Abstract

We have developed a new method to determine the photon statistics of a light source without the need for coincidence counting. Our method relies on using an asymmetric beam-splitter with intentional asymmetrical losses in a non-photon-number resolving detection system. We observe that the counts from one arm of the beam-splitter, when plotted as a function of the counts from the other arm, follow universal single-parameter curves that hint to the statistics of the photon source. We make a series of measurements on single photons detected from an attenuated laser source and show that the data clearly conforms to the universal curve established exclusively for coherent sources. We also show that the data cannot be fitted to the universal curve for thermal and photon-number sources.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. F. Arecchi, E. Gatti, and A. Sona, “Time distribution of photons from coherent and gaussian sources,” Phys. Lett. 20(1), 27–29 (1966).
    [Crossref]
  2. B. E. A. Saleh, D. Stoler, and M. C. Teich, “Coherence and photon statistics for optical fields generated by poisson random emissions,” Phys. Rev. A 27(1), 360–374 (1983).
    [Crossref]
  3. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
    [Crossref]
  4. T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, “Quantum computation with optical coherent states,” Phys. Rev. A 68(4), 042319 (2003).
    [Crossref]
  5. C. Silberhorn, “Detecting quantum light,” Contemp. Phys. 48(3), 143–156 (2007).
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  6. C. J. Chunnilall, I. P. Degiovanni, S. Kück, I. Müller, and A. G. Sinclair, “Metrology of single-photon sources and detectors: a review,” Opt. Eng. 53(8), 081910 (2014).
    [Crossref]
  7. R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130(6), 2529–2539 (1963).
    [Crossref]
  8. H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39(11), 691–695 (1977).
    [Crossref]
  9. R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177(4497), 27–29 (1956).
    [Crossref]
  10. P. Grangier, G. Roger, and A. Aspect, “Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences,” Europhys. Lett. 1(4), 173–179 (1986).
    [Crossref]
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    [Crossref]
  13. S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Evaluation of statistical noise in measurements based on correlated photons,” J. Opt. Soc. Am. B 19(6), 1247–1258 (2002).
    [Crossref]
  14. M. Beck, “Comparing measurements of g(2)(0) performed with different coincidence detection techniques,” J. Opt. Soc. Am. B 24(12), 2972–2978 (2007).
    [Crossref]
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  16. J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72(9), 1210–1219 (2004).
    [Crossref]
  17. M. Beck, Quantum Mechanics: Theory and Experiment (OUP USA, 2012).
  18. G. Brida, S. Castelletto, I. P. Degiovanni, C. Novero, and M. L. Rastello, “Quantum efficiency and dead time of single-photon counting photodiodes: a comparison between two measurement techniques,” Metrologia 37(5), 625–628 (2000).
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  25. B. L. Morgan and L. Mandel, “Measurement of photon bunching in a thermal light beam,” Phys. Rev. Lett. 16(22), 1012–1015 (1966).
    [Crossref]
  26. K. Banaszek and I. A. Walmsley, “Photon counting with a loop detector,” Opt. Lett. 28(1), 52 (2003).
    [Crossref]
  27. J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
    [Crossref]
  28. O. Haderka, M. Hamar, and J. Peřina, “Experimental multi-photon-resolving detector using a single avalanche photodiode,” Eur. Phys. J. D 28(1), 149–154 (2004).
    [Crossref]
  29. G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. Paris, “Experimental reconstruction of photon statistics without photon counting,” Phys. Rev. Lett. 95(6), 063602 (2005).
    [Crossref]

2014 (2)

C. J. Chunnilall, I. P. Degiovanni, S. Kück, I. Müller, and A. G. Sinclair, “Metrology of single-photon sources and detectors: a review,” Opt. Eng. 53(8), 081910 (2014).
[Crossref]

Y. Zhai, F. E. Becerra, J. Fan, and A. Migdall, “Direct measurement of sub-wavelength interference using thermal light and photon-number-resolved detection,” Appl. Phys. Lett. 105(10), 101104 (2014).
[Crossref]

2007 (2)

2005 (1)

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. Paris, “Experimental reconstruction of photon statistics without photon counting,” Phys. Rev. Lett. 95(6), 063602 (2005).
[Crossref]

2004 (2)

O. Haderka, M. Hamar, and J. Peřina, “Experimental multi-photon-resolving detector using a single avalanche photodiode,” Eur. Phys. J. D 28(1), 149–154 (2004).
[Crossref]

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72(9), 1210–1219 (2004).
[Crossref]

2003 (3)

T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, “Quantum computation with optical coherent states,” Phys. Rev. A 68(4), 042319 (2003).
[Crossref]

K. Banaszek and I. A. Walmsley, “Photon counting with a loop detector,” Opt. Lett. 28(1), 52 (2003).
[Crossref]

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
[Crossref]

2002 (1)

2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[Crossref]

2000 (2)

G. Brida, S. Castelletto, I. P. Degiovanni, C. Novero, and M. L. Rastello, “Quantum efficiency and dead time of single-photon counting photodiodes: a comparison between two measurement techniques,” Metrologia 37(5), 625–628 (2000).
[Crossref]

U. Leonhardt, “Measuring the quantum state of light,” Meas. Sci. Technol. 11(12), 1827–1828 (2000).
[Crossref]

1999 (1)

M. M. Hayat, S. N. Torres, and L. M. Pedrotti, “Theory of photon coincidence statistics in photon-correlated beams,” Opt. Commun. 169(1–6), 275–287 (1999).
[Crossref]

1986 (1)

P. Grangier, G. Roger, and A. Aspect, “Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences,” Europhys. Lett. 1(4), 173–179 (1986).
[Crossref]

1983 (1)

B. E. A. Saleh, D. Stoler, and M. C. Teich, “Coherence and photon statistics for optical fields generated by poisson random emissions,” Phys. Rev. A 27(1), 360–374 (1983).
[Crossref]

1977 (1)

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39(11), 691–695 (1977).
[Crossref]

1971 (2)

1966 (2)

B. L. Morgan and L. Mandel, “Measurement of photon bunching in a thermal light beam,” Phys. Rev. Lett. 16(22), 1012–1015 (1966).
[Crossref]

F. Arecchi, E. Gatti, and A. Sona, “Time distribution of photons from coherent and gaussian sources,” Phys. Lett. 20(1), 27–29 (1966).
[Crossref]

1964 (1)

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32(12), 919–926 (1964).
[Crossref]

1963 (1)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130(6), 2529–2539 (1963).
[Crossref]

1956 (1)

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177(4497), 27–29 (1956).
[Crossref]

1938 (1)

C. Eckart and F. R. Shonka, “Accidental coincidences in counter circuits,” Phys. Rev. 53(9), 752–756 (1938).
[Crossref]

Andreoni, A.

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. Paris, “Experimental reconstruction of photon statistics without photon counting,” Phys. Rev. Lett. 95(6), 063602 (2005).
[Crossref]

Arecchi, F.

F. Arecchi, E. Gatti, and A. Sona, “Time distribution of photons from coherent and gaussian sources,” Phys. Lett. 20(1), 27–29 (1966).
[Crossref]

Aspect, A.

P. Grangier, G. Roger, and A. Aspect, “Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences,” Europhys. Lett. 1(4), 173–179 (1986).
[Crossref]

Banaszek, K.

Becerra, F. E.

Y. Zhai, F. E. Becerra, J. Fan, and A. Migdall, “Direct measurement of sub-wavelength interference using thermal light and photon-number-resolved detection,” Appl. Phys. Lett. 105(10), 101104 (2014).
[Crossref]

Beck, M.

M. Beck, “Comparing measurements of g(2)(0) performed with different coincidence detection techniques,” J. Opt. Soc. Am. B 24(12), 2972–2978 (2007).
[Crossref]

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72(9), 1210–1219 (2004).
[Crossref]

M. Beck, Quantum Mechanics: Theory and Experiment (OUP USA, 2012).

Bergreen, G. S.

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72(9), 1210–1219 (2004).
[Crossref]

Bondani, M.

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. Paris, “Experimental reconstruction of photon statistics without photon counting,” Phys. Rev. Lett. 95(6), 063602 (2005).
[Crossref]

Brida, G.

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. Paris, “Experimental reconstruction of photon statistics without photon counting,” Phys. Rev. Lett. 95(6), 063602 (2005).
[Crossref]

G. Brida, S. Castelletto, I. P. Degiovanni, C. Novero, and M. L. Rastello, “Quantum efficiency and dead time of single-photon counting photodiodes: a comparison between two measurement techniques,” Metrologia 37(5), 625–628 (2000).
[Crossref]

Castelletto, S.

S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Evaluation of statistical noise in measurements based on correlated photons,” J. Opt. Soc. Am. B 19(6), 1247–1258 (2002).
[Crossref]

G. Brida, S. Castelletto, I. P. Degiovanni, C. Novero, and M. L. Rastello, “Quantum efficiency and dead time of single-photon counting photodiodes: a comparison between two measurement techniques,” Metrologia 37(5), 625–628 (2000).
[Crossref]

Chunnilall, C. J.

C. J. Chunnilall, I. P. Degiovanni, S. Kück, I. Müller, and A. G. Sinclair, “Metrology of single-photon sources and detectors: a review,” Opt. Eng. 53(8), 081910 (2014).
[Crossref]

Dagenais, M.

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39(11), 691–695 (1977).
[Crossref]

Davies, R. E.

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72(9), 1210–1219 (2004).
[Crossref]

Degiovanni, I. P.

C. J. Chunnilall, I. P. Degiovanni, S. Kück, I. Müller, and A. G. Sinclair, “Metrology of single-photon sources and detectors: a review,” Opt. Eng. 53(8), 081910 (2014).
[Crossref]

S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Evaluation of statistical noise in measurements based on correlated photons,” J. Opt. Soc. Am. B 19(6), 1247–1258 (2002).
[Crossref]

G. Brida, S. Castelletto, I. P. Degiovanni, C. Novero, and M. L. Rastello, “Quantum efficiency and dead time of single-photon counting photodiodes: a comparison between two measurement techniques,” Metrologia 37(5), 625–628 (2000).
[Crossref]

Donato, V. W.

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72(9), 1210–1219 (2004).
[Crossref]

Eckart, C.

C. Eckart and F. R. Shonka, “Accidental coincidences in counter circuits,” Phys. Rev. 53(9), 752–756 (1938).
[Crossref]

Estes, L. E.

Fan, J.

Y. Zhai, F. E. Becerra, J. Fan, and A. Migdall, “Direct measurement of sub-wavelength interference using thermal light and photon-number-resolved detection,” Appl. Phys. Lett. 105(10), 101104 (2014).
[Crossref]

Gatti, E.

F. Arecchi, E. Gatti, and A. Sona, “Time distribution of photons from coherent and gaussian sources,” Phys. Lett. 20(1), 27–29 (1966).
[Crossref]

Genovese, M.

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. Paris, “Experimental reconstruction of photon statistics without photon counting,” Phys. Rev. Lett. 95(6), 063602 (2005).
[Crossref]

Gerry, C.

C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, 2004).

Gilchrist, A.

T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, “Quantum computation with optical coherent states,” Phys. Rev. A 68(4), 042319 (2003).
[Crossref]

Glancy, S.

T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, “Quantum computation with optical coherent states,” Phys. Rev. A 68(4), 042319 (2003).
[Crossref]

Glauber, R. J.

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130(6), 2529–2539 (1963).
[Crossref]

Gramegna, M.

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. Paris, “Experimental reconstruction of photon statistics without photon counting,” Phys. Rev. Lett. 95(6), 063602 (2005).
[Crossref]

Grangier, P.

P. Grangier, G. Roger, and A. Aspect, “Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences,” Europhys. Lett. 1(4), 173–179 (1986).
[Crossref]

Haderka, O.

O. Haderka, M. Hamar, and J. Peřina, “Experimental multi-photon-resolving detector using a single avalanche photodiode,” Eur. Phys. J. D 28(1), 149–154 (2004).
[Crossref]

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
[Crossref]

Hamar, M.

O. Haderka, M. Hamar, and J. Peřina, “Experimental multi-photon-resolving detector using a single avalanche photodiode,” Eur. Phys. J. D 28(1), 149–154 (2004).
[Crossref]

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
[Crossref]

Hanbury Brown, R.

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177(4497), 27–29 (1956).
[Crossref]

Hayat, M. M.

M. M. Hayat, S. N. Torres, and L. M. Pedrotti, “Theory of photon coincidence statistics in photon-correlated beams,” Opt. Commun. 169(1–6), 275–287 (1999).
[Crossref]

Hradil, Z.

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
[Crossref]

Kimble, H. J.

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39(11), 691–695 (1977).
[Crossref]

Knight, P.

C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, 2004).

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[Crossref]

Kück, S.

C. J. Chunnilall, I. P. Degiovanni, S. Kück, I. Müller, and A. G. Sinclair, “Metrology of single-photon sources and detectors: a review,” Opt. Eng. 53(8), 081910 (2014).
[Crossref]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[Crossref]

Leonhardt, U.

U. Leonhardt, “Measuring the quantum state of light,” Meas. Sci. Technol. 11(12), 1827–1828 (2000).
[Crossref]

Mandel, L.

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39(11), 691–695 (1977).
[Crossref]

B. L. Morgan and L. Mandel, “Measurement of photon bunching in a thermal light beam,” Phys. Rev. Lett. 16(22), 1012–1015 (1966).
[Crossref]

Martienssen, W.

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32(12), 919–926 (1964).
[Crossref]

Migdall, A.

Y. Zhai, F. E. Becerra, J. Fan, and A. Migdall, “Direct measurement of sub-wavelength interference using thermal light and photon-number-resolved detection,” Appl. Phys. Lett. 105(10), 101104 (2014).
[Crossref]

Milburn, G. J.

T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, “Quantum computation with optical coherent states,” Phys. Rev. A 68(4), 042319 (2003).
[Crossref]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[Crossref]

Morgan, B. L.

B. L. Morgan and L. Mandel, “Measurement of photon bunching in a thermal light beam,” Phys. Rev. Lett. 16(22), 1012–1015 (1966).
[Crossref]

Müller, I.

C. J. Chunnilall, I. P. Degiovanni, S. Kück, I. Müller, and A. G. Sinclair, “Metrology of single-photon sources and detectors: a review,” Opt. Eng. 53(8), 081910 (2014).
[Crossref]

Munro, W. J.

T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, “Quantum computation with optical coherent states,” Phys. Rev. A 68(4), 042319 (2003).
[Crossref]

Narducci, L. M.

Neel, M. S.

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72(9), 1210–1219 (2004).
[Crossref]

Novero, C.

G. Brida, S. Castelletto, I. P. Degiovanni, C. Novero, and M. L. Rastello, “Quantum efficiency and dead time of single-photon counting photodiodes: a comparison between two measurement techniques,” Metrologia 37(5), 625–628 (2000).
[Crossref]

Paris, M. G.

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. Paris, “Experimental reconstruction of photon statistics without photon counting,” Phys. Rev. Lett. 95(6), 063602 (2005).
[Crossref]

Pedrotti, L. M.

M. M. Hayat, S. N. Torres, and L. M. Pedrotti, “Theory of photon coincidence statistics in photon-correlated beams,” Opt. Commun. 169(1–6), 275–287 (1999).
[Crossref]

Perina, J.

O. Haderka, M. Hamar, and J. Peřina, “Experimental multi-photon-resolving detector using a single avalanche photodiode,” Eur. Phys. J. D 28(1), 149–154 (2004).
[Crossref]

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
[Crossref]

Ralph, T. C.

T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, “Quantum computation with optical coherent states,” Phys. Rev. A 68(4), 042319 (2003).
[Crossref]

Rastello, M. L.

S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Evaluation of statistical noise in measurements based on correlated photons,” J. Opt. Soc. Am. B 19(6), 1247–1258 (2002).
[Crossref]

G. Brida, S. Castelletto, I. P. Degiovanni, C. Novero, and M. L. Rastello, “Quantum efficiency and dead time of single-photon counting photodiodes: a comparison between two measurement techniques,” Metrologia 37(5), 625–628 (2000).
[Crossref]

Rehácek, J.

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
[Crossref]

Roger, G.

P. Grangier, G. Roger, and A. Aspect, “Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences,” Europhys. Lett. 1(4), 173–179 (1986).
[Crossref]

Rossi, A.

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. Paris, “Experimental reconstruction of photon statistics without photon counting,” Phys. Rev. Lett. 95(6), 063602 (2005).
[Crossref]

Rousseau, M.

Saleh, B. E. A.

B. E. A. Saleh, D. Stoler, and M. C. Teich, “Coherence and photon statistics for optical fields generated by poisson random emissions,” Phys. Rev. A 27(1), 360–374 (1983).
[Crossref]

Shonka, F. R.

C. Eckart and F. R. Shonka, “Accidental coincidences in counter circuits,” Phys. Rev. 53(9), 752–756 (1938).
[Crossref]

Silberhorn, C.

C. Silberhorn, “Detecting quantum light,” Contemp. Phys. 48(3), 143–156 (2007).
[Crossref]

Sinclair, A. G.

C. J. Chunnilall, I. P. Degiovanni, S. Kück, I. Müller, and A. G. Sinclair, “Metrology of single-photon sources and detectors: a review,” Opt. Eng. 53(8), 081910 (2014).
[Crossref]

Sona, A.

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W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32(12), 919–926 (1964).
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B. E. A. Saleh, D. Stoler, and M. C. Teich, “Coherence and photon statistics for optical fields generated by poisson random emissions,” Phys. Rev. A 27(1), 360–374 (1983).
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B. E. A. Saleh, D. Stoler, and M. C. Teich, “Coherence and photon statistics for optical fields generated by poisson random emissions,” Phys. Rev. A 27(1), 360–374 (1983).
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J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72(9), 1210–1219 (2004).
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Torres, S. N.

M. M. Hayat, S. N. Torres, and L. M. Pedrotti, “Theory of photon coincidence statistics in photon-correlated beams,” Opt. Commun. 169(1–6), 275–287 (1999).
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G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. Paris, “Experimental reconstruction of photon statistics without photon counting,” Phys. Rev. Lett. 95(6), 063602 (2005).
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Y. Zhai, F. E. Becerra, J. Fan, and A. Migdall, “Direct measurement of sub-wavelength interference using thermal light and photon-number-resolved detection,” Appl. Phys. Lett. 105(10), 101104 (2014).
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J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72(9), 1210–1219 (2004).
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Y. Zhai, F. E. Becerra, J. Fan, and A. Migdall, “Direct measurement of sub-wavelength interference using thermal light and photon-number-resolved detection,” Appl. Phys. Lett. 105(10), 101104 (2014).
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R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177(4497), 27–29 (1956).
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M. M. Hayat, S. N. Torres, and L. M. Pedrotti, “Theory of photon coincidence statistics in photon-correlated beams,” Opt. Commun. 169(1–6), 275–287 (1999).
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C. J. Chunnilall, I. P. Degiovanni, S. Kück, I. Müller, and A. G. Sinclair, “Metrology of single-photon sources and detectors: a review,” Opt. Eng. 53(8), 081910 (2014).
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Figures (4)

Fig. 1.
Fig. 1. The conceptual framework of the experiment: the light source is coupled in port $\hat {a}$ of the beam-splitter $\textrm {BS}_\textrm{a}$. The reflected and transmitted photons from $\textrm {BS}_\textrm{a}$ appear in ports $\hat {a}_r$ and $\hat {a}_t$, respectively. $\hat {a}_v$ signifies the unused port (vacuum). The losses are modeled with the hypothetical beam-splitters $\textrm {BS}_\textrm{b}$ and $\textrm {BS}_\textrm{c}$. The non-photon-number resolving detectors are coupled to $\hat {b}_t$ and $\hat {c}_t$ ports. $\hat {b}_v$ and $\hat {c}_v$ are empty vacuum ports, and $\hat {b}_r$ and $\hat {c}_r$ represent the losses in their corresponding arms.
Fig. 2.
Fig. 2. A schematic of the experiment: the input power of the laser light is controlled by using a half-wave plate, a polarizing beam-splitter, and a linear polarizer. The attenuated laser then enters a 50:50 beam-splitter ($\textrm {BS}_\textrm{a}$). One output path of the beam-splitter goes directly to detector C (Path C), while the other path passes through another LP to introduce an intentional loss and is then collected by detector B (Path B). The pulses from photodiodes are processed by the FPGA, which also synchronizes the laser and the detectors.
Fig. 3.
Fig. 3. Measured data (dots) versus theoretical fits to Eq. (9) (solid lines) in an unbalanced beam-splitter using a laser beam as the coherent light source. Different colors show different values of imbalance corresponding to different values of $\beta$. From bottom to top, the fitted curves correspond to the loss induced in Path B using the LP at 0-degree angle (maximum transmission, red), 20-degree angle (green), 40-degree angle (blue), 60-degree angle (purple), and 80-degree angle (black). Excellent fits to Eq. (9) clearly show that the source is coherent.
Fig. 4.
Fig. 4. Similar to Fig. 3 except the solid lines represent best fits using Eq. (10) for thermal light. The low quality of fits clearly indicates that the source is not thermal.

Equations (11)

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

[ a r a t ] = [ t a i r a i r a t a ] [ a v a ] .
a ^ = i r a ( t c c ^ t + i r c c ^ r ) + t a ( i r b b ^ r + t b b ^ t ) .
ρ ^ = n = 0 P n | n ; a n ; a | = n = 0 P n n ! ( a ^ ) n | 0 ; a 0 ; a | ( a ^ ) n ,
P n ( coherent ) = exp ( n ¯ ) n ¯ n n ! , P n ( thermal ) = 1 1 + n ¯ ( n ¯ 1 + n ¯ ) n ,
P b v = Tr b r , c r , c t [ 0 ; b t | ρ ^ | 0 ; b t ] ,
P b v = n , p , q , s = 0 P n n ! δ p + q + s , n p ! q ! s ! ( T a R b ) p ( R a R c ) q ( R a T c ) s .
coherent: P b v = exp ( n ¯ T a T b ) , P c v = exp ( n ¯ R a T c ) ,
thermal: P b v = 1 1 + n ¯ T a T b , P c v = 1 1 + n ¯ R a T c .
coherent: P c s = 1 ( 1 P b s ) 1 / β ,
thermal: P c s = P b s β + ( 1 β ) P b s ,
β = T a T b R a T c .

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