Abstract

Pattern function quantum homodyne tomography (QHT) has been used for characterizing the ouput of a degenerate below-threshold type—I OPO. The recovered photon number distributions deviated from those relative to Gaussian thermal states. The Kurtosis of the homodyne data confirmed these deviations, thus proving the power of QHT to highlight unexpected features of quantum states.

©2005 Optical Society of America

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References

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  1. See for example: Quantum states estimation, M. G. A. Paris and J. Řeháček Eds., Lect. Not. Phys.649 (Springer, Heidelberg, 2004).
    [Crossref]
  2. G. Breitenbach, S. Schiller, and J. Mlynek “Measurement of the quantum states of squeezed light,” Nature,  387, 471–475 (1997);
    [Crossref]
  3. G. Breitenbach and S. Schiller, “Homodyne tomography of classical and non-classical light,” J. Mod. Opt. 44, 2207–2225 (1997);
  4. A. Zavatta, F. Marin, and G. Giacomelli, “Quantum-state reconstruction of a squeezed laser field by self-homodyne tomography,” Phys. Rev. A 66, 043805 (2002);
    [Crossref]
  5. G. Mauro D’Ariano, M. De Laurentis, M.G.A. Paris, A. Porzio, and S. Solimeno, “Quantum tomography as a tool for the characterization of optical devices,” J. Opt. B 4, S127–S132 (2002);
    [Crossref]
  6. 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]
  7. J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Non-Gaussian Statistics from Individual Pulses of Squeezed Light,” Phys. Rev. Lett. 92, 153601 (2004);
    [Crossref] [PubMed]
  8. Alessandro Zavatta, Silvia Viciani, and Marco Bellini “Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection,” Phys. Rev. A 70, 053821 (2004);
    [Crossref]
  9. G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, “Detection of the density matrix through optical homodyne tomography without filtered back projection,” Phys. Rev. A 50, 4298–4302 (1994).
    [Crossref] [PubMed]
  10. M.J. Collett and C.W. Gardiner, “Squeezing of intracavity and travelling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984);
    [Crossref]
  11. K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, “Critical fluctuations and entanglement in the nondegenerate parametric oscillator,” Phys. Rev. A 70, 053807 (2004);
    [Crossref]
  12. P. Marian, “Higher-order squeezing and photon statistics for squeezed thermal states,” Phys. Rev. A 45, 2044–2051 (1992);
    [Crossref] [PubMed]
  13. G. M. D’Ariano, M. G. A Paris, and M. F. Sacchi, “Quantum Tomography,” Advances in Imaging and Electron Physics 128, 205–308 (2003).
    [Crossref]
  14. A. Porzio, C. Altucci, M. Autiero, A. Chiummo, C. de Lisio, and S. Solimeno, “Tunable twin beams generated by a type—I LNB OPO,” Appl. Phys. B 73, 763–766, (2001);
    [Crossref]
  15. R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105, (1983);
    [Crossref]
  16. V. D’Auria, P. Aniello, Matteo G.A. Paris, A. Porzio, and S. Solimeno “Quadrature Fourth order moment in an OPO described by time dependent coefficient Langevin equation,” in preparation

2004 (3)

J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Non-Gaussian Statistics from Individual Pulses of Squeezed Light,” Phys. Rev. Lett. 92, 153601 (2004);
[Crossref] [PubMed]

Alessandro Zavatta, Silvia Viciani, and Marco Bellini “Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection,” Phys. Rev. A 70, 053821 (2004);
[Crossref]

K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, “Critical fluctuations and entanglement in the nondegenerate parametric oscillator,” Phys. Rev. A 70, 053807 (2004);
[Crossref]

2003 (1)

G. M. D’Ariano, M. G. A Paris, and M. F. Sacchi, “Quantum Tomography,” Advances in Imaging and Electron Physics 128, 205–308 (2003).
[Crossref]

2002 (2)

A. Zavatta, F. Marin, and G. Giacomelli, “Quantum-state reconstruction of a squeezed laser field by self-homodyne tomography,” Phys. Rev. A 66, 043805 (2002);
[Crossref]

G. Mauro D’Ariano, M. De Laurentis, M.G.A. Paris, A. Porzio, and S. Solimeno, “Quantum tomography as a tool for the characterization of optical devices,” J. Opt. B 4, S127–S132 (2002);
[Crossref]

2001 (2)

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]

A. Porzio, C. Altucci, M. Autiero, A. Chiummo, C. de Lisio, and S. Solimeno, “Tunable twin beams generated by a type—I LNB OPO,” Appl. Phys. B 73, 763–766, (2001);
[Crossref]

1997 (2)

G. Breitenbach, S. Schiller, and J. Mlynek “Measurement of the quantum states of squeezed light,” Nature,  387, 471–475 (1997);
[Crossref]

G. Breitenbach and S. Schiller, “Homodyne tomography of classical and non-classical light,” J. Mod. Opt. 44, 2207–2225 (1997);

1994 (1)

G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, “Detection of the density matrix through optical homodyne tomography without filtered back projection,” Phys. Rev. A 50, 4298–4302 (1994).
[Crossref] [PubMed]

1992 (1)

P. Marian, “Higher-order squeezing and photon statistics for squeezed thermal states,” Phys. Rev. A 45, 2044–2051 (1992);
[Crossref] [PubMed]

1984 (1)

M.J. Collett and C.W. Gardiner, “Squeezing of intracavity and travelling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984);
[Crossref]

1983 (1)

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

Altucci, C.

A. Porzio, C. Altucci, M. Autiero, A. Chiummo, C. de Lisio, and S. Solimeno, “Tunable twin beams generated by a type—I LNB OPO,” Appl. Phys. B 73, 763–766, (2001);
[Crossref]

Aniello, P.

V. D’Auria, P. Aniello, Matteo G.A. Paris, A. Porzio, and S. Solimeno “Quadrature Fourth order moment in an OPO described by time dependent coefficient Langevin equation,” in preparation

Autiero, M.

A. Porzio, C. Altucci, M. Autiero, A. Chiummo, C. de Lisio, and S. Solimeno, “Tunable twin beams generated by a type—I LNB OPO,” Appl. Phys. B 73, 763–766, (2001);
[Crossref]

Bellini, Marco

Alessandro Zavatta, Silvia Viciani, and Marco Bellini “Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection,” Phys. Rev. A 70, 053821 (2004);
[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]

Breitenbach, G.

G. Breitenbach, S. Schiller, and J. Mlynek “Measurement of the quantum states of squeezed light,” Nature,  387, 471–475 (1997);
[Crossref]

G. Breitenbach and S. Schiller, “Homodyne tomography of classical and non-classical light,” J. Mod. Opt. 44, 2207–2225 (1997);

Chaturvedi, S.

K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, “Critical fluctuations and entanglement in the nondegenerate parametric oscillator,” Phys. Rev. A 70, 053807 (2004);
[Crossref]

Chiummo, A.

A. Porzio, C. Altucci, M. Autiero, A. Chiummo, C. de Lisio, and S. Solimeno, “Tunable twin beams generated by a type—I LNB OPO,” Appl. Phys. B 73, 763–766, (2001);
[Crossref]

Collett, M.J.

M.J. Collett and C.W. Gardiner, “Squeezing of intracavity and travelling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984);
[Crossref]

D’Ariano, G. M.

G. M. D’Ariano, M. G. A Paris, and M. F. Sacchi, “Quantum Tomography,” Advances in Imaging and Electron Physics 128, 205–308 (2003).
[Crossref]

G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, “Detection of the density matrix through optical homodyne tomography without filtered back projection,” Phys. Rev. A 50, 4298–4302 (1994).
[Crossref] [PubMed]

D’Auria, V.

V. D’Auria, P. Aniello, Matteo G.A. Paris, A. Porzio, and S. Solimeno “Quadrature Fourth order moment in an OPO described by time dependent coefficient Langevin equation,” in preparation

De Laurentis, M.

G. Mauro D’Ariano, M. De Laurentis, M.G.A. Paris, A. Porzio, and S. Solimeno, “Quantum tomography as a tool for the characterization of optical devices,” J. Opt. B 4, S127–S132 (2002);
[Crossref]

de Lisio, C.

A. Porzio, C. Altucci, M. Autiero, A. Chiummo, C. de Lisio, and S. Solimeno, “Tunable twin beams generated by a type—I LNB OPO,” Appl. Phys. B 73, 763–766, (2001);
[Crossref]

Dechoum, K.

K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, “Critical fluctuations and entanglement in the nondegenerate parametric oscillator,” Phys. Rev. A 70, 053807 (2004);
[Crossref]

Drever, R.W.P.

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

Drummond, P. D.

K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, “Critical fluctuations and entanglement in the nondegenerate parametric oscillator,” Phys. Rev. A 70, 053807 (2004);
[Crossref]

Ford, G.M.

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

Gardiner, C.W.

M.J. Collett and C.W. Gardiner, “Squeezing of intracavity and travelling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984);
[Crossref]

Giacomelli, G.

A. Zavatta, F. Marin, and G. Giacomelli, “Quantum-state reconstruction of a squeezed laser field by self-homodyne tomography,” Phys. Rev. A 66, 043805 (2002);
[Crossref]

Grangier, Ph.

J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Non-Gaussian Statistics from Individual Pulses of Squeezed Light,” Phys. Rev. Lett. 92, 153601 (2004);
[Crossref] [PubMed]

Hall, J.L.

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

Hough, J.

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

Kowalski, F.V.

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

Lvovsky, A. I.

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]

Macchiavello, C.

G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, “Detection of the density matrix through optical homodyne tomography without filtered back projection,” Phys. Rev. A 50, 4298–4302 (1994).
[Crossref] [PubMed]

Marian, P.

P. Marian, “Higher-order squeezing and photon statistics for squeezed thermal states,” Phys. Rev. A 45, 2044–2051 (1992);
[Crossref] [PubMed]

Marin, F.

A. Zavatta, F. Marin, and G. Giacomelli, “Quantum-state reconstruction of a squeezed laser field by self-homodyne tomography,” Phys. Rev. A 66, 043805 (2002);
[Crossref]

Mauro D’Ariano, G.

G. Mauro D’Ariano, M. De Laurentis, M.G.A. Paris, A. Porzio, and S. Solimeno, “Quantum tomography as a tool for the characterization of optical devices,” J. Opt. B 4, S127–S132 (2002);
[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]

G. Breitenbach, S. Schiller, and J. Mlynek “Measurement of the quantum states of squeezed light,” Nature,  387, 471–475 (1997);
[Crossref]

Munley, A.J.

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

Paris, M. G. A

G. M. D’Ariano, M. G. A Paris, and M. F. Sacchi, “Quantum Tomography,” Advances in Imaging and Electron Physics 128, 205–308 (2003).
[Crossref]

Paris, M. G. A.

G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, “Detection of the density matrix through optical homodyne tomography without filtered back projection,” Phys. Rev. A 50, 4298–4302 (1994).
[Crossref] [PubMed]

Paris, M.G.A.

G. Mauro D’Ariano, M. De Laurentis, M.G.A. Paris, A. Porzio, and S. Solimeno, “Quantum tomography as a tool for the characterization of optical devices,” J. Opt. B 4, S127–S132 (2002);
[Crossref]

Paris, Matteo G.A.

V. D’Auria, P. Aniello, Matteo G.A. Paris, A. Porzio, and S. Solimeno “Quadrature Fourth order moment in an OPO described by time dependent coefficient Langevin equation,” in preparation

Porzio, A.

G. Mauro D’Ariano, M. De Laurentis, M.G.A. Paris, A. Porzio, and S. Solimeno, “Quantum tomography as a tool for the characterization of optical devices,” J. Opt. B 4, S127–S132 (2002);
[Crossref]

A. Porzio, C. Altucci, M. Autiero, A. Chiummo, C. de Lisio, and S. Solimeno, “Tunable twin beams generated by a type—I LNB OPO,” Appl. Phys. B 73, 763–766, (2001);
[Crossref]

V. D’Auria, P. Aniello, Matteo G.A. Paris, A. Porzio, and S. Solimeno “Quadrature Fourth order moment in an OPO described by time dependent coefficient Langevin equation,” in preparation

Reid, M. D.

K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, “Critical fluctuations and entanglement in the nondegenerate parametric oscillator,” Phys. Rev. A 70, 053807 (2004);
[Crossref]

Sacchi, M. F.

G. M. D’Ariano, M. G. A Paris, and M. F. Sacchi, “Quantum Tomography,” Advances in Imaging and Electron Physics 128, 205–308 (2003).
[Crossref]

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]

G. Breitenbach and S. Schiller, “Homodyne tomography of classical and non-classical light,” J. Mod. Opt. 44, 2207–2225 (1997);

G. Breitenbach, S. Schiller, and J. Mlynek “Measurement of the quantum states of squeezed light,” Nature,  387, 471–475 (1997);
[Crossref]

Solimeno, S.

G. Mauro D’Ariano, M. De Laurentis, M.G.A. Paris, A. Porzio, and S. Solimeno, “Quantum tomography as a tool for the characterization of optical devices,” J. Opt. B 4, S127–S132 (2002);
[Crossref]

A. Porzio, C. Altucci, M. Autiero, A. Chiummo, C. de Lisio, and S. Solimeno, “Tunable twin beams generated by a type—I LNB OPO,” Appl. Phys. B 73, 763–766, (2001);
[Crossref]

V. D’Auria, P. Aniello, Matteo G.A. Paris, A. Porzio, and S. Solimeno “Quadrature Fourth order moment in an OPO described by time dependent coefficient Langevin equation,” in preparation

Tualle-Brouri, R.

J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Non-Gaussian Statistics from Individual Pulses of Squeezed Light,” Phys. Rev. Lett. 92, 153601 (2004);
[Crossref] [PubMed]

Viciani, Silvia

Alessandro Zavatta, Silvia Viciani, and Marco Bellini “Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection,” Phys. Rev. A 70, 053821 (2004);
[Crossref]

Ward, H.

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

Wenger, J.

J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Non-Gaussian Statistics from Individual Pulses of Squeezed Light,” Phys. Rev. Lett. 92, 153601 (2004);
[Crossref] [PubMed]

Zavatta, A.

A. Zavatta, F. Marin, and G. Giacomelli, “Quantum-state reconstruction of a squeezed laser field by self-homodyne tomography,” Phys. Rev. A 66, 043805 (2002);
[Crossref]

Zavatta, Alessandro

Alessandro Zavatta, Silvia Viciani, and Marco Bellini “Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection,” Phys. Rev. A 70, 053821 (2004);
[Crossref]

Advances in Imaging and Electron Physics (1)

G. M. D’Ariano, M. G. A Paris, and M. F. Sacchi, “Quantum Tomography,” Advances in Imaging and Electron Physics 128, 205–308 (2003).
[Crossref]

Appl. Phys. B (2)

A. Porzio, C. Altucci, M. Autiero, A. Chiummo, C. de Lisio, and S. Solimeno, “Tunable twin beams generated by a type—I LNB OPO,” Appl. Phys. B 73, 763–766, (2001);
[Crossref]

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

J. Mod. Opt. (1)

G. Breitenbach and S. Schiller, “Homodyne tomography of classical and non-classical light,” J. Mod. Opt. 44, 2207–2225 (1997);

J. Opt. B (1)

G. Mauro D’Ariano, M. De Laurentis, M.G.A. Paris, A. Porzio, and S. Solimeno, “Quantum tomography as a tool for the characterization of optical devices,” J. Opt. B 4, S127–S132 (2002);
[Crossref]

Nature (1)

G. Breitenbach, S. Schiller, and J. Mlynek “Measurement of the quantum states of squeezed light,” Nature,  387, 471–475 (1997);
[Crossref]

Phys. Rev. A (6)

A. Zavatta, F. Marin, and G. Giacomelli, “Quantum-state reconstruction of a squeezed laser field by self-homodyne tomography,” Phys. Rev. A 66, 043805 (2002);
[Crossref]

Alessandro Zavatta, Silvia Viciani, and Marco Bellini “Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection,” Phys. Rev. A 70, 053821 (2004);
[Crossref]

G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, “Detection of the density matrix through optical homodyne tomography without filtered back projection,” Phys. Rev. A 50, 4298–4302 (1994).
[Crossref] [PubMed]

M.J. Collett and C.W. Gardiner, “Squeezing of intracavity and travelling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984);
[Crossref]

K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, “Critical fluctuations and entanglement in the nondegenerate parametric oscillator,” Phys. Rev. A 70, 053807 (2004);
[Crossref]

P. Marian, “Higher-order squeezing and photon statistics for squeezed thermal states,” Phys. Rev. A 45, 2044–2051 (1992);
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

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]

J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Non-Gaussian Statistics from Individual Pulses of Squeezed Light,” Phys. Rev. Lett. 92, 153601 (2004);
[Crossref] [PubMed]

Other (2)

V. D’Auria, P. Aniello, Matteo G.A. Paris, A. Porzio, and S. Solimeno “Quadrature Fourth order moment in an OPO described by time dependent coefficient Langevin equation,” in preparation

See for example: Quantum states estimation, M. G. A. Paris and J. Řeháček Eds., Lect. Not. Phys.649 (Springer, Heidelberg, 2004).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1. Schematic of the experimental setup. It essentially consists of two main parts: I — the OPO source (described into details in Ref. [14]) II — detection and acquisition bench made of a homodyne detector, a demodulation module and a PCI acquisition card (14 bits resolution).
Fig. 2.
Fig. 2. Photon number distribution for �� = P P th = 0.5 (a), 0.8 (b) and 0.95 (c) as recovered by pattern function tomography (ρnn - black columns) and in the Gaussian state hypothesis (pn - grey columns). The two determinations are different with a deviation increasing with pump power. Confidence intervals (not shown) are much smaller that the difference between the two determinations.
Fig. 3.
Fig. 3. Relative difference between the two experimental determinations of ρ 00 (by pattern function tomography) and p 0 (Gaussian hyphotesis). The reported deviations correspond to ��=0.5, 0.6, 0.65, 0.7, and 0.8 (η out =0.5), and ��=0.5, 0.8 and 0.95 (η out =0.4).
Fig. 4.
Fig. 4. Kurtosis of p(x n ) (red triangles) for three homodyne data sets: �� = P P th = 0.5 (a), 0.8 (b) and 0.95 (c). Empty circles indicate the variance (given in a.u.) for the same θ n . The phase BIN at which the variance and the Kurtosis are maximum coincides. The Kurtosis goes practically to 0 in correspondance of variance minima. The highest Kurtosis is ≈0.5 for ��=0.95. In this case the relative deviation between ρ 00 and p 0 (see text for details) reaches 10%. It is worth noting that it has been observed a maximum noise reduction of 2.4 dB.

Equations (4)

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

O = Tr [ ρ O ] = 0 2 π d θ 2 π dx p η ( x , θ ) R η [ O ] ( x , θ )
R η [ n n ] ( x , θ ) = + dk k e 1 2 η 2 η k 2 i 2 kx L n ( k 2 ) ,
R η [ Δ X 2 ( ψ ) ] ( x , θ ) = R η [ X 2 ( ψ ) ] ( x , θ ) R η [ X ( ψ ) ] 2 ¯
p n = C n A n + 1 2 P n ( B C )

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