border between the squeezing and the classical access noise. The insets show the initial part of the dependence with the corresponding error bars.

Equations (3)

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i 1 , 2 = 1 2 α LO 2 + α LO ( δ X LO ± δ X ϕ ) + δ i e l 1 , 2 ,
( i 1 i 2 ) 2 = 4 α LO 2 δ X ϕ 2 + δ i e l 1 2 + δ i e l 2 2 .
cov ( i 1 , i 2 ) i 1 i 2 i 1 i 2 = α LO 2 [ δ X LO 2 δ X ϕ 2 ] ,

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