Abstract

Quantum correlation and its measurement are essential in exploring fundamental quantum physics problems and developing quantum-enhanced technologies. A quantum correlation may be generated and manipulated in different spaces, which demands different measurement approaches corresponding to the position, time, frequency, and polarization of quantum particles. In addition, after early proof-of-principle demonstrations, it is of great demand to measure quantum correlation in a Hilbert space large enough for real quantum applications. When the number of modes goes up to several hundreds, the single-mode addressing becomes economically unfeasible, and the processing of correlation events with hardware also becomes extremely challenging. Here, we present a general and large-scale measurement approach of the Correlation on the Spatially Mapped Photon-Level Image. The quantum correlations in other spaces are mapped into the position space and are captured by a single-photon-sensitive imaging system. Synthetic methods are developed to suppress noises so that single-photon registrations can be faithfully identified in images. We eventually succeeded in retrieving all the correlations with a big-data technique from tens of millions of images.

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

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2018 (2)

H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4, eaat3174 (2018).
[Crossref]

H.-S. Zhong, Y. Li, W. Li, L.-C. Peng, Z.-E. Su, Y. Hu, Y.-M. He, X. Ding, W. Zhang, H. Li, L. Zhang, Z. Wang, L. You, X.-L. Wang, X. Jiang, L. Li, Y.-A. Chen, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion,” Phys. Rev. Lett. 121, 250505 (2018).
[Crossref]

2017 (3)

2016 (4)

J. Gao, L.-F. Qiao, X.-F. Lin, Z.-Q. Jiao, Z. Feng, Z. Zhou, Z.-W. Gao, X.-Y. Xu, Y. Chen, H. Tang, and X.-M. Jin, “Non-classical photon correlation in a two-dimensional photonic lattice,” Opt. Express 24, 12607–12616 (2016).
[Crossref]

E. Poem, T. Hiemstra, A. Eckstein, X.-M. Jin, and I. A. Walmsley, “Free-space spectro-temporal and spatio-temporal conversion for pulsed light,” Opt. Lett. 41, 4328–4331 (2016).
[Crossref]

R. Chrapkiewicz, M. Jachura, K. Banaszek, and W. Wasilewski, “Hologram of a single photon,” Nat. Photonics 10, 576–579 (2016).
[Crossref]

M. Jachura, R. Chrapkiewicz, R. Demkowicz-Dobrzański, W. Wasilewski, and K. Banaszek, “Mode engineering for realistic quantum-enhanced interferometry,” Nat. Commun. 7, 11411 (2016).
[Crossref]

2015 (4)

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of n00n state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
[Crossref]

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
[Crossref]

M. Jachura and R. Chrapkiewicz, “Shot-by-shot imaging of Hong-Ou–Mandel interference with an intensified sCMOS camera,” Opt. Lett. 40, 1540–1543 (2015).
[Crossref]

2014 (5)

S. A. Goorden, M. Horstmann, A. P. Mosk, B. Škorić, and P. W. H. Pinkse, “Quantum-secure authentication of a physical unclonable key,” Optica 1, 421–424 (2014).
[Crossref]

M. Cifra and P. Pospíšil, “Ultra-weak photon emission from biological samples: Definition, mechanisms, properties, detection and applications,” J. Photochem. Photobiol. B 139, 2–10 (2014).
[Crossref]

R. Tang and J. Dai, “Spatiotemporal imaging of glutamate-induced biophotonic activities and transmission in neural circuits,” PLoS ONE 9, 1–8 (2014).
[Crossref]

K. Poulios, R. Keil, D. Fry, J. D. A. Meinecke, J. C. F. Matthews, A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, “Quantum walks of correlated photon pairs in two-dimensional waveguide arrays,” Phys. Rev. Lett. 112, 143604 (2014).
[Crossref]

J. Carolan, J. D. A. Meinecke, P. J. Shadbolt, N. J. Russell, N. Ismail, K. Wörhoff, T. Rudolph, M. G. Thompson, J. L. O’Brien, J. C. F. Matthews, and A. Laing, “On the experimental verification of quantum complexity in linear optics,” Nat. Photonics 8, 621–626 (2014).
[Crossref]

2013 (5)

N. Spagnolo, C. Vitelli, L. Sansoni, E. Maiorino, P. Mataloni, F. Sciarrino, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, and R. Osellame, “General rules for bosonic bunching in multimode interferometers,” Phys. Rev. Lett. 111, 130503 (2013).
[Crossref]

M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, “Photonic boson sampling in a tunable circuit,” Science 339, 794–798 (2013).
[Crossref]

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref]

J. B. Spring, P. S. Salter, B. J. Metcalf, P. C. Humphreys, M. Moore, N. Thomas-Peter, M. Barbieri, X.-M. Jin, N. K. Langford, W. S. Kolthammer, M. J. Booth, and I. A. Walmsley, “On-chip low loss heralded source of pure single photons,” Opt. Express 21, 13522–13532 (2013).
[Crossref]

2012 (1)

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref]

2011 (4)

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13, 075003 (2011).
[Crossref]

A. Prasad and P. Pospišil, “Two-dimensional imaging of spontaneous ultra-weak photon emission from the human skin: role of reactive oxygen species,” J. Biophoton. 4, 840–849 (2011).
[Crossref]

D. Stucki, M. Legré, F. Buntschu, B. Clausen, N. Felber, N. Gisin, L. Henzen, P. Junod, G. Litzistorf, P. Monbaron, L. Monat, J.-B. Page, D. Perroud, G. Ribordy, A. Rochas, S. Robyr, J. Tavares, R. Thew, P. Trinkler, S. Ventura, R. Voirol, N. Walenta, and H. Zbinden, “Long-term performance of the swiss quantum quantum key distribution network in a field environment,” New J. Phys. 13, 123001 (2011).
[Crossref]

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref]

2010 (5)

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[Crossref]

C. Wagenknecht, C.-M. Li, A. Reingruber, X.-H. Bao, A. Goebel, Y.-A. Chen, Q. Zhang, K. Chen, and J.-W. Pan, “Experimental demonstration of a heralded entanglement source,” Nat. Photonics 4, 549–552 (2010).
[Crossref]

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photonics 4, 553–556 (2010).
[Crossref]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

M. Aßmann, F. Veit, M. Bayer, C. Gies, F. Jahnke, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers,” Phys. Rev. B 81, 165314 (2010).
[Crossref]

2009 (2)

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

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, 245–249 (2009).
[Crossref]

2008 (1)

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008).
[Crossref]

2006 (1)

2005 (2)

Y.-H. Kim and W. P. Grice, “Measurement of the spectral properties of the two-photon state generated via type ii spontaneous parametric downconversion,” Opt. Lett. 30, 908–910 (2005).
[Crossref]

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over 13  km: Towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
[Crossref]

2004 (1)

H. Ou-Yang, G. Stamatas, C. Saliou, and N. Kollias, “A chemiluminescence study of uva-induced oxidative stress in human skin in vivo,” J. Investig. Dermatol. 122, 1020–1029 (2004).
[Crossref]

2003 (1)

Y.-H. Kim, “Quantum interference with beamlike type-ii spontaneous parametric down-conversion,” Phys. Rev. A 68, 013804 (2003).
[Crossref]

2002 (2)

T. Ohya, S. Yoshida, R. Kawabata, H. Okabe, and S. Kai, “Biophoton emission due to drought injury in red beans: Possibility of early detection of drought injury,” Jpn. J. Appl. Phys. 41, 4766–4771 (2002).
[Crossref]

T. Iida, Y. Yoshiki, S. Someya, and K. Okubo, “Generation of reactive oxygen species and photon emission from a browned product,” Biosci. Biotechnol. Biochem. 66, 1641–1645 (2002).
[Crossref]

2001 (1)

W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A 64, 063815 (2001).
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1995 (1)

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1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
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Ams, M.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13, 075003 (2011).
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Arkhipov, A.

S. Aaronson and A. Arkhipov, “The computational complexity of linear optics,” in STOC’11 Proceedings of the Forty-third Annual ACM Symposium on Theory of Computing (ACM, 2011), pp. 333–342.

Aßmann, M.

M. Aßmann, F. Veit, M. Bayer, C. Gies, F. Jahnke, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers,” Phys. Rev. B 81, 165314 (2010).
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M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325, 297–300 (2009).
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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, 245–249 (2009).
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Banaszek, K.

R. Chrapkiewicz, M. Jachura, K. Banaszek, and W. Wasilewski, “Hologram of a single photon,” Nat. Photonics 10, 576–579 (2016).
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M. Jachura, R. Chrapkiewicz, R. Demkowicz-Dobrzański, W. Wasilewski, and K. Banaszek, “Mode engineering for realistic quantum-enhanced interferometry,” Nat. Commun. 7, 11411 (2016).
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W. Wasilewski, P. Wasylczyk, P. Kolenderski, K. Banaszek, and C. Radzewicz, “Joint spectrum of photon pairs measured by coincidence Fourier spectroscopy,” Opt. Lett. 31, 1130–1132 (2006).
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C. Wagenknecht, C.-M. Li, A. Reingruber, X.-H. Bao, A. Goebel, Y.-A. Chen, Q. Zhang, K. Chen, and J.-W. Pan, “Experimental demonstration of a heralded entanglement source,” Nat. Photonics 4, 549–552 (2010).
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C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over 13  km: Towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
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J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
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J. B. Spring, P. S. Salter, B. J. Metcalf, P. C. Humphreys, M. Moore, N. Thomas-Peter, M. Barbieri, X.-M. Jin, N. K. Langford, W. S. Kolthammer, M. J. Booth, and I. A. Walmsley, “On-chip low loss heralded source of pure single photons,” Opt. Express 21, 13522–13532 (2013).
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S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photonics 4, 553–556 (2010).
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M. Aßmann, F. Veit, M. Bayer, C. Gies, F. Jahnke, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers,” Phys. Rev. B 81, 165314 (2010).
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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, 245–249 (2009).
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M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325, 297–300 (2009).
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M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
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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, 245–249 (2009).
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J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13, 075003 (2011).
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Booth, M. J.

Boyd, R. W.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
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M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
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N. Spagnolo, C. Vitelli, L. Sansoni, E. Maiorino, P. Mataloni, F. Sciarrino, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, and R. Osellame, “General rules for bosonic bunching in multimode interferometers,” Phys. Rev. Lett. 111, 130503 (2013).
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Bromberg, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
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M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, “Photonic boson sampling in a tunable circuit,” Science 339, 794–798 (2013).
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J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13, 075003 (2011).
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Buller, G. S.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
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D. Stucki, M. Legré, F. Buntschu, B. Clausen, N. Felber, N. Gisin, L. Henzen, P. Junod, G. Litzistorf, P. Monbaron, L. Monat, J.-B. Page, D. Perroud, G. Ribordy, A. Rochas, S. Robyr, J. Tavares, R. Thew, P. Trinkler, S. Ventura, R. Voirol, N. Walenta, and H. Zbinden, “Long-term performance of the swiss quantum quantum key distribution network in a field environment,” New J. Phys. 13, 123001 (2011).
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H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4, eaat3174 (2018).
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X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
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C. Wagenknecht, C.-M. Li, A. Reingruber, X.-H. Bao, A. Goebel, Y.-A. Chen, Q. Zhang, K. Chen, and J.-W. Pan, “Experimental demonstration of a heralded entanglement source,” Nat. Photonics 4, 549–552 (2010).
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Chen, Y.

Chen, Y.-A.

H.-S. Zhong, Y. Li, W. Li, L.-C. Peng, Z.-E. Su, Y. Hu, Y.-M. He, X. Ding, W. Zhang, H. Li, L. Zhang, Z. Wang, L. You, X.-L. Wang, X. Jiang, L. Li, Y.-A. Chen, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion,” Phys. Rev. Lett. 121, 250505 (2018).
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C. Wagenknecht, C.-M. Li, A. Reingruber, X.-H. Bao, A. Goebel, Y.-A. Chen, Q. Zhang, K. Chen, and J.-W. Pan, “Experimental demonstration of a heralded entanglement source,” Nat. Photonics 4, 549–552 (2010).
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Chrapkiewicz, R.

R. Chrapkiewicz, M. Dąbrowski, and W. Wasilewski, “High-capacity angularly multiplexed holographic memory operating at the single-photon level,” Phys. Rev. Lett. 118, 063603 (2017).
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M. Jachura, R. Chrapkiewicz, R. Demkowicz-Dobrzański, W. Wasilewski, and K. Banaszek, “Mode engineering for realistic quantum-enhanced interferometry,” Nat. Commun. 7, 11411 (2016).
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R. Chrapkiewicz, M. Jachura, K. Banaszek, and W. Wasilewski, “Hologram of a single photon,” Nat. Photonics 10, 576–579 (2016).
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M. Jachura and R. Chrapkiewicz, “Shot-by-shot imaging of Hong-Ou–Mandel interference with an intensified sCMOS camera,” Opt. Lett. 40, 1540–1543 (2015).
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Christ, A.

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011).
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Cifra, M.

M. Cifra and P. Pospíšil, “Ultra-weak photon emission from biological samples: Definition, mechanisms, properties, detection and applications,” J. Photochem. Photobiol. B 139, 2–10 (2014).
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Clausen, B.

D. Stucki, M. Legré, F. Buntschu, B. Clausen, N. Felber, N. Gisin, L. Henzen, P. Junod, G. Litzistorf, P. Monbaron, L. Monat, J.-B. Page, D. Perroud, G. Ribordy, A. Rochas, S. Robyr, J. Tavares, R. Thew, P. Trinkler, S. Ventura, R. Voirol, N. Walenta, and H. Zbinden, “Long-term performance of the swiss quantum quantum key distribution network in a field environment,” New J. Phys. 13, 123001 (2011).
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Crespi, A.

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
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N. Spagnolo, C. Vitelli, L. Sansoni, E. Maiorino, P. Mataloni, F. Sciarrino, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, and R. Osellame, “General rules for bosonic bunching in multimode interferometers,” Phys. Rev. Lett. 111, 130503 (2013).
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Cronenberg, G.

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photonics 4, 553–556 (2010).
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Dabrowski, M.

R. Chrapkiewicz, M. Dąbrowski, and W. Wasilewski, “High-capacity angularly multiplexed holographic memory operating at the single-photon level,” Phys. Rev. Lett. 118, 063603 (2017).
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Dai, J.

R. Tang and J. Dai, “Spatiotemporal imaging of glutamate-induced biophotonic activities and transmission in neural circuits,” PLoS ONE 9, 1–8 (2014).
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J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
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Davis, A. O. C.

Demkowicz-Dobrzanski, R.

M. Jachura, R. Chrapkiewicz, R. Demkowicz-Dobrzański, W. Wasilewski, and K. Banaszek, “Mode engineering for realistic quantum-enhanced interferometry,” Nat. Commun. 7, 11411 (2016).
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O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13, 5832–5836 (2013).
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H.-S. Zhong, Y. Li, W. Li, L.-C. Peng, Z.-E. Su, Y. Hu, Y.-M. He, X. Ding, W. Zhang, H. Li, L. Zhang, Z. Wang, L. You, X.-L. Wang, X. Jiang, L. Li, Y.-A. Chen, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion,” Phys. Rev. Lett. 121, 250505 (2018).
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Dove, J.

M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, “Photonic boson sampling in a tunable circuit,” Science 339, 794–798 (2013).
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Eckstein, A.

E. Poem, T. Hiemstra, A. Eckstein, X.-M. Jin, and I. A. Walmsley, “Free-space spectro-temporal and spatio-temporal conversion for pulsed light,” Opt. Lett. 41, 4328–4331 (2016).
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A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011).
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Edgar, M. P.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
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Fedrizzi, A.

M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, “Photonic boson sampling in a tunable circuit,” Science 339, 794–798 (2013).
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J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13, 075003 (2011).
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Felber, N.

D. Stucki, M. Legré, F. Buntschu, B. Clausen, N. Felber, N. Gisin, L. Henzen, P. Junod, G. Litzistorf, P. Monbaron, L. Monat, J.-B. Page, D. Perroud, G. Ribordy, A. Rochas, S. Robyr, J. Tavares, R. Thew, P. Trinkler, S. Ventura, R. Voirol, N. Walenta, and H. Zbinden, “Long-term performance of the swiss quantum quantum key distribution network in a field environment,” New J. Phys. 13, 123001 (2011).
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Feng, F.-Y.

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over 13  km: Towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
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Feng, Z.

Flamini, F.

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
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Forchel, A.

M. Aßmann, F. Veit, M. Bayer, C. Gies, F. Jahnke, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers,” Phys. Rev. B 81, 165314 (2010).
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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, 245–249 (2009).
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Fry, D.

K. Poulios, R. Keil, D. Fry, J. D. A. Meinecke, J. C. F. Matthews, A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, “Quantum walks of correlated photon pairs in two-dimensional waveguide arrays,” Phys. Rev. Lett. 112, 143604 (2014).
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Galvão, E. F.

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
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N. Spagnolo, C. Vitelli, L. Sansoni, E. Maiorino, P. Mataloni, F. Sciarrino, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, and R. Osellame, “General rules for bosonic bunching in multimode interferometers,” Phys. Rev. Lett. 111, 130503 (2013).
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Gao, J.

Gao, Z.-W.

Gates, J. C.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
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T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
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M. Aßmann, F. Veit, M. Bayer, C. Gies, F. Jahnke, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers,” Phys. Rev. B 81, 165314 (2010).
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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, 245–249 (2009).
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D. Stucki, M. Legré, F. Buntschu, B. Clausen, N. Felber, N. Gisin, L. Henzen, P. Junod, G. Litzistorf, P. Monbaron, L. Monat, J.-B. Page, D. Perroud, G. Ribordy, A. Rochas, S. Robyr, J. Tavares, R. Thew, P. Trinkler, S. Ventura, R. Voirol, N. Walenta, and H. Zbinden, “Long-term performance of the swiss quantum quantum key distribution network in a field environment,” New J. Phys. 13, 123001 (2011).
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Goebel, A.

C. Wagenknecht, C.-M. Li, A. Reingruber, X.-H. Bao, A. Goebel, Y.-A. Chen, Q. Zhang, K. Chen, and J.-W. Pan, “Experimental demonstration of a heralded entanglement source,” Nat. Photonics 4, 549–552 (2010).
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Goggin, M. E.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13, 075003 (2011).
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Goorden, S. A.

Gräfe, M.

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of n00n state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
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K. Poulios, R. Keil, D. Fry, J. D. A. Meinecke, J. C. F. Matthews, A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, “Quantum walks of correlated photon pairs in two-dimensional waveguide arrays,” Phys. Rev. Lett. 112, 143604 (2014).
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Y.-H. Kim and W. P. Grice, “Measurement of the spectral properties of the two-photon state generated via type ii spontaneous parametric downconversion,” Opt. Lett. 30, 908–910 (2005).
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H.-S. Zhong, Y. Li, W. Li, L.-C. Peng, Z.-E. Su, Y. Hu, Y.-M. He, X. Ding, W. Zhang, H. Li, L. Zhang, Z. Wang, L. You, X.-L. Wang, X. Jiang, L. Li, Y.-A. Chen, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion,” Phys. Rev. Lett. 121, 250505 (2018).
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M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of n00n state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
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Supplementary Material (2)

NameDescription
» Supplement 1       Supplementary Materials
» Visualization 1       Kinetic one-shot imaging of joint spectrum with an ICCD

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Figures (4)

Fig. 1.
Fig. 1. (a) Schematic of COSPLI. (b)–(d) Sketched solutions of mapping different variables into positions. (b) Mapping frequency to position. (c) Mapping time to position. TDFS represents a time-dependent frequency shifter. (d) Mapping polarization to position. (e) Experimental setup of mapping frequency to position and joint spectrum measurement. A mode-lock Ti:sapphire oscillator centered at 780 nm, with a laser pulse duration of 130 fs and a repetition rate of 77 MHz, pumps a 1.3-mm-thick LiB3O5 (LBO) crystal to double the laser frequency to 390 nm. The ultraviolet laser then pumps a 2-mm-thick β-BaB2O4 (BBO) crystal to create identical photon pairs via a χ(2) Type 2 spontaneous parametric down-conversion process in the beam-like scheme [30]. The correlation of the frequency space of signal and idler photons is mapped into the correlation in the position space by a blazed grating with a line density of 1200 l/mm. (f) The spectra of signal and idler photons derived from the accumulated image. (g) (Top) An accumulated image with all spectral components. The upper and lower spots are signal and idler photons, respectively. (Middle) One of the frames that possess two registered photons. The two shiny spots are distributed in the two characterized areas in the accumulated image, respectively. (Bottom) The white grids define the resolution of the correlation measurement by dividing the mapped space into many individual parts.
Fig. 2.
Fig. 2. Theoretical and experimental results of the correlation measurement. (a) and (b) are theoretical and experimental results of a time-independent joint spectral intensity matrix of photons, respectively. The vertically elliptical shape suggests the photons share no correlation. (c) and (d) are theoretical and experimental results of a time-dependent joint spectral intensity matrix, respectively. The joint spectrum of correlated photons generated by BBO is an obliquely elliptical shape rather than a strict one-to-one relationship, because the two photons are not maximally correlated in the frequency space [34].
Fig. 3.
Fig. 3. Theoretical and experimental results of a filtered joint spectrum. (a) The theoretical spectrum reshaped by filters. The white curve is the spectrum transmission rate of the bandpass filter, centered at 779.5 nm and with a full width at half maximum (FWHM) of 3 nm. (b) and (c) are theoretical and experimental results of a joint spectral intensity matrix of correlated photons, respectively.
Fig. 4.
Fig. 4. Experimental results of correlation measurements with Fourier transformation. (a) and (b) show the corrected joint spectra of correlated photons without and with bandpass filters, respectively.

Equations (2)

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Sdep(ωs,ωi)=|f(ωs,ωi)|2=|Aα(ωs+ωi)ϕ(ωs,ωi)|2,
Sindep(ωs,ωi)=ps(ωs)pi(ωi),