Abstract

We demonstrate a new approach to measuring high-order temporal coherences that uses a four-element superconducting nanowire single-photon detector. The four independent, interleaved single-photon-sensitive elements parse a single spatial mode of an optical beam over dimensions smaller than the minimum diffraction-limited spot size. Integrating this device with four-channel time-tagging electronics to generate multi-start, multi-stop histograms enables measurement of temporal coherences up to fourth order for a continuous range of all associated time delays. We observe high-order photon bunching from a chaotic, pseudo-thermal light source, measuring maximum third- and fourth-order coherence values of 5.87 ± 0.17 and 23.1 ± 1.8, respectively, in agreement with the theoretically predicted values of 3! = 6 and 4! = 24. Laser light, by contrast, is confirmed to have coherence values of approximately 1 for second, third and fourth orders at all time delays.

© 2010 OSA

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2009

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

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]

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Goltsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2), 364–373 (2009).
[CrossRef]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[CrossRef]

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and L.-A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56(2), 422–431 (2009).
[CrossRef]

J. Liu and Y. Shih, “Nth-order coherence of thermal light,” Phys. Rev. A 79(2), 023819 (2009).
[CrossRef]

2008

E. A. Dauler, M. J. Stevens, B. Baek, R. J. Molnar, S. A. Hamilton, R. P. Mirin, S. W. Nam, and K. K. Berggren, “Measuring intensity correlations with a two-element superconducting nanowire single-photon detector,” Phys. Rev. A 78(5), 053826 (2008).
[CrossRef]

2006

A. Ofir and E. N. Ribak, “Offline, multidetector intensity interferometers – I. Theory,” Mon. Not. R. Astron. Soc. 368(4), 1646–1651 (2006).
[CrossRef]

A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance- limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88(11), 111116 (2006).
[CrossRef]

K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, and K. K. Berggren, “Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express 14(2), 527–534 (2006).
[CrossRef] [PubMed]

2005

2004

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

H. Qian and E. L. Elson, “Fluorescence correlation spectroscopy with high-order and dual-color correlation to probe nonequilibrium steady states,” Proc. Natl. Acad. Sci. U.S.A. 101(9), 2828–2833 (2004).
[CrossRef] [PubMed]

2002

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[CrossRef] [PubMed]

2001

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705 (2001).
[CrossRef]

1999

1997

E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell, and C. E. Wieman, “Coherence, Correlations, and Collisions: What One Learns about Bose-Einstein Condensates from Their Decay,” Phys. Rev. Lett. 79(3), 337–340 (1997).
[CrossRef]

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]

1987

A. G. Palmer and N. L. Thompson, “Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy,” Biophys. J. 52(2), 257–270 (1987).
[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]

1976

M. Corti and V. Degiorgio, “Intrinsic third-order correlations in laser light near threshold,” Phys. Rev. A 14(4), 1475–1478 (1976).
[CrossRef]

1969

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, “Correlations in Light from a Laser at Threshold,” Phys. Rev. 178(2), 612–621 (1969).
[CrossRef]

F. Davidson, “Measurements of Photon Correlations in a Laser Beam near Threshold with Time-to-Amplitude Converter Techniques,” Phys. Rev. 185(2), 446–453 (1969).
[CrossRef]

1956

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

Agafonov, I. N.

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and L.-A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56(2), 422–431 (2009).
[CrossRef]

Alley, C. O.

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, “Correlations in Light from a Laser at Threshold,” Phys. Rev. 178(2), 612–621 (1969).
[CrossRef]

Anant, V.

Aßmann, M.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[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]

Baek, B.

E. A. Dauler, M. J. Stevens, B. Baek, R. J. Molnar, S. A. Hamilton, R. P. Mirin, S. W. Nam, and K. K. Berggren, “Measuring intensity correlations with a two-element superconducting nanowire single-photon detector,” Phys. Rev. A 78(5), 053826 (2008).
[CrossRef]

Bayer, M.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

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]

Berggren, K. K.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Goltsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2), 364–373 (2009).
[CrossRef]

E. A. Dauler, M. J. Stevens, B. Baek, R. J. Molnar, S. A. Hamilton, R. P. Mirin, S. W. Nam, and K. K. Berggren, “Measuring intensity correlations with a two-element superconducting nanowire single-photon detector,” Phys. Rev. A 78(5), 053826 (2008).
[CrossRef]

A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance- limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88(11), 111116 (2006).
[CrossRef]

K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, and K. K. Berggren, “Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express 14(2), 527–534 (2006).
[CrossRef] [PubMed]

Berstermann, T.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

Bloch, J.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[CrossRef] [PubMed]

Boitier, F.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[CrossRef]

Burt, E. A.

E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell, and C. E. Wieman, “Coherence, Correlations, and Collisions: What One Learns about Bose-Einstein Condensates from Their Decay,” Phys. Rev. Lett. 79(3), 337–340 (1997).
[CrossRef]

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, R. F.

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, “Correlations in Light from a Laser at Threshold,” Phys. Rev. 178(2), 612–621 (1969).
[CrossRef]

Chekhova, M. V.

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and L.-A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56(2), 422–431 (2009).
[CrossRef]

Chulkova, G.

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705 (2001).
[CrossRef]

Cornell, E. A.

E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell, and C. E. Wieman, “Coherence, Correlations, and Collisions: What One Learns about Bose-Einstein Condensates from Their Decay,” Phys. Rev. Lett. 79(3), 337–340 (1997).
[CrossRef]

Corti, M.

M. Corti and V. Degiorgio, “Intrinsic third-order correlations in laser light near threshold,” Phys. Rev. A 14(4), 1475–1478 (1976).
[CrossRef]

Currie, M.

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

Dagenais, M.

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

Dauler, E. A.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Goltsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2), 364–373 (2009).
[CrossRef]

E. A. Dauler, M. J. Stevens, B. Baek, R. J. Molnar, S. A. Hamilton, R. P. Mirin, S. W. Nam, and K. K. Berggren, “Measuring intensity correlations with a two-element superconducting nanowire single-photon detector,” Phys. Rev. A 78(5), 053826 (2008).
[CrossRef]

A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance- limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88(11), 111116 (2006).
[CrossRef]

K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, and K. K. Berggren, “Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express 14(2), 527–534 (2006).
[CrossRef] [PubMed]

Davidson, F.

F. Davidson, “Measurements of Photon Correlations in a Laser Beam near Threshold with Time-to-Amplitude Converter Techniques,” Phys. Rev. 185(2), 446–453 (1969).
[CrossRef]

Degiorgio, V.

M. Corti and V. Degiorgio, “Intrinsic third-order correlations in laser light near threshold,” Phys. Rev. A 14(4), 1475–1478 (1976).
[CrossRef]

Deng, H.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[CrossRef] [PubMed]

Detenbeck, R. W.

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, “Correlations in Light from a Laser at Threshold,” Phys. Rev. 178(2), 612–621 (1969).
[CrossRef]

Durian, D. J.

Dzardanov, A.

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705 (2001).
[CrossRef]

Elson, E. L.

H. Qian and E. L. Elson, “Fluorescence correlation spectroscopy with high-order and dual-color correlation to probe nonequilibrium steady states,” Proc. Natl. Acad. Sci. U.S.A. 101(9), 2828–2833 (2004).
[CrossRef] [PubMed]

Fabre, C.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[CrossRef]

Forchel, A.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

Ghrist, R. W.

E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell, and C. E. Wieman, “Coherence, Correlations, and Collisions: What One Learns about Bose-Einstein Condensates from Their Decay,” Phys. Rev. Lett. 79(3), 337–340 (1997).
[CrossRef]

Gies, C.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

Godard, A.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[CrossRef]

Gol’tsman, G.

A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance- limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88(11), 111116 (2006).
[CrossRef]

Gol’tsman, G. N.

K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, and K. K. Berggren, “Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express 14(2), 527–534 (2006).
[CrossRef] [PubMed]

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705 (2001).
[CrossRef]

Goltsman, G.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Goltsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2), 364–373 (2009).
[CrossRef]

Gruber, S. S.

Hadfield, R. H.

Hamilton, S. A.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Goltsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2), 364–373 (2009).
[CrossRef]

E. A. Dauler, M. J. Stevens, B. Baek, R. J. Molnar, S. A. Hamilton, R. P. Mirin, S. W. Nam, and K. K. Berggren, “Measuring intensity correlations with a two-element superconducting nanowire single-photon detector,” Phys. Rev. A 78(5), 053826 (2008).
[CrossRef]

Hanbury Brown, R.

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

Höfling, S.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

Holland, M. J.

E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell, and C. E. Wieman, “Coherence, Correlations, and Collisions: What One Learns about Bose-Einstein Condensates from Their Decay,” Phys. Rev. Lett. 79(3), 337–340 (1997).
[CrossRef]

Hommel, D.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[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]

Iskhakov, T. Sh.

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and L.-A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56(2), 422–431 (2009).
[CrossRef]

Jahnke, F.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

Kalden, J.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

Keicher, W. E.

A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance- limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88(11), 111116 (2006).
[CrossRef]

Kerman, A. J.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Goltsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2), 364–373 (2009).
[CrossRef]

K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, and K. K. Berggren, “Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express 14(2), 527–534 (2006).
[CrossRef] [PubMed]

A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance- limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88(11), 111116 (2006).
[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]

Kistner, C.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

Korenman, V.

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, “Correlations in Light from a Laser at Threshold,” Phys. Rev. 178(2), 612–621 (1969).
[CrossRef]

Korneev, A.

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

Kouminov, P.

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

Kruse, C.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

Lemieux, P.-A.

Lipatov, A.

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705 (2001).
[CrossRef]

Liu, J.

J. Liu and Y. Shih, “Nth-order coherence of thermal light,” Phys. Rev. A 79(2), 023819 (2009).
[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]

Miller, A. J.

Mirin, R. P.

E. A. Dauler, M. J. Stevens, B. Baek, R. J. Molnar, S. A. Hamilton, R. P. Mirin, S. W. Nam, and K. K. Berggren, “Measuring intensity correlations with a two-element superconducting nanowire single-photon detector,” Phys. Rev. A 78(5), 053826 (2008).
[CrossRef]

R. H. Hadfield, M. J. Stevens, S. S. Gruber, A. J. Miller, R. E. Schwall, R. P. Mirin, and S. W. Nam, “Single photon source characterization with a superconducting single photon detector,” Opt. Express 13(26), 10846–10853 (2005).
[CrossRef] [PubMed]

Molnar, R. J.

E. A. Dauler, M. J. Stevens, B. Baek, R. J. Molnar, S. A. Hamilton, R. P. Mirin, S. W. Nam, and K. K. Berggren, “Measuring intensity correlations with a two-element superconducting nanowire single-photon detector,” Phys. Rev. A 78(5), 053826 (2008).
[CrossRef]

Myatt, C. J.

E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell, and C. E. Wieman, “Coherence, Correlations, and Collisions: What One Learns about Bose-Einstein Condensates from Their Decay,” Phys. Rev. Lett. 79(3), 337–340 (1997).
[CrossRef]

Nam, S. W.

E. A. Dauler, M. J. Stevens, B. Baek, R. J. Molnar, S. A. Hamilton, R. P. Mirin, S. W. Nam, and K. K. Berggren, “Measuring intensity correlations with a two-element superconducting nanowire single-photon detector,” Phys. Rev. A 78(5), 053826 (2008).
[CrossRef]

R. H. Hadfield, M. J. Stevens, S. S. Gruber, A. J. Miller, R. E. Schwall, R. P. Mirin, and S. W. Nam, “Single photon source characterization with a superconducting single photon detector,” Opt. Express 13(26), 10846–10853 (2005).
[CrossRef] [PubMed]

Ofir, A.

A. Ofir and E. N. Ribak, “Offline, multidetector intensity interferometers – I. Theory,” Mon. Not. R. Astron. Soc. 368(4), 1646–1651 (2006).
[CrossRef]

Okunev, O.

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705 (2001).
[CrossRef]

Palmer, A. G.

A. G. Palmer and N. L. Thompson, “Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy,” Biophys. J. 52(2), 257–270 (1987).
[CrossRef] [PubMed]

Pearlman, A.

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

Qian, H.

H. Qian and E. L. Elson, “Fluorescence correlation spectroscopy with high-order and dual-color correlation to probe nonequilibrium steady states,” Proc. Natl. Acad. Sci. U.S.A. 101(9), 2828–2833 (2004).
[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]

Reitzenstein, S.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

Ribak, E. N.

A. Ofir and E. N. Ribak, “Offline, multidetector intensity interferometers – I. Theory,” Mon. Not. R. Astron. Soc. 368(4), 1646–1651 (2006).
[CrossRef]

Robinson, B. S.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Goltsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2), 364–373 (2009).
[CrossRef]

Rosencher, E.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[CrossRef]

Rosfjord, K. M.

Santori, C.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[CrossRef] [PubMed]

Schneider, C.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

Schwall, R. E.

Semenov, A.

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705 (2001).
[CrossRef]

Shih, Y.

J. Liu and Y. Shih, “Nth-order coherence of thermal light,” Phys. Rev. A 79(2), 023819 (2009).
[CrossRef]

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]

Slysz, W.

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

Smirnov, K.

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705 (2001).
[CrossRef]

Sobolewski, R.

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705 (2001).
[CrossRef]

Stevens, M. J.

E. A. Dauler, M. J. Stevens, B. Baek, R. J. Molnar, S. A. Hamilton, R. P. Mirin, S. W. Nam, and K. K. Berggren, “Measuring intensity correlations with a two-element superconducting nanowire single-photon detector,” Phys. Rev. A 78(5), 053826 (2008).
[CrossRef]

R. H. Hadfield, M. J. Stevens, S. S. Gruber, A. J. Miller, R. E. Schwall, R. P. Mirin, and S. W. Nam, “Single photon source characterization with a superconducting single photon detector,” Opt. Express 13(26), 10846–10853 (2005).
[CrossRef] [PubMed]

Thompson, N. L.

A. G. Palmer and N. L. Thompson, “Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy,” Biophys. J. 52(2), 257–270 (1987).
[CrossRef] [PubMed]

Twiss, R. Q.

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

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]

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]

Verevkin, A.

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

Voronov, B.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Goltsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2), 364–373 (2009).
[CrossRef]

A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance- limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88(11), 111116 (2006).
[CrossRef]

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705 (2001).
[CrossRef]

Voronov, B. M.

Weihs, G.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[CrossRef] [PubMed]

Wieman, C. E.

E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell, and C. E. Wieman, “Coherence, Correlations, and Collisions: What One Learns about Bose-Einstein Condensates from Their Decay,” Phys. Rev. Lett. 79(3), 337–340 (1997).
[CrossRef]

Wiersig, J.

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

Williams, C.

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705 (2001).
[CrossRef]

Wu, L.-A.

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and L.-A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56(2), 422–431 (2009).
[CrossRef]

Yamamoto, Y.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[CrossRef] [PubMed]

Yang, J. K. W.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Goltsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2), 364–373 (2009).
[CrossRef]

K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, and K. K. Berggren, “Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express 14(2), 527–534 (2006).
[CrossRef] [PubMed]

A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance- limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88(11), 111116 (2006).
[CrossRef]

Zhang, J.

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

Appl. Phys. Lett.

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705 (2001).
[CrossRef]

A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance- limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88(11), 111116 (2006).
[CrossRef]

Biophys. J.

A. G. Palmer and N. L. Thompson, “Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy,” Biophys. J. 52(2), 257–270 (1987).
[CrossRef] [PubMed]

J. Mod. Opt.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Goltsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2), 364–373 (2009).
[CrossRef]

A. Verevkin, A. Pearlman, W. Słysz, J. Zhang, M. Currie, A. Korneev, G. Chulkova, O. Okunev, P. Kouminov, K. Smirnov, B. Voronov, G. N. Gol’tsman, and R. Sobolewski, “Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications,” J. Mod. Opt. 51, 1447 (2004).

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and L.-A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56(2), 422–431 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Mon. Not. R. Astron. Soc.

A. Ofir and E. N. Ribak, “Offline, multidetector intensity interferometers – I. Theory,” Mon. Not. R. Astron. Soc. 368(4), 1646–1651 (2006).
[CrossRef]

Nat. Phys.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[CrossRef]

Nature

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[CrossRef] [PubMed]

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

Opt. Express

Phys. Rev.

F. Davidson, “Measurements of Photon Correlations in a Laser Beam near Threshold with Time-to-Amplitude Converter Techniques,” Phys. Rev. 185(2), 446–453 (1969).
[CrossRef]

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, “Correlations in Light from a Laser at Threshold,” Phys. Rev. 178(2), 612–621 (1969).
[CrossRef]

Phys. Rev. A

M. Corti and V. Degiorgio, “Intrinsic third-order correlations in laser light near threshold,” Phys. Rev. A 14(4), 1475–1478 (1976).
[CrossRef]

E. A. Dauler, M. J. Stevens, B. Baek, R. J. Molnar, S. A. Hamilton, R. P. Mirin, S. W. Nam, and K. K. Berggren, “Measuring intensity correlations with a two-element superconducting nanowire single-photon detector,” Phys. Rev. A 78(5), 053826 (2008).
[CrossRef]

J. Liu and Y. Shih, “Nth-order coherence of thermal light,” Phys. Rev. A 79(2), 023819 (2009).
[CrossRef]

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Supplementary Material (1)

» Media 1: MOV (2364 KB)     

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Figures (4)

Fig. 1
Fig. 1

Scanning-electron microscope image of the four-element SNSPD, with nanowire elements 0-3 traced out in color. Each element consists of a ~5 nm-thick × 80 nm-wide NbN nanowire on a sapphire substrate, with 60 nm gaps between wires. The 9.4 µm-diameter active area is well matched to the spatial mode of a single mode optical fiber, the cleaved end of which is held within ~10 µm of the detector surface. The interleaved design ensures that all four elements equally sample this spatial mode.

Fig. 2
Fig. 2

Measured nth -order temporal coherences for n = 2 (○), 3 (▲) and 4 (■). (a) Chaotic source data. The magnitude of photon bunching scales roughly as n!, as can be seen from the expected peak g (2), g (3) and g (4) values of 2 (dashed green line), 6 (dashed red line) and 24 (top axis). (b) Laser source data, also showing the expected value of 1 (black line) and the mean measured g (4) value of 1.011 (dashed blue line). In both (a) and (b), the g (2) data are displayed as a function of τ, while the g (3) and g (4) data are plotted against parameterized delays that measure temporal distance from the origin, τP 3 = ± (τ 1 2 + τ 2 2)1/2 and τP4 = ± (τ 1 2 + τ 2 2 + τ 3 2)1/2, respectively, where ± is determined by the sign of τ 1. These trace out cross sections from (τ 1, τ 2) = (−6/√2 μs, 6/√2 μs) to (6/√2 μs, −6/√2 μs) and (τ 1, τ 2, τ 3) from (−4 μs, 2 μs, 4 μs) to (4 μs, −2 μs, −4 μs).

Fig. 3
Fig. 3

(a) Measured third-order coherence from the chaotic source, where both color and height indicate measured value of g (3). The cross-section in Fig. 2(a) samples these data along a diagonal line (not shown) extending from the far left corner to the far right corner as plotted here. (b) Calculated third-order coherence for a chaotic source derived from an ideal Gaussian scattering process with a coherence time of 900 ns, as discussed in the text.

Fig. 4
Fig. 4

Four frames from a movie (Media 1) of fourth-order coherence data (left) and theory (right) for the chaotic source for four values of τ 3. Color bar at the bottom shows g (4) values.

Equations (5)

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g ( 2 ) ( τ ) = a ^ ( t ) a ^ ( t + τ ) a ^ ( t + τ ) a ^ ( t ) a ^ ( t ) a ^ ( t ) 2 ,
g ( 3 ) ( τ 1 , τ 2 ) = a ^ ( t ) a ^ ( t + τ 1 ) a ^ ( t + τ 2 ) a ^ ( t + τ 2 ) a ^ ( t + τ 1 ) a ^ ( t ) a ^ ( t ) a ^ ( t ) 3 ,
g ( 4 ) ( τ 1 , τ 2 , τ 3 ) = a ^ ( t ) a ^ ( t + τ 1 ) a ^ ( t + τ 2 ) a ^ ( t + τ 3 ) a ^ ( t + τ 3 ) a ^ ( t + τ 2 ) a ^ ( t + τ 1 ) a ^ ( t ) a ^ ( t ) a ^ ( t ) 4 ,
g ( 3 ) ( τ 1 , τ 2 ) = I ( t ) I ( t + τ 1 ) I ( t + τ 2 ) I ( t ) 3
g ( 4 ) ( τ 1 , τ 2 , τ 3 ) = I ( t ) I ( t + τ 1 ) I ( t + τ 2 ) I ( t + τ 3 ) I ( t ) 4

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