Abstract

Using a binomial model of sub-Poissonian light statistics, we determine and analyze the Cramer–Rao lower bound for the estimation of the contrast between two sub-Poissonian light beams. The study of this bound shows that the optimal precision of contrast estimation can be maximally improved in proportion to the Fano factor of the sub-Poissonian light sources in comparison with standard coherent light. Numerical simulations show that a simple contrast estimator can reach this bound. The general results obtained are analyzed for two practical situations involving contrast estimation between two intensity levels of a single sub-Poissonian beam.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. A. Goodman and J. W. Chipman, “Analog optical signal and image processing” in Handbook of Optics (McGraw-Hill, 1994), pp. 30.3–30.23.
  2. J. M. López-Higuera, Handbook of Optical Fibre Sensing Technology (Wiley, 2002).
  3. H. Paul, “Photon antibunching,” Rev. Mod. Phys. 54, 1061–1102(1982).
    [CrossRef]
  4. L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68, 127–173 (1996).
    [CrossRef]
  5. H. Cable and G. A. Durkin, “Parameter estimation with entangled photons produced by parametric down-conversion,” Phys. Rev. Lett. 105, 013603 (2010).
    [CrossRef] [PubMed]
  6. H. A. Bachor, A Guide to Experiments in Quantum Optics(Wiley, 2003).
  7. N. Treps, U. Andersen, B. Buchler, P. K. Lam, H.-A. Bachor, A. Maître, and C. Fabre, “Crossing the standard quantum limit for high sensitivity measurements in optical images using non classical light,” Phys. Rev. Lett. 88, 203601 (2002).
    [CrossRef] [PubMed]
  8. N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
    [CrossRef] [PubMed]
  9. V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum measurements of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537–1539(2006).
    [CrossRef] [PubMed]
  10. V. Delaubert, N. Treps, C. Fabre, H. A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett. 81, 44001 (2008).
    [CrossRef]
  11. M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Modern Phys. 71, 1539–1589 (1999).
    [CrossRef]
  12. G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge University Press, 2010).
  13. J. Fade, N. Treps, C. Fabre, and P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
    [CrossRef]
  14. J. Fade, P. Réfrégier, N. Treps, and C. Fabre, “A gain criterion for the improvement of detection tasks with sub-Poissonian light,” J. Opt. Soc. Am. A 26, 1139–1146 (2009).
    [CrossRef]
  15. P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Use of parametric down-conversion to generate sub-Poissonian light,” Phys. Rev. A 37, 2963–2967 (1988).
    [CrossRef] [PubMed]
  16. P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-Poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett. 4, 293–299 (1987).
    [CrossRef]
  17. W. H. Richardson, S. Machida, and Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867–2870(1991).
    [CrossRef] [PubMed]
  18. R. L. Franco, G. Compagno, A. Messina, and A. Napoli, “Efficient generation of N-photon binomial states and their use in quantum gates in cavity QED,” Phys. Lett. A 374, 2235–2242 (2010).
    [CrossRef]
  19. U. Fano, “Ionization yield of radiations. ii: the fluctuations of the number of ions,” Phys. Rev. 72, 26–29 (1947).
    [CrossRef]
  20. P. L. Kelley and W. H. Kleiner, “Theory of electromagnetic field measurement and photoelectron counting,” Phys. Rev. 136, A316–A334 (1964).
    [CrossRef]
  21. M. C. Teich and B. E. A. Saleh, “Effects of random deletion and additive noise on bunched and antibunched photon-counting statistics,” Opt. Lett. 7, 365–367 (1982).
    [CrossRef] [PubMed]
  22. A. L. Chaudhari and A. D. Shaligram, “Multi-wavelength optical fiber liquid refractometry based on intensity modulation,” Sens. Actuators A: Phys. 100, 160–164 (2002).
    [CrossRef]
  23. J. M. Senior, Optical Fiber Communications: Principle and Practice, 3rd ed. (Pearson Prentice-Hall, 2009).
  24. Z. Xiaoming and J. M. Khan, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
    [CrossRef]
  25. H.-P. D. Shieh, Y.-L. Chen, and C.-H. Wu, “Multilevel recording in erasable phase-change media by light intensity modulation,” Jpn. J. Appl. Phys. 40, 1850–1854 (2001).
    [CrossRef]
  26. D. Stoler, B. Saleh, and M. Teich, “Binomial states of the quantized radiation field,” J. Mod. Opt. 32, 345–355 (1985).
    [CrossRef]
  27. P. Garthwaite, I. Jolliffe, and B. Jones, Statistical Inference(Prentice-Hall, 1995).
  28. P. Réfrégier, M. Roche, and F. Goudail, “Cramer–Rao lower bound for the estimation of the degree of polarization in active coherent imagery at low photon level,” Opt. Lett. 31 (24), 3565–3567 (2006).
    [CrossRef] [PubMed]
  29. R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: Su(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
    [CrossRef] [PubMed]
  30. F. Goudail and P. Réfrégier, Statistical Image Processing Techniques for Noisy Images: An Application-Oriented Approach (Kluwer, 2004).
  31. N. Roux, F. Goudail, and P. Réfrégier, “Cramer–Rao lower bounds on the estimation of the degree of polarization in coherent imaging systems,” J. Opt. Soc. Am. A 22, 2532–2541(2005).
    [CrossRef]
  32. F. Goudail, P. Réfrégier, and N. Roux, “Estimation of the degree of polarization of coherent light in the presence of uniform and nonuniform illumination,” J. Opt. Soc. Am. A 23, 2845–2854(2006).
    [CrossRef]
  33. M. C. Teich, B. E. A. Saleh, and J. Perina, “Role of primary excitation statistics in the generation of antibunched and sub-Poisson light,” J. Opt. Soc. Am. B 1, 366–389 (1984).
    [CrossRef]
  34. S. M. Kay, “Statistical decision theory II,” in Fundamentals of Statistical Signal Processing—Volume II: Detection Theory (Prentice-Hall, 1998), pp. 186–247.

2010

H. Cable and G. A. Durkin, “Parameter estimation with entangled photons produced by parametric down-conversion,” Phys. Rev. Lett. 105, 013603 (2010).
[CrossRef] [PubMed]

R. L. Franco, G. Compagno, A. Messina, and A. Napoli, “Efficient generation of N-photon binomial states and their use in quantum gates in cavity QED,” Phys. Lett. A 374, 2235–2242 (2010).
[CrossRef]

2009

2008

J. Fade, N. Treps, C. Fabre, and P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
[CrossRef]

V. Delaubert, N. Treps, C. Fabre, H. A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett. 81, 44001 (2008).
[CrossRef]

2006

2005

2003

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

2002

N. Treps, U. Andersen, B. Buchler, P. K. Lam, H.-A. Bachor, A. Maître, and C. Fabre, “Crossing the standard quantum limit for high sensitivity measurements in optical images using non classical light,” Phys. Rev. Lett. 88, 203601 (2002).
[CrossRef] [PubMed]

A. L. Chaudhari and A. D. Shaligram, “Multi-wavelength optical fiber liquid refractometry based on intensity modulation,” Sens. Actuators A: Phys. 100, 160–164 (2002).
[CrossRef]

Z. Xiaoming and J. M. Khan, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
[CrossRef]

2001

H.-P. D. Shieh, Y.-L. Chen, and C.-H. Wu, “Multilevel recording in erasable phase-change media by light intensity modulation,” Jpn. J. Appl. Phys. 40, 1850–1854 (2001).
[CrossRef]

1999

M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Modern Phys. 71, 1539–1589 (1999).
[CrossRef]

1996

L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68, 127–173 (1996).
[CrossRef]

1991

W. H. Richardson, S. Machida, and Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867–2870(1991).
[CrossRef] [PubMed]

1989

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: Su(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef] [PubMed]

1988

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Use of parametric down-conversion to generate sub-Poissonian light,” Phys. Rev. A 37, 2963–2967 (1988).
[CrossRef] [PubMed]

1987

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-Poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett. 4, 293–299 (1987).
[CrossRef]

1985

D. Stoler, B. Saleh, and M. Teich, “Binomial states of the quantized radiation field,” J. Mod. Opt. 32, 345–355 (1985).
[CrossRef]

1984

1982

1964

P. L. Kelley and W. H. Kleiner, “Theory of electromagnetic field measurement and photoelectron counting,” Phys. Rev. 136, A316–A334 (1964).
[CrossRef]

1947

U. Fano, “Ionization yield of radiations. ii: the fluctuations of the number of ions,” Phys. Rev. 72, 26–29 (1947).
[CrossRef]

Andersen, U.

N. Treps, U. Andersen, B. Buchler, P. K. Lam, H.-A. Bachor, A. Maître, and C. Fabre, “Crossing the standard quantum limit for high sensitivity measurements in optical images using non classical light,” Phys. Rev. Lett. 88, 203601 (2002).
[CrossRef] [PubMed]

Aspect, A.

G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge University Press, 2010).

Bachor, H. A.

V. Delaubert, N. Treps, C. Fabre, H. A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett. 81, 44001 (2008).
[CrossRef]

H. A. Bachor, A Guide to Experiments in Quantum Optics(Wiley, 2003).

Bachor, H.-A.

V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum measurements of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537–1539(2006).
[CrossRef] [PubMed]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

N. Treps, U. Andersen, B. Buchler, P. K. Lam, H.-A. Bachor, A. Maître, and C. Fabre, “Crossing the standard quantum limit for high sensitivity measurements in optical images using non classical light,” Phys. Rev. Lett. 88, 203601 (2002).
[CrossRef] [PubMed]

Bowen, W. P.

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

Buchler, B.

N. Treps, U. Andersen, B. Buchler, P. K. Lam, H.-A. Bachor, A. Maître, and C. Fabre, “Crossing the standard quantum limit for high sensitivity measurements in optical images using non classical light,” Phys. Rev. Lett. 88, 203601 (2002).
[CrossRef] [PubMed]

Cable, H.

H. Cable and G. A. Durkin, “Parameter estimation with entangled photons produced by parametric down-conversion,” Phys. Rev. Lett. 105, 013603 (2010).
[CrossRef] [PubMed]

Campos, R. A.

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: Su(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef] [PubMed]

Chaudhari, A. L.

A. L. Chaudhari and A. D. Shaligram, “Multi-wavelength optical fiber liquid refractometry based on intensity modulation,” Sens. Actuators A: Phys. 100, 160–164 (2002).
[CrossRef]

Chen, Y.-L.

H.-P. D. Shieh, Y.-L. Chen, and C.-H. Wu, “Multilevel recording in erasable phase-change media by light intensity modulation,” Jpn. J. Appl. Phys. 40, 1850–1854 (2001).
[CrossRef]

Chipman, J. W.

R. A. Goodman and J. W. Chipman, “Analog optical signal and image processing” in Handbook of Optics (McGraw-Hill, 1994), pp. 30.3–30.23.

Compagno, G.

R. L. Franco, G. Compagno, A. Messina, and A. Napoli, “Efficient generation of N-photon binomial states and their use in quantum gates in cavity QED,” Phys. Lett. A 374, 2235–2242 (2010).
[CrossRef]

Davidovich, L.

L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68, 127–173 (1996).
[CrossRef]

Delaubert, V.

Durkin, G. A.

H. Cable and G. A. Durkin, “Parameter estimation with entangled photons produced by parametric down-conversion,” Phys. Rev. Lett. 105, 013603 (2010).
[CrossRef] [PubMed]

Fabre, C.

J. Fade, P. Réfrégier, N. Treps, and C. Fabre, “A gain criterion for the improvement of detection tasks with sub-Poissonian light,” J. Opt. Soc. Am. A 26, 1139–1146 (2009).
[CrossRef]

J. Fade, N. Treps, C. Fabre, and P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
[CrossRef]

V. Delaubert, N. Treps, C. Fabre, H. A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett. 81, 44001 (2008).
[CrossRef]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

N. Treps, U. Andersen, B. Buchler, P. K. Lam, H.-A. Bachor, A. Maître, and C. Fabre, “Crossing the standard quantum limit for high sensitivity measurements in optical images using non classical light,” Phys. Rev. Lett. 88, 203601 (2002).
[CrossRef] [PubMed]

G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge University Press, 2010).

Fade, J.

J. Fade, P. Réfrégier, N. Treps, and C. Fabre, “A gain criterion for the improvement of detection tasks with sub-Poissonian light,” J. Opt. Soc. Am. A 26, 1139–1146 (2009).
[CrossRef]

J. Fade, N. Treps, C. Fabre, and P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
[CrossRef]

Fano, U.

U. Fano, “Ionization yield of radiations. ii: the fluctuations of the number of ions,” Phys. Rev. 72, 26–29 (1947).
[CrossRef]

Franco, R. L.

R. L. Franco, G. Compagno, A. Messina, and A. Napoli, “Efficient generation of N-photon binomial states and their use in quantum gates in cavity QED,” Phys. Lett. A 374, 2235–2242 (2010).
[CrossRef]

Garthwaite, P.

P. Garthwaite, I. Jolliffe, and B. Jones, Statistical Inference(Prentice-Hall, 1995).

Goodman, R. A.

R. A. Goodman and J. W. Chipman, “Analog optical signal and image processing” in Handbook of Optics (McGraw-Hill, 1994), pp. 30.3–30.23.

Goudail, F.

Grosse, N.

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

Grynberg, G.

G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge University Press, 2010).

Harb, C. C.

Jolliffe, I.

P. Garthwaite, I. Jolliffe, and B. Jones, Statistical Inference(Prentice-Hall, 1995).

Jones, B.

P. Garthwaite, I. Jolliffe, and B. Jones, Statistical Inference(Prentice-Hall, 1995).

Kay, S. M.

S. M. Kay, “Statistical decision theory II,” in Fundamentals of Statistical Signal Processing—Volume II: Detection Theory (Prentice-Hall, 1998), pp. 186–247.

Kelley, P. L.

P. L. Kelley and W. H. Kleiner, “Theory of electromagnetic field measurement and photoelectron counting,” Phys. Rev. 136, A316–A334 (1964).
[CrossRef]

Khan, J. M.

Z. Xiaoming and J. M. Khan, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
[CrossRef]

Kleiner, W. H.

P. L. Kelley and W. H. Kleiner, “Theory of electromagnetic field measurement and photoelectron counting,” Phys. Rev. 136, A316–A334 (1964).
[CrossRef]

Kolobov, M.

M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Modern Phys. 71, 1539–1589 (1999).
[CrossRef]

Lam, P. K.

V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum measurements of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537–1539(2006).
[CrossRef] [PubMed]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

N. Treps, U. Andersen, B. Buchler, P. K. Lam, H.-A. Bachor, A. Maître, and C. Fabre, “Crossing the standard quantum limit for high sensitivity measurements in optical images using non classical light,” Phys. Rev. Lett. 88, 203601 (2002).
[CrossRef] [PubMed]

López-Higuera, J. M.

J. M. López-Higuera, Handbook of Optical Fibre Sensing Technology (Wiley, 2002).

Machida, S.

W. H. Richardson, S. Machida, and Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867–2870(1991).
[CrossRef] [PubMed]

Maître, A.

N. Treps, U. Andersen, B. Buchler, P. K. Lam, H.-A. Bachor, A. Maître, and C. Fabre, “Crossing the standard quantum limit for high sensitivity measurements in optical images using non classical light,” Phys. Rev. Lett. 88, 203601 (2002).
[CrossRef] [PubMed]

Messina, A.

R. L. Franco, G. Compagno, A. Messina, and A. Napoli, “Efficient generation of N-photon binomial states and their use in quantum gates in cavity QED,” Phys. Lett. A 374, 2235–2242 (2010).
[CrossRef]

Napoli, A.

R. L. Franco, G. Compagno, A. Messina, and A. Napoli, “Efficient generation of N-photon binomial states and their use in quantum gates in cavity QED,” Phys. Lett. A 374, 2235–2242 (2010).
[CrossRef]

Paul, H.

H. Paul, “Photon antibunching,” Rev. Mod. Phys. 54, 1061–1102(1982).
[CrossRef]

Perina, J.

Rarity, J. G.

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Use of parametric down-conversion to generate sub-Poissonian light,” Phys. Rev. A 37, 2963–2967 (1988).
[CrossRef] [PubMed]

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-Poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett. 4, 293–299 (1987).
[CrossRef]

Réfrégier, P.

Richardson, W. H.

W. H. Richardson, S. Machida, and Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867–2870(1991).
[CrossRef] [PubMed]

Roche, M.

Roux, N.

Saleh, B.

D. Stoler, B. Saleh, and M. Teich, “Binomial states of the quantized radiation field,” J. Mod. Opt. 32, 345–355 (1985).
[CrossRef]

Saleh, B. E. A.

Satchell, J. S.

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Use of parametric down-conversion to generate sub-Poissonian light,” Phys. Rev. A 37, 2963–2967 (1988).
[CrossRef] [PubMed]

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-Poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett. 4, 293–299 (1987).
[CrossRef]

Senior, J. M.

J. M. Senior, Optical Fiber Communications: Principle and Practice, 3rd ed. (Pearson Prentice-Hall, 2009).

Shaligram, A. D.

A. L. Chaudhari and A. D. Shaligram, “Multi-wavelength optical fiber liquid refractometry based on intensity modulation,” Sens. Actuators A: Phys. 100, 160–164 (2002).
[CrossRef]

Shieh, H.-P. D.

H.-P. D. Shieh, Y.-L. Chen, and C.-H. Wu, “Multilevel recording in erasable phase-change media by light intensity modulation,” Jpn. J. Appl. Phys. 40, 1850–1854 (2001).
[CrossRef]

Stoler, D.

D. Stoler, B. Saleh, and M. Teich, “Binomial states of the quantized radiation field,” J. Mod. Opt. 32, 345–355 (1985).
[CrossRef]

Tapster, P. R.

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Use of parametric down-conversion to generate sub-Poissonian light,” Phys. Rev. A 37, 2963–2967 (1988).
[CrossRef] [PubMed]

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-Poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett. 4, 293–299 (1987).
[CrossRef]

Teich, M.

D. Stoler, B. Saleh, and M. Teich, “Binomial states of the quantized radiation field,” J. Mod. Opt. 32, 345–355 (1985).
[CrossRef]

Teich, M. C.

Treps, N.

J. Fade, P. Réfrégier, N. Treps, and C. Fabre, “A gain criterion for the improvement of detection tasks with sub-Poissonian light,” J. Opt. Soc. Am. A 26, 1139–1146 (2009).
[CrossRef]

J. Fade, N. Treps, C. Fabre, and P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
[CrossRef]

V. Delaubert, N. Treps, C. Fabre, H. A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett. 81, 44001 (2008).
[CrossRef]

V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum measurements of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537–1539(2006).
[CrossRef] [PubMed]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

N. Treps, U. Andersen, B. Buchler, P. K. Lam, H.-A. Bachor, A. Maître, and C. Fabre, “Crossing the standard quantum limit for high sensitivity measurements in optical images using non classical light,” Phys. Rev. Lett. 88, 203601 (2002).
[CrossRef] [PubMed]

Wu, C.-H.

H.-P. D. Shieh, Y.-L. Chen, and C.-H. Wu, “Multilevel recording in erasable phase-change media by light intensity modulation,” Jpn. J. Appl. Phys. 40, 1850–1854 (2001).
[CrossRef]

Xiaoming, Z.

Z. Xiaoming and J. M. Khan, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
[CrossRef]

Yamamoto, Y.

W. H. Richardson, S. Machida, and Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867–2870(1991).
[CrossRef] [PubMed]

Eur. Phys. J. D

J. Fade, N. Treps, C. Fabre, and P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
[CrossRef]

Europhys. Lett.

V. Delaubert, N. Treps, C. Fabre, H. A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett. 81, 44001 (2008).
[CrossRef]

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-Poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett. 4, 293–299 (1987).
[CrossRef]

IEEE Trans. Commun.

Z. Xiaoming and J. M. Khan, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
[CrossRef]

J. Mod. Opt.

D. Stoler, B. Saleh, and M. Teich, “Binomial states of the quantized radiation field,” J. Mod. Opt. 32, 345–355 (1985).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

H.-P. D. Shieh, Y.-L. Chen, and C.-H. Wu, “Multilevel recording in erasable phase-change media by light intensity modulation,” Jpn. J. Appl. Phys. 40, 1850–1854 (2001).
[CrossRef]

Opt. Lett.

Phys. Lett. A

R. L. Franco, G. Compagno, A. Messina, and A. Napoli, “Efficient generation of N-photon binomial states and their use in quantum gates in cavity QED,” Phys. Lett. A 374, 2235–2242 (2010).
[CrossRef]

Phys. Rev.

U. Fano, “Ionization yield of radiations. ii: the fluctuations of the number of ions,” Phys. Rev. 72, 26–29 (1947).
[CrossRef]

P. L. Kelley and W. H. Kleiner, “Theory of electromagnetic field measurement and photoelectron counting,” Phys. Rev. 136, A316–A334 (1964).
[CrossRef]

Phys. Rev. A

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Use of parametric down-conversion to generate sub-Poissonian light,” Phys. Rev. A 37, 2963–2967 (1988).
[CrossRef] [PubMed]

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: Su(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett.

W. H. Richardson, S. Machida, and Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867–2870(1991).
[CrossRef] [PubMed]

H. Cable and G. A. Durkin, “Parameter estimation with entangled photons produced by parametric down-conversion,” Phys. Rev. Lett. 105, 013603 (2010).
[CrossRef] [PubMed]

N. Treps, U. Andersen, B. Buchler, P. K. Lam, H.-A. Bachor, A. Maître, and C. Fabre, “Crossing the standard quantum limit for high sensitivity measurements in optical images using non classical light,” Phys. Rev. Lett. 88, 203601 (2002).
[CrossRef] [PubMed]

Rev. Mod. Phys.

H. Paul, “Photon antibunching,” Rev. Mod. Phys. 54, 1061–1102(1982).
[CrossRef]

L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68, 127–173 (1996).
[CrossRef]

Rev. Modern Phys.

M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Modern Phys. 71, 1539–1589 (1999).
[CrossRef]

Science

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

Sens. Actuators A: Phys.

A. L. Chaudhari and A. D. Shaligram, “Multi-wavelength optical fiber liquid refractometry based on intensity modulation,” Sens. Actuators A: Phys. 100, 160–164 (2002).
[CrossRef]

Other

J. M. Senior, Optical Fiber Communications: Principle and Practice, 3rd ed. (Pearson Prentice-Hall, 2009).

F. Goudail and P. Réfrégier, Statistical Image Processing Techniques for Noisy Images: An Application-Oriented Approach (Kluwer, 2004).

P. Garthwaite, I. Jolliffe, and B. Jones, Statistical Inference(Prentice-Hall, 1995).

S. M. Kay, “Statistical decision theory II,” in Fundamentals of Statistical Signal Processing—Volume II: Detection Theory (Prentice-Hall, 1998), pp. 186–247.

H. A. Bachor, A Guide to Experiments in Quantum Optics(Wiley, 2003).

R. A. Goodman and J. W. Chipman, “Analog optical signal and image processing” in Handbook of Optics (McGraw-Hill, 1994), pp. 30.3–30.23.

J. M. López-Higuera, Handbook of Optical Fibre Sensing Technology (Wiley, 2002).

G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge University Press, 2010).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

The gain factor G ( F X , F Y , P ) [ G μ T ( F X , F Y , P ) ] with unknown (known) mean total intensity μ T is plotted in the solid (dashed) curve as a function of the contrast P for F X = 0.6 and F Y = 0.2 .

Fig. 2
Fig. 2

Evolution of the gain factor G ( F 0 , P ) as a function of P for F 0 = 0.5 and F 0 = 0.05 . The maximum value of the gain G max is reported by the dashed line.

Fig. 3
Fig. 3

Evolution of the CRB and the variance of estimator P ^ ML as a function of the contrast P between two intensity levels of a modulated Poissonian source (filled triangles), or a modulated light source perturbed with binomial (filled squares) or phenomenological (open circles) sub-Poissonian fluctuations. Two modulation schemes are considered, either by varying the source intensity (red, dashed–dotted curve and symbols), or by applying a partial absorption to the beam (blue, dashed curve and blue symbols).

Fig. 4
Fig. 4

Evolution of the gain factors G ( F 0 , P ) and G μ T ( F 0 , P ) as a function of the contrast P between two sub-Poissonian lights, resulting from a lossless beam splitting of an initial beam with Fano factor F 0 = 0.5 or F 0 = 0.05 .

Equations (20)

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

n { 0 , N 0 } , P N ( n ) = ( N 0 n ) η n ( 1 η ) N 0 n .
P = μ X μ Y μ X + μ Y , P [ 0 , 1 ] .
θ α :     { μ X = μ T ( 1 + P ) 2 μ Y = μ T ( 1 P ) 2 θ β :     { P = μ X μ Y μ X + μ Y μ T = μ X + μ Y .
u , u T C ( θ ^ ) u u T I F 1 ( θ ) u ,
[ I F ( θ ) ] i , j = 2 ln P N ( n | θ ) θ i θ j .
CRB ( P , F X , F Y ) = 1 P 2 μ T [ F X 1 P 2 + F Y 1 + P 2 ] .
CRB p ( P ) = 1 P 2 μ T ,
G ( F X , F Y , P ) = 2 F X ( 1 P ) + F Y ( 1 + P ) .
CRB μ T ( P , F X , F Y ) = CRB p ( P ) G μ T ( F X , F Y , P ) ,
G μ T ( F X , F Y , P ) = F X ( 1 + P ) + F Y ( 1 P ) 2 F X F Y .
G ( F 0 , P ) = 1 F 0 + P ( 1 F 0 ) .
P ^ ML = k = 1 M n X k k = 1 M n Y k k = 1 M n X k + k = 1 M n Y k ,
G ( F 0 , P ) = 2 ( 1 + F 0 ) + P 2 ( 1 F 0 ) .
G μ T ( F 0 , P ) = 2 [ ( 1 + F 0 ) P 2 ( 1 F 0 ) ] ( 1 + F 0 ) 2 P 2 ( 1 F 0 ) 2 .
ln [ P N ( n ; θ α ) ] = ln [ P N X ( n X ) × P N Y ( n Y ) ] = J = X , Y { ln ( N 0 J n J ) + n J ln ( η J ) + ( N 0 J n J ) ln ( 1 η J ) } ,
I F ( θ α ) = N 0 X μ X ( N 0 X μ X ) 0 0 N 0 Y μ Y ( N 0 Y μ Y ) ,
2 ln [ P N ( n | μ X , μ Y ) ] μ J 2 = n J μ J 2 ( N 0 J n J ) ( N 0 J μ J ) 2 ,
G = μ T 2 1 + P 2 μ T 2 1 P 2 .
I F ( θ β ) = 1 B X B Y μ T A 1 P 2 N 0 X B Y N 0 Y B X N 0 X B Y N 0 Y B X C μ T ,
I F 1 ( θ β ) = 1 P 2 4 N 0 X N 0 Y ( C μ T N 0 Y B X N 0 X B Y N 0 Y B X N 0 X B Y A μ T 1 P 2 ) .

Metrics