Abstract

We present the reconstruction of the Wigner function of a classical phase-sensitive state, a pulsed coherent state, by measurements of the distributions of detected-photons of the state displaced by a coherent probe field. By using a hybrid photodetector operated above its photon-resolving regime, we obtain both the statistics at different values of the probe field and the values of the probe phase required to reconstruct the Wigner function.

© 2010 Optical Society of America

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  1. J. Wenger, R. Tualle-Brouri, and P. Grangier, “Pulsed homodyne measurements of femtosecond squeezed pulses generated by single-pass parametric deamplification,” Opt. Lett. 29, 1267-1269 (2004).
    [CrossRef] [PubMed]
  2. H. Vahlbrouch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
    [CrossRef]
  3. J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).
    [CrossRef] [PubMed]
  4. A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006).
    [CrossRef] [PubMed]
  5. A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
    [CrossRef] [PubMed]
  6. A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
    [CrossRef]
  7. M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin-beam of light,” Phys. Rev. A 76, 013833 (2007).
    [CrossRef]
  8. A. I. Lvovsky and S. A. Babichev, “Synthesis and tomographic characterization of the displaced Fock state of light,” Phys. Rev. A 66, 011801(R) (2002).
    [CrossRef]
  9. For a review, see A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum state tomography,” Rev. Mod. Phys. 81, 299-332 (2009).
    [CrossRef]
  10. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244-1247 (1993).
    [CrossRef] [PubMed]
  11. K. Vogel and H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847-2849(R) (1989).
    [CrossRef] [PubMed]
  12. H. P. Yuen and V. W. S. Chan, “Noise in homodyne and heterodyne detection,” Opt. Lett. 8, 177-179 (1983).
    [CrossRef] [PubMed]
  13. G. L. Abbas, V. W. S. Chan, and T. K. Yee, “Local-oscillator excess-noise suppression for homodyne and heterodyne detection,” Opt. Lett. 8, 419-421 (1983).
    [CrossRef] [PubMed]
  14. A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
    [CrossRef] [PubMed]
  15. J. Wenger, A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Time-resolved homodyne characterization of individual quadrature-entangled pulses,” Eur. Phys. J. D 32, 391-396 (2005).
    [CrossRef]
  16. A. Zavatta, S. Viciani, and M. Bellini, “Non-classical field characterization by high-frequency, time-domain quantum homodyne tomography,” Laser Phys. Lett. 3, 3-16 (2006).
    [CrossRef]
  17. K. E. Cahill and R. J. Glauber, “Density operators and quasi-probability distributions,” Phys. Rev. 177, 1882-1902 (1969).
    [CrossRef]
  18. M. Bondani, A. Allevi, and A. Andreoni, “Wigner function of pulsed fields by direct detection,” Opt. Lett. 34, 1444-1446 (2009).
    [CrossRef] [PubMed]
  19. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambrige Univ. Press, 1995).
  20. M. Bondani, A. Allevi, and A. Andreoni, “Light statistics by non-calibrated linear photodetectors,” Adv. Sci. Lett. 2, 463-468 (2009).
    [CrossRef]
  21. E. Casini and A. Martinelli are preparing a manuscript to be called “A family of distributions stable with respect to random sums.”
  22. K. Banaszek and K. Wódkiewicz, “Direct probing of quantum phase space by photon counting,” Phys. Rev. Lett. 76, 4344-4347 (1996).
    [CrossRef] [PubMed]
  23. F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912-916 (1965).
    [CrossRef]
  24. G. Zambra, M. Bondani, A. S. Spinelli, and A. Andreoni, “Counting photoelectrons in the response of a photomultiplier tube to single picosecond light pulses,” Rev. Sci. Instrum. 75, 2762-2765 (2004).
    [CrossRef]
  25. J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999).
    [CrossRef]
  26. E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, “Direct observation of nonclassical photon statistics in parametric down-conversion,” Phys. Rev. Lett. 92, 113602 (2004).
    [CrossRef] [PubMed]
  27. A. V. Akindinov, A. N. Martemianov, P. A. Polozov, V. M. Golovin, and E. A. Grigoriev, “New results on MRS APDs,” Nucl. Instrum. Methods Phys. Res. A 387, 231-234 (1997).
    [CrossRef]
  28. D. Achilles, C. Silberhorn, C. Sliwá, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499-1515 (2004).
  29. K. Laiho, M. Avenhaus, K. N. Cassemiro, and Ch. Silberhorn, “Direct probing of the Wigner function by time-multiplexed detection of photon statistics,” New J. Phys. 11, 043012 (2009).
    [CrossRef]
  30. J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, Jr., and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67, 061801(R) (2003).
    [CrossRef]
  31. K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674-677 (1999).
    [CrossRef]
  32. M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self-consistent characterization of light statistics,” J. Mod. Opt. 56, 226-231 (2009).
    [CrossRef]
  33. A. Andreoni and M. Bondani, “Photon statistics in the macroscopic realm measured without photon-counters,” Phys. Rev. A 80, 013819 (2009).
    [CrossRef]
  34. L. Mandel, E. C. G. Sudarshan, and E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. London 84, 435-444 (1964).
    [CrossRef]
  35. K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell's inequalities,” Phys. Rev. A 66, 043803 (2002).
    [CrossRef]

2009

For a review, see A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum state tomography,” Rev. Mod. Phys. 81, 299-332 (2009).
[CrossRef]

M. Bondani, A. Allevi, and A. Andreoni, “Wigner function of pulsed fields by direct detection,” Opt. Lett. 34, 1444-1446 (2009).
[CrossRef] [PubMed]

M. Bondani, A. Allevi, and A. Andreoni, “Light statistics by non-calibrated linear photodetectors,” Adv. Sci. Lett. 2, 463-468 (2009).
[CrossRef]

K. Laiho, M. Avenhaus, K. N. Cassemiro, and Ch. Silberhorn, “Direct probing of the Wigner function by time-multiplexed detection of photon statistics,” New J. Phys. 11, 043012 (2009).
[CrossRef]

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self-consistent characterization of light statistics,” J. Mod. Opt. 56, 226-231 (2009).
[CrossRef]

A. Andreoni and M. Bondani, “Photon statistics in the macroscopic realm measured without photon-counters,” Phys. Rev. A 80, 013819 (2009).
[CrossRef]

2008

H. Vahlbrouch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

2007

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef] [PubMed]

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[CrossRef]

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin-beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

2006

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[CrossRef] [PubMed]

A. Zavatta, S. Viciani, and M. Bellini, “Non-classical field characterization by high-frequency, time-domain quantum homodyne tomography,” Laser Phys. Lett. 3, 3-16 (2006).
[CrossRef]

2005

J. Wenger, A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Time-resolved homodyne characterization of individual quadrature-entangled pulses,” Eur. Phys. J. D 32, 391-396 (2005).
[CrossRef]

2004

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Pulsed homodyne measurements of femtosecond squeezed pulses generated by single-pass parametric deamplification,” Opt. Lett. 29, 1267-1269 (2004).
[CrossRef] [PubMed]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).
[CrossRef] [PubMed]

D. Achilles, C. Silberhorn, C. Sliwá, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499-1515 (2004).

G. Zambra, M. Bondani, A. S. Spinelli, and A. Andreoni, “Counting photoelectrons in the response of a photomultiplier tube to single picosecond light pulses,” Rev. Sci. Instrum. 75, 2762-2765 (2004).
[CrossRef]

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, “Direct observation of nonclassical photon statistics in parametric down-conversion,” Phys. Rev. Lett. 92, 113602 (2004).
[CrossRef] [PubMed]

2003

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, Jr., and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67, 061801(R) (2003).
[CrossRef]

2002

K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell's inequalities,” Phys. Rev. A 66, 043803 (2002).
[CrossRef]

A. I. Lvovsky and S. A. Babichev, “Synthesis and tomographic characterization of the displaced Fock state of light,” Phys. Rev. A 66, 011801(R) (2002).
[CrossRef]

2001

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

1999

K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674-677 (1999).
[CrossRef]

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999).
[CrossRef]

1997

A. V. Akindinov, A. N. Martemianov, P. A. Polozov, V. M. Golovin, and E. A. Grigoriev, “New results on MRS APDs,” Nucl. Instrum. Methods Phys. Res. A 387, 231-234 (1997).
[CrossRef]

1996

K. Banaszek and K. Wódkiewicz, “Direct probing of quantum phase space by photon counting,” Phys. Rev. Lett. 76, 4344-4347 (1996).
[CrossRef] [PubMed]

1993

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244-1247 (1993).
[CrossRef] [PubMed]

1989

K. Vogel and H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847-2849(R) (1989).
[CrossRef] [PubMed]

1983

1969

K. E. Cahill and R. J. Glauber, “Density operators and quasi-probability distributions,” Phys. Rev. 177, 1882-1902 (1969).
[CrossRef]

1965

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912-916 (1965).
[CrossRef]

1964

L. Mandel, E. C. G. Sudarshan, and E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. London 84, 435-444 (1964).
[CrossRef]

Abbas, G. L.

Achilles, D.

D. Achilles, C. Silberhorn, C. Sliwá, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499-1515 (2004).

Agliati, A.

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self-consistent characterization of light statistics,” J. Mod. Opt. 56, 226-231 (2009).
[CrossRef]

Aichele, T.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Akindinov, A. V.

A. V. Akindinov, A. N. Martemianov, P. A. Polozov, V. M. Golovin, and E. A. Grigoriev, “New results on MRS APDs,” Nucl. Instrum. Methods Phys. Res. A 387, 231-234 (1997).
[CrossRef]

Allevi, A.

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self-consistent characterization of light statistics,” J. Mod. Opt. 56, 226-231 (2009).
[CrossRef]

M. Bondani, A. Allevi, and A. Andreoni, “Wigner function of pulsed fields by direct detection,” Opt. Lett. 34, 1444-1446 (2009).
[CrossRef] [PubMed]

M. Bondani, A. Allevi, and A. Andreoni, “Light statistics by non-calibrated linear photodetectors,” Adv. Sci. Lett. 2, 463-468 (2009).
[CrossRef]

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin-beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

Andreoni, A.

M. Bondani, A. Allevi, and A. Andreoni, “Light statistics by non-calibrated linear photodetectors,” Adv. Sci. Lett. 2, 463-468 (2009).
[CrossRef]

M. Bondani, A. Allevi, and A. Andreoni, “Wigner function of pulsed fields by direct detection,” Opt. Lett. 34, 1444-1446 (2009).
[CrossRef] [PubMed]

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self-consistent characterization of light statistics,” J. Mod. Opt. 56, 226-231 (2009).
[CrossRef]

A. Andreoni and M. Bondani, “Photon statistics in the macroscopic realm measured without photon-counters,” Phys. Rev. A 80, 013819 (2009).
[CrossRef]

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin-beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

G. Zambra, M. Bondani, A. S. Spinelli, and A. Andreoni, “Counting photoelectrons in the response of a photomultiplier tube to single picosecond light pulses,” Rev. Sci. Instrum. 75, 2762-2765 (2004).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912-916 (1965).
[CrossRef]

Avenhaus, M.

K. Laiho, M. Avenhaus, K. N. Cassemiro, and Ch. Silberhorn, “Direct probing of the Wigner function by time-multiplexed detection of photon statistics,” New J. Phys. 11, 043012 (2009).
[CrossRef]

Babichev, S. A.

A. I. Lvovsky and S. A. Babichev, “Synthesis and tomographic characterization of the displaced Fock state of light,” Phys. Rev. A 66, 011801(R) (2002).
[CrossRef]

Banaszek, K.

D. Achilles, C. Silberhorn, C. Sliwá, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499-1515 (2004).

K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell's inequalities,” Phys. Rev. A 66, 043803 (2002).
[CrossRef]

K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674-677 (1999).
[CrossRef]

K. Banaszek and K. Wódkiewicz, “Direct probing of quantum phase space by photon counting,” Phys. Rev. Lett. 76, 4344-4347 (1996).
[CrossRef] [PubMed]

Bartlett, S. D.

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, “Direct observation of nonclassical photon statistics in parametric down-conversion,” Phys. Rev. Lett. 92, 113602 (2004).
[CrossRef] [PubMed]

Beck, M.

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244-1247 (1993).
[CrossRef] [PubMed]

Bellini, M.

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, “Non-classical field characterization by high-frequency, time-domain quantum homodyne tomography,” Laser Phys. Lett. 3, 3-16 (2006).
[CrossRef]

Benson, O.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Bondani, M.

M. Bondani, A. Allevi, and A. Andreoni, “Wigner function of pulsed fields by direct detection,” Opt. Lett. 34, 1444-1446 (2009).
[CrossRef] [PubMed]

M. Bondani, A. Allevi, and A. Andreoni, “Light statistics by non-calibrated linear photodetectors,” Adv. Sci. Lett. 2, 463-468 (2009).
[CrossRef]

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self-consistent characterization of light statistics,” J. Mod. Opt. 56, 226-231 (2009).
[CrossRef]

A. Andreoni and M. Bondani, “Photon statistics in the macroscopic realm measured without photon-counters,” Phys. Rev. A 80, 013819 (2009).
[CrossRef]

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin-beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

G. Zambra, M. Bondani, A. S. Spinelli, and A. Andreoni, “Counting photoelectrons in the response of a photomultiplier tube to single picosecond light pulses,” Rev. Sci. Instrum. 75, 2762-2765 (2004).
[CrossRef]

Cahill, K. E.

K. E. Cahill and R. J. Glauber, “Density operators and quasi-probability distributions,” Phys. Rev. 177, 1882-1902 (1969).
[CrossRef]

Casini, E.

E. Casini and A. Martinelli are preparing a manuscript to be called “A family of distributions stable with respect to random sums.”

Cassemiro, K. N.

K. Laiho, M. Avenhaus, K. N. Cassemiro, and Ch. Silberhorn, “Direct probing of the Wigner function by time-multiplexed detection of photon statistics,” New J. Phys. 11, 043012 (2009).
[CrossRef]

Chan, V. W. S.

Chelkowski, S.

H. Vahlbrouch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Dantan, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef] [PubMed]

Danzmann, K.

H. Vahlbrouch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Diamanti, E.

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, “Direct observation of nonclassical photon statistics in parametric down-conversion,” Phys. Rev. Lett. 92, 113602 (2004).
[CrossRef] [PubMed]

Dragan, A.

K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell's inequalities,” Phys. Rev. A 66, 043803 (2002).
[CrossRef]

Faridani, A.

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244-1247 (1993).
[CrossRef] [PubMed]

Fitch, M. J.

D. Achilles, C. Silberhorn, C. Sliwá, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499-1515 (2004).

Franson, J. D.

D. Achilles, C. Silberhorn, C. Sliwá, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499-1515 (2004).

Franzen, A.

H. Vahlbrouch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Glauber, R. J.

K. E. Cahill and R. J. Glauber, “Density operators and quasi-probability distributions,” Phys. Rev. 177, 1882-1902 (1969).
[CrossRef]

Golovin, V. M.

A. V. Akindinov, A. N. Martemianov, P. A. Polozov, V. M. Golovin, and E. A. Grigoriev, “New results on MRS APDs,” Nucl. Instrum. Methods Phys. Res. A 387, 231-234 (1997).
[CrossRef]

Goßler, S.

H. Vahlbrouch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Grangier, P.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef] [PubMed]

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[CrossRef] [PubMed]

J. Wenger, A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Time-resolved homodyne characterization of individual quadrature-entangled pulses,” Eur. Phys. J. D 32, 391-396 (2005).
[CrossRef]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).
[CrossRef] [PubMed]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Pulsed homodyne measurements of femtosecond squeezed pulses generated by single-pass parametric deamplification,” Opt. Lett. 29, 1267-1269 (2004).
[CrossRef] [PubMed]

Grigoriev, E. A.

A. V. Akindinov, A. N. Martemianov, P. A. Polozov, V. M. Golovin, and E. A. Grigoriev, “New results on MRS APDs,” Nucl. Instrum. Methods Phys. Res. A 387, 231-234 (1997).
[CrossRef]

Haderka, O.

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, Jr., and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67, 061801(R) (2003).
[CrossRef]

Hage, B.

H. Vahlbrouch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Hamar, M.

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, Jr., and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67, 061801(R) (2003).
[CrossRef]

Hansen, H.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Hogue, H. H.

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999).
[CrossRef]

Hradil, Z.

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, Jr., and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67, 061801(R) (2003).
[CrossRef]

Jacobs, B. C.

D. Achilles, C. Silberhorn, C. Sliwá, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499-1515 (2004).

Kim, J.

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999).
[CrossRef]

Krasinski, J. S.

K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674-677 (1999).
[CrossRef]

Laiho, K.

K. Laiho, M. Avenhaus, K. N. Cassemiro, and Ch. Silberhorn, “Direct probing of the Wigner function by time-multiplexed detection of photon statistics,” New J. Phys. 11, 043012 (2009).
[CrossRef]

Lastzka, N.

H. Vahlbrouch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Lvovsky, A. I.

For a review, see A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum state tomography,” Rev. Mod. Phys. 81, 299-332 (2009).
[CrossRef]

A. I. Lvovsky and S. A. Babichev, “Synthesis and tomographic characterization of the displaced Fock state of light,” Phys. Rev. A 66, 011801(R) (2002).
[CrossRef]

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Mandel, L.

L. Mandel, E. C. G. Sudarshan, and E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. London 84, 435-444 (1964).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambrige Univ. Press, 1995).

Martemianov, A. N.

A. V. Akindinov, A. N. Martemianov, P. A. Polozov, V. M. Golovin, and E. A. Grigoriev, “New results on MRS APDs,” Nucl. Instrum. Methods Phys. Res. A 387, 231-234 (1997).
[CrossRef]

Martinelli, A.

E. Casini and A. Martinelli are preparing a manuscript to be called “A family of distributions stable with respect to random sums.”

Mehmet, M.

H. Vahlbrouch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Mlynek, J.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Ourjoumtsev, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef] [PubMed]

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[CrossRef] [PubMed]

J. Wenger, A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Time-resolved homodyne characterization of individual quadrature-entangled pulses,” Eur. Phys. J. D 32, 391-396 (2005).
[CrossRef]

Parigi, V.

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[CrossRef]

Paris, M. G. A.

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin-beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

Perina, J.

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, Jr., and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67, 061801(R) (2003).
[CrossRef]

Pittman, T. B.

D. Achilles, C. Silberhorn, C. Sliwá, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499-1515 (2004).

Polozov, P. A.

A. V. Akindinov, A. N. Martemianov, P. A. Polozov, V. M. Golovin, and E. A. Grigoriev, “New results on MRS APDs,” Nucl. Instrum. Methods Phys. Res. A 387, 231-234 (1997).
[CrossRef]

Radzewicz, C.

K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell's inequalities,” Phys. Rev. A 66, 043803 (2002).
[CrossRef]

K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674-677 (1999).
[CrossRef]

Raymer, M. G.

For a review, see A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum state tomography,” Rev. Mod. Phys. 81, 299-332 (2009).
[CrossRef]

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244-1247 (1993).
[CrossRef] [PubMed]

Rehácek, J.

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, Jr., and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67, 061801(R) (2003).
[CrossRef]

Risken, H.

K. Vogel and H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847-2849(R) (1989).
[CrossRef] [PubMed]

Sanders, B. C.

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, “Direct observation of nonclassical photon statistics in parametric down-conversion,” Phys. Rev. Lett. 92, 113602 (2004).
[CrossRef] [PubMed]

Schiller, S.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Schnabel, R.

H. Vahlbrouch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Silberhorn, C.

D. Achilles, C. Silberhorn, C. Sliwá, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499-1515 (2004).

Silberhorn, Ch.

K. Laiho, M. Avenhaus, K. N. Cassemiro, and Ch. Silberhorn, “Direct probing of the Wigner function by time-multiplexed detection of photon statistics,” New J. Phys. 11, 043012 (2009).
[CrossRef]

Sliwá, C.

D. Achilles, C. Silberhorn, C. Sliwá, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499-1515 (2004).

Smithey, D. T.

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244-1247 (1993).
[CrossRef] [PubMed]

Spinelli, A. S.

G. Zambra, M. Bondani, A. S. Spinelli, and A. Andreoni, “Counting photoelectrons in the response of a photomultiplier tube to single picosecond light pulses,” Rev. Sci. Instrum. 75, 2762-2765 (2004).
[CrossRef]

Sudarshan, E. C. G.

L. Mandel, E. C. G. Sudarshan, and E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. London 84, 435-444 (1964).
[CrossRef]

Takeuchi, S.

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999).
[CrossRef]

Tualle-Brouri, R.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef] [PubMed]

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[CrossRef] [PubMed]

J. Wenger, A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Time-resolved homodyne characterization of individual quadrature-entangled pulses,” Eur. Phys. J. D 32, 391-396 (2005).
[CrossRef]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Pulsed homodyne measurements of femtosecond squeezed pulses generated by single-pass parametric deamplification,” Opt. Lett. 29, 1267-1269 (2004).
[CrossRef] [PubMed]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).
[CrossRef] [PubMed]

Vahlbrouch, H.

H. Vahlbrouch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Viciani, S.

A. Zavatta, S. Viciani, and M. Bellini, “Non-classical field characterization by high-frequency, time-domain quantum homodyne tomography,” Laser Phys. Lett. 3, 3-16 (2006).
[CrossRef]

Vogel, K.

K. Vogel and H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847-2849(R) (1989).
[CrossRef] [PubMed]

Waks, E.

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, “Direct observation of nonclassical photon statistics in parametric down-conversion,” Phys. Rev. Lett. 92, 113602 (2004).
[CrossRef] [PubMed]

Walmsley, I. A.

D. Achilles, C. Silberhorn, C. Sliwá, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499-1515 (2004).

Wenger, J.

J. Wenger, A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Time-resolved homodyne characterization of individual quadrature-entangled pulses,” Eur. Phys. J. D 32, 391-396 (2005).
[CrossRef]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Pulsed homodyne measurements of femtosecond squeezed pulses generated by single-pass parametric deamplification,” Opt. Lett. 29, 1267-1269 (2004).
[CrossRef] [PubMed]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).
[CrossRef] [PubMed]

Wódkiewicz, K.

K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell's inequalities,” Phys. Rev. A 66, 043803 (2002).
[CrossRef]

K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674-677 (1999).
[CrossRef]

K. Banaszek and K. Wódkiewicz, “Direct probing of quantum phase space by photon counting,” Phys. Rev. Lett. 76, 4344-4347 (1996).
[CrossRef] [PubMed]

Wolf, E.

L. Mandel, E. C. G. Sudarshan, and E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. London 84, 435-444 (1964).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambrige Univ. Press, 1995).

Yamamoto, Y.

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, “Direct observation of nonclassical photon statistics in parametric down-conversion,” Phys. Rev. Lett. 92, 113602 (2004).
[CrossRef] [PubMed]

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999).
[CrossRef]

Yee, T. K.

Yuen, H. P.

Zambra, G.

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin-beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

G. Zambra, M. Bondani, A. S. Spinelli, and A. Andreoni, “Counting photoelectrons in the response of a photomultiplier tube to single picosecond light pulses,” Rev. Sci. Instrum. 75, 2762-2765 (2004).
[CrossRef]

Zavatta, A.

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, “Non-classical field characterization by high-frequency, time-domain quantum homodyne tomography,” Laser Phys. Lett. 3, 3-16 (2006).
[CrossRef]

Adv. Sci. Lett.

M. Bondani, A. Allevi, and A. Andreoni, “Light statistics by non-calibrated linear photodetectors,” Adv. Sci. Lett. 2, 463-468 (2009).
[CrossRef]

Appl. Phys. Lett.

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999).
[CrossRef]

Eur. Phys. J. D

J. Wenger, A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Time-resolved homodyne characterization of individual quadrature-entangled pulses,” Eur. Phys. J. D 32, 391-396 (2005).
[CrossRef]

J. Mod. Opt.

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self-consistent characterization of light statistics,” J. Mod. Opt. 56, 226-231 (2009).
[CrossRef]

D. Achilles, C. Silberhorn, C. Sliwá, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499-1515 (2004).

Laser Phys. Lett.

A. Zavatta, S. Viciani, and M. Bellini, “Non-classical field characterization by high-frequency, time-domain quantum homodyne tomography,” Laser Phys. Lett. 3, 3-16 (2006).
[CrossRef]

New J. Phys.

K. Laiho, M. Avenhaus, K. N. Cassemiro, and Ch. Silberhorn, “Direct probing of the Wigner function by time-multiplexed detection of photon statistics,” New J. Phys. 11, 043012 (2009).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A

A. V. Akindinov, A. N. Martemianov, P. A. Polozov, V. M. Golovin, and E. A. Grigoriev, “New results on MRS APDs,” Nucl. Instrum. Methods Phys. Res. A 387, 231-234 (1997).
[CrossRef]

Opt. Lett.

Phys. Rev.

K. E. Cahill and R. J. Glauber, “Density operators and quasi-probability distributions,” Phys. Rev. 177, 1882-1902 (1969).
[CrossRef]

Phys. Rev. A

K. Vogel and H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847-2849(R) (1989).
[CrossRef] [PubMed]

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[CrossRef]

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin-beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

A. I. Lvovsky and S. A. Babichev, “Synthesis and tomographic characterization of the displaced Fock state of light,” Phys. Rev. A 66, 011801(R) (2002).
[CrossRef]

K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell's inequalities,” Phys. Rev. A 66, 043803 (2002).
[CrossRef]

A. Andreoni and M. Bondani, “Photon statistics in the macroscopic realm measured without photon-counters,” Phys. Rev. A 80, 013819 (2009).
[CrossRef]

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, Jr., and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67, 061801(R) (2003).
[CrossRef]

K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674-677 (1999).
[CrossRef]

Phys. Rev. Lett.

K. Banaszek and K. Wódkiewicz, “Direct probing of quantum phase space by photon counting,” Phys. Rev. Lett. 76, 4344-4347 (1996).
[CrossRef] [PubMed]

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912-916 (1965).
[CrossRef]

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, “Direct observation of nonclassical photon statistics in parametric down-conversion,” Phys. Rev. Lett. 92, 113602 (2004).
[CrossRef] [PubMed]

H. Vahlbrouch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).
[CrossRef] [PubMed]

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[CrossRef] [PubMed]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef] [PubMed]

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244-1247 (1993).
[CrossRef] [PubMed]

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Proc. Phys. Soc. London

L. Mandel, E. C. G. Sudarshan, and E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. London 84, 435-444 (1964).
[CrossRef]

Rev. Mod. Phys.

For a review, see A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum state tomography,” Rev. Mod. Phys. 81, 299-332 (2009).
[CrossRef]

Rev. Sci. Instrum.

G. Zambra, M. Bondani, A. S. Spinelli, and A. Andreoni, “Counting photoelectrons in the response of a photomultiplier tube to single picosecond light pulses,” Rev. Sci. Instrum. 75, 2762-2765 (2004).
[CrossRef]

Other

E. Casini and A. Martinelli are preparing a manuscript to be called “A family of distributions stable with respect to random sums.”

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambrige Univ. Press, 1995).

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. HPD, hybrid photo-detector; BS, beam splitter; F, neutral density filter; Pz, piezoelectric movement; P, polarizer; SGI, synchronous gated integrator.

Fig. 2
Fig. 2

Bars: examples of reconstructed probability distributions p ¯ m ( β ) at four values of β. Lines + symbols : theoretical Poissonian distributions p ¯ m , th at the same mean values.

Fig. 3
Fig. 3

Columns: measurements taken at the indicated values of probe, | β | 2 , and signal, | β 0 | 2 , intensities. First row: Wigner functions reconstructed according to Eq. (3) as a function of the piezo step, i. Second row: mean value of the output voltages at η max . Third row: experimental cosine of the interference pattern. Fourth row: phase values obtained from the cosine.

Fig. 4
Fig. 4

Dots: experimental reconstruction of sections of the Wigner function at fixed values of probe, | β | 2 , and signal, | β 0 | 2 , intensities (same values as in Fig. 3) and variable ϕ; dash-dotted lines: expected theoretical curves; full lines: theoretical curves corrected for the overlap ξ of signal and probe.

Fig. 5
Fig. 5

Main: experimental reconstruction of the Wigner function (dots) and theoretical prediction. Inset: contour plot of the experimental data.

Equations (8)

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

W ( α ) = 2 π n = 0 ( 1 ) n p n ( α ) ,
p ¯ m ( β ) = n = m ( n m ) η m ( 1 η ) n m p n ( α ) ,
W ¯ ( β ) = 2 π m = 0 ( 1 ) m p ¯ m ( β ) ,
W ¯ ( β ) = 2 π ( 1 η ) d 2 β e 2 | β β | 2 ( 1 η )
W ¯ ( β ) = 2 π exp ( 2 | β β 0 | 2 ) ,
F v = Q n ¯ v ¯ + γ ,
f = m p ¯ m ( β ) p ¯ m , th .
W ¯ ( β ) = 2 π exp ( 2 ( 1 ξ ) | β | 2 ) exp ( 2 | ξ β β 0 | 2 ) .

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