Abstract

We demonstrate the use of two high speed avalanche photodiodes in exploring higher order photon correlations. By employing the photon number resolving capability of the photodiodes the response to higher order photon coincidences can be measured. As an example we show experimentally the sensitivity to higher order correlations for three types of photon sources with distinct photon statistics. This higher order correlation technique could be used as a low cost and compact tool for quantifying the degree of correlation of photon sources employed in quantum information science.

© 2011 OSA

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    [CrossRef]
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  3. K. Usami, Y. Nambu, B. S. Shi, A. Tomita, and K. Nakamura, “Observation of antinormally ordered Hanbury Brown-Twiss correlations,” Phys. Rev. Lett. 92(11), 113601 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  5. T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
    [CrossRef] [PubMed]
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  8. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
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  9. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single–photon turnstile device,” Science 290(5500), 2282–2285 (2000).
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    [CrossRef]
  23. A. W. Smith and J. A. Armstrong, “Laser photon counting distributions near threshold,” Phys. Rev. Lett. 16(25), 1169–1172 (1966).
    [CrossRef]
  24. G. Lachs, “Theoretical aspects of mixtures of thermal and coherent radiation,” Phys. Rev. 138(4B), B1012–B1016 (1965).
    [CrossRef]
  25. The value of g(2) ∼ 1.2 is corroborated experimentally by an independent measurement of g(2).
  26. M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325(5938), 297–300 (2009).
    [CrossRef] [PubMed]
  27. P. Meystre and M. Sargent, “Field quantization,” in Elements of Quantum Optics (Springer–Verlag, 1998), pp. 263–285.
  28. E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8(1), 4 (2006).
    [CrossRef]

2010

M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104(6), 063602 (2010).
[CrossRef] [PubMed]

O. Thomas, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Efficient photon number detection with silicon avalanche photodiodes,” Appl. Phys. Lett. 97(3), 031102 (2010).
[CrossRef]

2009

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[CrossRef]

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3, 696–705 (2009).
[CrossRef]

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11(11), 113033 (2009).
[CrossRef]

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325(5938), 297–300 (2009).
[CrossRef] [PubMed]

2008

B. E. Kardynal, Z. L. Yuan, and A. J. Shields, “An avalanche–photodiode–based photon–number–resolving detector,” Nat. Photonics 2(7), 425–428 (2008).

2007

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett. 91(4), 041114 (2007).
[CrossRef]

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

2006

E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8(1), 4 (2006).
[CrossRef]

2004

K. Usami, Y. Nambu, B. S. Shi, A. Tomita, and K. Nakamura, “Observation of antinormally ordered Hanbury Brown-Twiss correlations,” Phys. Rev. Lett. 92(11), 113601 (2004).
[CrossRef] [PubMed]

2002

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[CrossRef]

Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single–photon source,” Science 295(5552), 102–105 (2002).
[CrossRef]

2001

C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86(8), 1502–1505 (2001).
[CrossRef] [PubMed]

2000

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single–photon turnstile device,” Science 290(5500), 2282–2285 (2000).
[CrossRef] [PubMed]

1996

Y. Qu, S. Singh, and C. D. Cantrell, “Measurements of higher order photon bunching of light beams,” Phys. Rev. Lett. 76(8), 1236–1239 (1996).
[CrossRef] [PubMed]

1977

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

1970

G. S. Agarwal, “Field–correlation effects in multiphoton absorption processes,” Phys. Rev. A 1(5), 1445–1459 (1970).
[CrossRef]

1966

A. W. Smith and J. A. Armstrong, “Laser photon counting distributions near threshold,” Phys. Rev. Lett. 16(25), 1169–1172 (1966).
[CrossRef]

1965

G. Lachs, “Theoretical aspects of mixtures of thermal and coherent radiation,” Phys. Rev. 138(4B), B1012–B1016 (1965).
[CrossRef]

1963

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

1956

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

Adachi, Y.

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11(11), 113033 (2009).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, “Field–correlation effects in multiphoton absorption processes,” Phys. Rev. A 1(5), 1445–1459 (1970).
[CrossRef]

Armstrong, J. A.

A. W. Smith and J. A. Armstrong, “Laser photon counting distributions near threshold,” Phys. Rev. Lett. 16(25), 1169–1172 (1966).
[CrossRef]

Aspect, A.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

Aßmann, M.

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325(5938), 297–300 (2009).
[CrossRef] [PubMed]

Avenhaus, M.

M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104(6), 063602 (2010).
[CrossRef] [PubMed]

Bayer, M.

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325(5938), 297–300 (2009).
[CrossRef] [PubMed]

Beattie, N. S.

Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single–photon source,” Science 295(5552), 102–105 (2002).
[CrossRef]

Becher, C.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single–photon turnstile device,” Science 290(5500), 2282–2285 (2000).
[CrossRef] [PubMed]

Bennett, A. J.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[CrossRef]

Boiron, D.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

Cantrell, C. D.

Y. Qu, S. Singh, and C. D. Cantrell, “Measurements of higher order photon bunching of light beams,” Phys. Rev. Lett. 76(8), 1236–1239 (1996).
[CrossRef] [PubMed]

Chang, H.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

Chekhova, M. V.

M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104(6), 063602 (2010).
[CrossRef] [PubMed]

Cooper, K.

Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single–photon source,” Science 295(5552), 102–105 (2002).
[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]

Dale, Y.

C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86(8), 1502–1505 (2001).
[CrossRef] [PubMed]

Diamanti, E.

E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8(1), 4 (2006).
[CrossRef]

Dixon, A. R.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[CrossRef]

Dynes, J. F.

O. Thomas, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Efficient photon number detection with silicon avalanche photodiodes,” Appl. Phys. Lett. 97(3), 031102 (2010).
[CrossRef]

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[CrossRef]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[CrossRef]

Glauber, R. J.

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

Hadfield, R. H.

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3, 696–705 (2009).
[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]

Hogervorst, W.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

Hu, E.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single–photon turnstile device,” Science 290(5500), 2282–2285 (2000).
[CrossRef] [PubMed]

Hvam, J. M.

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325(5938), 297–300 (2009).
[CrossRef] [PubMed]

Imamoglu, A.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single–photon turnstile device,” Science 290(5500), 2282–2285 (2000).
[CrossRef] [PubMed]

Imoto, N.

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11(11), 113033 (2009).
[CrossRef]

Jeltes, T.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

Kardynal, B. E.

B. E. Kardynal, Z. L. Yuan, and A. J. Shields, “An avalanche–photodiode–based photon–number–resolving detector,” Nat. Photonics 2(7), 425–428 (2008).

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett. 91(4), 041114 (2007).
[CrossRef]

Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single–photon source,” Science 295(5552), 102–105 (2002).
[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]

Kiraz, A.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single–photon turnstile device,” Science 290(5500), 2282–2285 (2000).
[CrossRef] [PubMed]

Koashi, M.

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11(11), 113033 (2009).
[CrossRef]

Krachmalnicoff, V.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

Lachs, G.

G. Lachs, “Theoretical aspects of mixtures of thermal and coherent radiation,” Phys. Rev. 138(4B), B1012–B1016 (1965).
[CrossRef]

Laiho, K.

M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104(6), 063602 (2010).
[CrossRef] [PubMed]

Lobo, C. J.

Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single–photon source,” Science 295(5552), 102–105 (2002).
[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]

L. Mandel and E. Wolf, “Quantum theory of photoelectric light detection,” in Optical Coherence and Quantum Optics (Cambridge University Press, 1995), pp. 683–740.

McNamara, J. M.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

Meystre, P.

P. Meystre and M. Sargent, “Field quantization,” in Elements of Quantum Optics (Springer–Verlag, 1998), pp. 263–285.

Michler, P.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single–photon turnstile device,” Science 290(5500), 2282–2285 (2000).
[CrossRef] [PubMed]

Milburn, G. J.

D. F. Walls and G. J. Milburn, “Coherence properties of the electromagnetic field,” in Quantum Optics (Springer-Verlag, 2008), pp. 29–55.
[CrossRef]

Nakamura, K.

K. Usami, Y. Nambu, B. S. Shi, A. Tomita, and K. Nakamura, “Observation of antinormally ordered Hanbury Brown-Twiss correlations,” Phys. Rev. Lett. 92(11), 113601 (2004).
[CrossRef] [PubMed]

Nambu, Y.

K. Usami, Y. Nambu, B. S. Shi, A. Tomita, and K. Nakamura, “Observation of antinormally ordered Hanbury Brown-Twiss correlations,” Phys. Rev. Lett. 92(11), 113601 (2004).
[CrossRef] [PubMed]

Pelton, M.

C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86(8), 1502–1505 (2001).
[CrossRef] [PubMed]

Pepper, M.

Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single–photon source,” Science 295(5552), 102–105 (2002).
[CrossRef]

Perrin, A.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

Petroff, P. M.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single–photon turnstile device,” Science 290(5500), 2282–2285 (2000).
[CrossRef] [PubMed]

Qu, Y.

Y. Qu, S. Singh, and C. D. Cantrell, “Measurements of higher order photon bunching of light beams,” Phys. Rev. Lett. 76(8), 1236–1239 (1996).
[CrossRef] [PubMed]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[CrossRef]

Ritchie, D. A.

Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single–photon source,” Science 295(5552), 102–105 (2002).
[CrossRef]

Santori, C.

C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86(8), 1502–1505 (2001).
[CrossRef] [PubMed]

Sargent, M.

P. Meystre and M. Sargent, “Field quantization,” in Elements of Quantum Optics (Springer–Verlag, 1998), pp. 263–285.

Schellekens, M.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

Schoenfeld, W. V.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single–photon turnstile device,” Science 290(5500), 2282–2285 (2000).
[CrossRef] [PubMed]

Sharpe, A. W.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[CrossRef]

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett. 91(4), 041114 (2007).
[CrossRef]

Shi, B. S.

K. Usami, Y. Nambu, B. S. Shi, A. Tomita, and K. Nakamura, “Observation of antinormally ordered Hanbury Brown-Twiss correlations,” Phys. Rev. Lett. 92(11), 113601 (2004).
[CrossRef] [PubMed]

Shields, A. J.

O. Thomas, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Efficient photon number detection with silicon avalanche photodiodes,” Appl. Phys. Lett. 97(3), 031102 (2010).
[CrossRef]

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[CrossRef]

B. E. Kardynal, Z. L. Yuan, and A. J. Shields, “An avalanche–photodiode–based photon–number–resolving detector,” Nat. Photonics 2(7), 425–428 (2008).

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett. 91(4), 041114 (2007).
[CrossRef]

Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single–photon source,” Science 295(5552), 102–105 (2002).
[CrossRef]

Silberhorn, C.

M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104(6), 063602 (2010).
[CrossRef] [PubMed]

Singh, S.

Y. Qu, S. Singh, and C. D. Cantrell, “Measurements of higher order photon bunching of light beams,” Phys. Rev. Lett. 76(8), 1236–1239 (1996).
[CrossRef] [PubMed]

Smith, A. W.

A. W. Smith and J. A. Armstrong, “Laser photon counting distributions near threshold,” Phys. Rev. Lett. 16(25), 1169–1172 (1966).
[CrossRef]

Solomon, G.

C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86(8), 1502–1505 (2001).
[CrossRef] [PubMed]

Stevenson, R. M.

Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single–photon source,” Science 295(5552), 102–105 (2002).
[CrossRef]

Thomas, O.

O. Thomas, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Efficient photon number detection with silicon avalanche photodiodes,” Appl. Phys. Lett. 97(3), 031102 (2010).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[CrossRef]

Tomita, A.

K. Usami, Y. Nambu, B. S. Shi, A. Tomita, and K. Nakamura, “Observation of antinormally ordered Hanbury Brown-Twiss correlations,” Phys. Rev. Lett. 92(11), 113601 (2004).
[CrossRef] [PubMed]

Twiss, R. Q.

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

Usami, K.

K. Usami, Y. Nambu, B. S. Shi, A. Tomita, and K. Nakamura, “Observation of antinormally ordered Hanbury Brown-Twiss correlations,” Phys. Rev. Lett. 92(11), 113601 (2004).
[CrossRef] [PubMed]

van der Poel, M.

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325(5938), 297–300 (2009).
[CrossRef] [PubMed]

Vassen, W.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

Veit, F.

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325(5938), 297–300 (2009).
[CrossRef] [PubMed]

Waks, E.

E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8(1), 4 (2006).
[CrossRef]

Walls, D. F.

D. F. Walls and G. J. Milburn, “Coherence properties of the electromagnetic field,” in Quantum Optics (Springer-Verlag, 2008), pp. 29–55.
[CrossRef]

Westbrook, C. I.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

Wolf, E.

L. Mandel and E. Wolf, “Quantum theory of photoelectric light detection,” in Optical Coherence and Quantum Optics (Cambridge University Press, 1995), pp. 683–740.

Yamamoto, T.

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11(11), 113033 (2009).
[CrossRef]

Yamamoto, Y.

E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8(1), 4 (2006).
[CrossRef]

C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86(8), 1502–1505 (2001).
[CrossRef] [PubMed]

Yuan, Z.

Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single–photon source,” Science 295(5552), 102–105 (2002).
[CrossRef]

Yuan, Z. L.

O. Thomas, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Efficient photon number detection with silicon avalanche photodiodes,” Appl. Phys. Lett. 97(3), 031102 (2010).
[CrossRef]

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[CrossRef]

B. E. Kardynal, Z. L. Yuan, and A. J. Shields, “An avalanche–photodiode–based photon–number–resolving detector,” Nat. Photonics 2(7), 425–428 (2008).

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett. 91(4), 041114 (2007).
[CrossRef]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[CrossRef]

Zhang, L.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single–photon turnstile device,” Science 290(5500), 2282–2285 (2000).
[CrossRef] [PubMed]

Appl. Phys. Lett.

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett. 91(4), 041114 (2007).
[CrossRef]

O. Thomas, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Efficient photon number detection with silicon avalanche photodiodes,” Appl. Phys. Lett. 97(3), 031102 (2010).
[CrossRef]

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[CrossRef]

Nat. Photonics

B. E. Kardynal, Z. L. Yuan, and A. J. Shields, “An avalanche–photodiode–based photon–number–resolving detector,” Nat. Photonics 2(7), 425–428 (2008).

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3, 696–705 (2009).
[CrossRef]

Nature

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

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445(7126), 402–405 (2007).
[CrossRef] [PubMed]

New J. Phys.

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11(11), 113033 (2009).
[CrossRef]

E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8(1), 4 (2006).
[CrossRef]

Phys. Rev.

G. Lachs, “Theoretical aspects of mixtures of thermal and coherent radiation,” Phys. Rev. 138(4B), B1012–B1016 (1965).
[CrossRef]

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

Phys. Rev. A

G. S. Agarwal, “Field–correlation effects in multiphoton absorption processes,” Phys. Rev. A 1(5), 1445–1459 (1970).
[CrossRef]

Phys. Rev. Lett.

C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86(8), 1502–1505 (2001).
[CrossRef] [PubMed]

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

Y. Qu, S. Singh, and C. D. Cantrell, “Measurements of higher order photon bunching of light beams,” Phys. Rev. Lett. 76(8), 1236–1239 (1996).
[CrossRef] [PubMed]

M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104(6), 063602 (2010).
[CrossRef] [PubMed]

K. Usami, Y. Nambu, B. S. Shi, A. Tomita, and K. Nakamura, “Observation of antinormally ordered Hanbury Brown-Twiss correlations,” Phys. Rev. Lett. 92(11), 113601 (2004).
[CrossRef] [PubMed]

A. W. Smith and J. A. Armstrong, “Laser photon counting distributions near threshold,” Phys. Rev. Lett. 16(25), 1169–1172 (1966).
[CrossRef]

Rev. Mod. Phys.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[CrossRef]

Science

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single–photon turnstile device,” Science 290(5500), 2282–2285 (2000).
[CrossRef] [PubMed]

Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single–photon source,” Science 295(5552), 102–105 (2002).
[CrossRef]

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325(5938), 297–300 (2009).
[CrossRef] [PubMed]

Other

P. Meystre and M. Sargent, “Field quantization,” in Elements of Quantum Optics (Springer–Verlag, 1998), pp. 263–285.

The value of g(2) ∼ 1.2 is corroborated experimentally by an independent measurement of g(2).

L. Mandel and E. Wolf, “Quantum theory of photoelectric light detection,” in Optical Coherence and Quantum Optics (Cambridge University Press, 1995), pp. 683–740.

D. F. Walls and G. J. Milburn, “Coherence properties of the electromagnetic field,” in Quantum Optics (Springer-Verlag, 2008), pp. 29–55.
[CrossRef]

D. A. Kalashikov, S. H. Tan, M. V. Chekhova, and L. A. Krivitsky, “Accessing photon bunching with photon number resolving multi-pixel detector,” Opt. Express 19(10), 9352–9363 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-10-9352 .
[CrossRef]

M. J. Stevens, B. Baek, E. A. Dauler, A. J. Kerman, R. J. Molnar, S. A. Hamilton, K. K. Berggren, R. P. Mirin, and S. W. Nam, “High–order temporal coherences of chaotic and laser light,” Opt. Express 18(2), 1430–1437 (2010), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-18-2-1430 .
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the experimental setup. The solid circles represent photons from the source under test. SD-APD1 & SD-APD2: self-differencing avalanche photodiodes (APDs), discr.: electrical signal discriminator.(b) Electrical setup for measuring weak avalanches. (c) The three types of photon source employed and pictorial representations of their frequency spectra: (i) Filtered multi-mode laser operating slightly above lasing threshold (FML) (the mode in red box denotes allowed mode), (ii) DFB laser operating near lasing threshold (LNT) & (iii) DFB laser operated well above threshold (LAT).

Fig. 2
Fig. 2

The experimentally measured distribution of avalanche voltages for a pulsed laser source operating well above threshold (black circles) and for a pulsed, mode filtered non-DFB laser source operating close to threshold (red circles). Also shown are the theoretical distributions of avalanches for a Poissonian source (black line) and a partially bunched source (red line). The dashed lines correspond to the cross-over avalanche voltages for the experimental and theoretical avalanche distributions, as described in the text. Inset: Depicts the theoretical avalanche distributions for the Poissonian source (black line) and the partially bunched source (red line) up to an avalanche voltage of 0.75V.

Fig. 3
Fig. 3

(a) Experimentally measured photon count histogram as a function of detector relative delay for source FML. SD-APD 1 and SD-APD 2 discrimination levels are both set at a high value. Inset: Second order correlation measurement for source FML with g(2) = 1.2. SD-APD 1 and SD-APD 2 discrimination levels are both set at the lowest possible discrimination level. (b) Photon correlations, γ of the three sources shown in Fig. 1(c): FML (squares), LNT (circles) & LAT (triangles). The arrows correspond to the mean positions of the photon number states assuming a avalanche voltage linear dependence on photon number. Inset: Detail of γ for source LAT. Error bars are ± 1 standard deviation of the plotted (mean) values and are plotted for all data; however only some error bars are visible due to the size of the data points.

Fig. 4
Fig. 4

Simulated correlation value as a function of discriminated SD-APD 2 Avalanche Voltage (V) state for SD-APD1 discriminator level set at n = 7 photon number state. FML (squares), LNT (circles) & LAT (triangles).

Equations (6)

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

g ( n ) = < â n â n > < â â > n
γ ( 4 ) = < â 4 â 4 > < â 2 â 2 > < â 2 â 2 >
γ ( 4 ) = g ( 4 ) g ( 2 ) * g ( 2 )
γ ( n 1 + n 2 ) = < â ( n 1 + n 2 ) â ( n 1 + n 2 ) > < â n 2 â n 2 > < â n 1 â n 1 >
γ ( n 1 + n 2 ) = g ( n 1 + n 2 ) g ( n 1 ) * g ( n 2 )
γ ( n 1 + n 2 ) = Σ n 1 , n 2 n max < â ( n 1 + n 2 ) â ( n 1 + n 2 ) > η 1 n 1 η 2 n 2 Σ n 1 , n 2 n max < â n 2 â n 2 > < â n 1 â n 1 > η 1 n 1 η 2 n 2

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