Abstract

We report measurement of the noise statistics of spontaneous parametric fluorescence in a fiber parametric amplifier with single-mode, single-photon resolution. We employ optical homodyne tomography for this purpose, which also provides a self-calibrating measurement of the noise figure of the amplifier. The measured photon statistics agree with quantum-mechanical predictions, and the amplifier’s noise figure is found to be almost quantum limited.

© 2003 Optical Society of America

Full Article  |  PDF Article

Corrections

Paul L. Voss, Renyong Tang, and Prem Kumar, "Measurement of the photon statistics and the noise figure of a fiber-optic parametric amplifier: erratum," Opt. Lett. 29, 2815-2815 (2004)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-29-23-2815

References

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  1. L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
    [CrossRef]
  2. Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  7. J. L. Blows and S. E. French, Opt. Lett. 27, 491 (2002).
    [CrossRef]
  8. M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
    [CrossRef]
  9. G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, Phys. Rev. A 50, 4298 (1994).
    [CrossRef] [PubMed]
  10. M. Vasilyev, S.-K. Choi, P. Kumar, and G. M. D’Ariano, Opt. Lett. 23, 1393 (1998).
    [CrossRef]
  11. P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, Photon. Technol. Lett. 12, 1340 (2000).
    [CrossRef]
  12. P. Voss, M. Vasilyev, Y. Su, and P. Kumar, in Optical Fiber Communication Conference (OFC), Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper WDD23-1.
  13. E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, New York, 1994), Chap. 2 and references therein.
  14. R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. 18, 1062 (1982).
    [CrossRef]

2002 (4)

L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
[CrossRef]

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, IEEE Photon. Technol. Lett. 14, 911 (2002).
[CrossRef]

J. L. Blows and S. E. French, Opt. Lett. 27, 491 (2002).
[CrossRef]

2000 (3)

W. Imajuku, A. Takada, and Y. Yamabayashi, Electron. Lett. 36, 16 (2000).
[CrossRef]

Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
[CrossRef]

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, Photon. Technol. Lett. 12, 1340 (2000).
[CrossRef]

1998 (1)

1995 (1)

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
[CrossRef]

1994 (1)

G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, Phys. Rev. A 50, 4298 (1994).
[CrossRef] [PubMed]

1987 (1)

1982 (1)

R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. 18, 1062 (1982).
[CrossRef]

Agarwal, A.

L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
[CrossRef]

Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
[CrossRef]

Anderson, M. E.

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
[CrossRef]

Andrekson, P. A.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. 18, 1062 (1982).
[CrossRef]

Blows, J. L.

Boggavarapu, D.

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
[CrossRef]

Choi, S.-K.

D’Ariano, G. M.

M. Vasilyev, S.-K. Choi, P. Kumar, and G. M. D’Ariano, Opt. Lett. 23, 1393 (1998).
[CrossRef]

G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, Phys. Rev. A 50, 4298 (1994).
[CrossRef] [PubMed]

Desurvire, E.

E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, New York, 1994), Chap. 2 and references therein.

French, S. E.

Hansryd, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Hedekvist, P. O.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Imajuku, W.

W. Imajuku, A. Takada, and Y. Yamabayashi, Electron. Lett. 36, 16 (2000).
[CrossRef]

Kazovsky, L. G.

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, IEEE Photon. Technol. Lett. 14, 911 (2002).
[CrossRef]

Kumar, P.

L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
[CrossRef]

Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
[CrossRef]

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, Photon. Technol. Lett. 12, 1340 (2000).
[CrossRef]

M. Vasilyev, S.-K. Choi, P. Kumar, and G. M. D’Ariano, Opt. Lett. 23, 1393 (1998).
[CrossRef]

P. Voss, M. Vasilyev, Y. Su, and P. Kumar, in Optical Fiber Communication Conference (OFC), Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper WDD23-1.

Levandovsky, D.

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, Photon. Technol. Lett. 12, 1340 (2000).
[CrossRef]

Li, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Macchiavello, C.

G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, Phys. Rev. A 50, 4298 (1994).
[CrossRef] [PubMed]

Marhic, M. E.

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, IEEE Photon. Technol. Lett. 14, 911 (2002).
[CrossRef]

Munroe, M.

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
[CrossRef]

Noh, T. G.

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, Photon. Technol. Lett. 12, 1340 (2000).
[CrossRef]

Paris, M. G. A.

G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, Phys. Rev. A 50, 4298 (1994).
[CrossRef] [PubMed]

Raymer, M. G.

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
[CrossRef]

Stolen, R. H.

R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. 18, 1062 (1982).
[CrossRef]

Su, Y.

L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
[CrossRef]

Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
[CrossRef]

P. Voss, M. Vasilyev, Y. Su, and P. Kumar, in Optical Fiber Communication Conference (OFC), Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper WDD23-1.

Takada, A.

W. Imajuku, A. Takada, and Y. Yamabayashi, Electron. Lett. 36, 16 (2000).
[CrossRef]

Uesaka, K.

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, IEEE Photon. Technol. Lett. 14, 911 (2002).
[CrossRef]

Vasilyev, M.

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, Photon. Technol. Lett. 12, 1340 (2000).
[CrossRef]

M. Vasilyev, S.-K. Choi, P. Kumar, and G. M. D’Ariano, Opt. Lett. 23, 1393 (1998).
[CrossRef]

P. Voss, M. Vasilyev, Y. Su, and P. Kumar, in Optical Fiber Communication Conference (OFC), Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper WDD23-1.

Voss, P.

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, Photon. Technol. Lett. 12, 1340 (2000).
[CrossRef]

P. Voss, M. Vasilyev, Y. Su, and P. Kumar, in Optical Fiber Communication Conference (OFC), Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper WDD23-1.

Wang, L.

L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
[CrossRef]

Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
[CrossRef]

Westlund, M.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Wong, K. K. Y.

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, IEEE Photon. Technol. Lett. 14, 911 (2002).
[CrossRef]

Yamabayashi, Y.

W. Imajuku, A. Takada, and Y. Yamabayashi, Electron. Lett. 36, 16 (2000).
[CrossRef]

Yuen, H. P.

Electron. Lett. (2)

Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
[CrossRef]

W. Imajuku, A. Takada, and Y. Yamabayashi, Electron. Lett. 36, 16 (2000).
[CrossRef]

IEEE J. Quantum Electron. (2)

L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
[CrossRef]

R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. 18, 1062 (1982).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, IEEE Photon. Technol. Lett. 14, 911 (2002).
[CrossRef]

Opt. Lett. (3)

Photon. Technol. Lett. (1)

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, Photon. Technol. Lett. 12, 1340 (2000).
[CrossRef]

Phys. Rev. A (2)

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A 52, R924 (1995).
[CrossRef]

G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris, Phys. Rev. A 50, 4298 (1994).
[CrossRef] [PubMed]

Other (2)

P. Voss, M. Vasilyev, Y. Su, and P. Kumar, in Optical Fiber Communication Conference (OFC), Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper WDD23-1.

E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, New York, 1994), Chap. 2 and references therein.

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Figures (3)

Fig. 1
Fig. 1

Gain profile of our FOPA. Circles, experimental data; solid curve, theoretical fit. Inset, schematic of the FOPA; abbreviations defined in text.

Fig. 2
Fig. 2

Measured photon-number distributions of PF (circles) with signal gains of (left to right) G=3.5, G=10, G=30, and G=100. Each distribution is reconstructed from 50×106 homodyne samples. Curves are plots of the BE distribution for the measured N. Inset, optical detection setup for homodyne tomography measurements: PCs, polarization controllers; PBSs, polarization beam splitters; L, lens; HWP, half-wave plate; LPF, electrical low-pass filter; BPF, electrical bandpass filter; A, electronic amplifier; A/D, analog-to-digital converter; rf LO, radio-frequency local oscillator.

Fig. 3
Fig. 3

Measured photon-number distributions of amplified CS light with G=16 and (circles) N=2.1, Nin=0.11 (circles) and (triangles) N=2.0, Nin=0.36. Each distribution was reconstructed from 5×106 million homodyne samples. The curves are plots of Eq. (1) for the measured N, G, and Nin. Inset, NF versus FOPA gain. Solid curve, the displayed equation for nsp=1; dotted curve, fit for nsp=1.17. We used 106 homodyne samples for each gain setting.

Equations (1)

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Pn,Nin,G,N=NnN+1n+1expξLnξN,

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