Abstract

States with sub-Poissonian photon-number statistics obtained by post-selection from twin beams are experimentally generated. States with Fano factors down to 0.62 and mean photon numbers around 12 are reached. Their quasi-distributions of integrated intensities attaining negative values are reconstructed. An intensified CCD camera with a quantum detection efficiency exceeding 20% is utilized both for post-selection and beam characterization. Experimental results are compared with theory that provides the optimum experimental conditions.

© 2013 OSA

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2013 (1)

J. Peřina, O. Haderka, V. Michálek, and M. Hamar, “State reconstruction of a multimode twin beam using photodetection,” Phys. Rev. A87, 022108 (2013).
[CrossRef]

2012 (3)

J. Peřina, M. Hamar, V. Michálek, and O. Haderka, “Photon-number distributions of twin beams generated in spontaneous parametric down-conversion and measured by an intensified CCD camera,” Phys. Rev. A85, 023816 (2012).
[CrossRef]

G. Brida, I. P. Degiovanni, M. Genovese, F. Piacentini, P. Traina, A. Della Frera, A. Tosi, A. Bahgat Shehata, C. Scarcella, A. Gulinatti, M. Ghioni, S. V. Polyakov, A. Migdall, and A. Giudice, “An extremely low-noise heralded single-photon source: A breakthrough for quantum technologies,” Appl. Phys. Lett.101, 221112 (2012).
[CrossRef]

J. Perina, O. Haderka, M. Hamar, and V. Michálek, “Absolute detector calibration using twin beams,” Opt. Lett.37, 2475–2477 (2012).
[CrossRef] [PubMed]

2011 (4)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74, 145–195 (2011).
[CrossRef]

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Phot.5, 301–305 (2011).
[CrossRef]

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98% detection efficiency with index-matched small-gap fiber coupling,” Opt. Express19, 870–875 (2011).
[CrossRef] [PubMed]

L. Lolli, G. Brida, I. P. Degiovanni, M. Gramegna, E. Monticone, F. Piacentini, C. Portesi, M. Rajteri, I. Ruo-Berchera, E. Taralli, and P. Traina, “Ti/Au TES as superconducting detector for quantum technologies,” Int. J. Quant. Inf.9, 405–413 (2011).
[CrossRef]

2010 (3)

2009 (2)

A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum state tomography,” Rev. Mod. Phys.81, 299–332 (2009).
[CrossRef]

J. Peřina, J. Křepelka, J. Peřina, M. Bondani, A. Allevi, and A. Andreoni, “Correlations in photon-numbers and integrated intensities in parametric processes involving three optical fields,” Eur. Phys. J. D53, 373–382 (2009).
[CrossRef]

2008 (3)

O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-performance guided-wave asynchronous heralded single-photon source,” Opt. Lett.30, 1539–1541 (2008).
[CrossRef]

J. Peřina and J. Křepelka, “Joint probability distributions of stimulated parametric down-conversion for controllable nonclassical fluctuations,” Eur. Phys. J. D281, 4705–4711 (2008).

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Goltsman, K. G. Lagoudakis, M. Benkahoul, F. Levy, and A. Fiore, “Superconducting nanowire photonnumber-resolving detector at telecommunication wavelengths,” Nat. Phot.2, 302–306 (2008).
[CrossRef]

2007 (2)

J. Peřina, J. Křepelka, J. Peřina, M. Bondani, A. Allevi, and A. Andreoni, “Experimental joint signal-idler quasidistributions and photon-number statistics for mesoscopic twin beams,” Phys. Rev. A76, 043806 (2007).
[CrossRef]

L. A. Jiang, E. A. Dauler, and J. T. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A75, 062325 (2007).
[CrossRef]

2006 (3)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett.96, 010401 (2006).
[CrossRef] [PubMed]

G. Brida, M. Genovese, and M. Gramegna, “Twin-photon techniques for photo-detector calibration,” Laser Phys. Lett.3, 115–123 (2006).
[CrossRef]

M. Lindenthal and J. Kofler, “Measuring the absolute photodetection efficiency using photon number correlations,” Appl. Opt.45, 6059–6063 (2006).
[CrossRef] [PubMed]

2005 (3)

M. Genovese, “Research on hidden variable theories: A review of recent progresses,” Phys. Rep.413, 319–396 (2005).
[CrossRef]

J. Peřina and J. Křepelka, “Multimode description of spontaneous parametric down-conversion,” J. Opt. B: Quant. Semiclass. Opt.7, 246–252 (2005).
[CrossRef]

O. Haderka, J. Peřina, M. Hamar, and J. Peřina, “Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion,” Phys. Rev. A71, 033815 (2005).
[CrossRef]

2004 (3)

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, “Single-photon generation with InAs quantum dots,” New. J. Phys.6, 89 (2004).
[CrossRef]

B. T. H. Varcoe, S. Brattke, and H. Walther, “The creation and detection of arbitrary photon number states using cavity QED,” New J. Phys.6, 97 (2004).
[CrossRef]

O. Haderka, M. Hamar, and J. Peřina, “Experimental multi-photon-resolving detector using a single avalanche photodiode,” Eur. Phys. J. D28, 149–154 (2004).
[CrossRef]

2003 (5)

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A67, 061801(R) (2003).
[CrossRef]

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett.28, 2387 (2003).
[CrossRef] [PubMed]

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A68, 043814 (2003).
[CrossRef]

J. Laurat, T. Coudreau, N. Treps, A. Maitre, and C. Fabre, “Conditional preparation of a quantum state in the continuous variable regime: Generation of a sub-Poissonian state from twin beams,” Phys. Rev. Lett.91, 213601 (2003).
[CrossRef] [PubMed]

A. J. Miller, S. W. Nam, J. M. Martinis, and A. V. Sergienko, “Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination,” Appl. Phys. Lett.83, 791–793 (2003).
[CrossRef]

2002 (1)

2001 (2)

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys.73, 565–583 (2001).
[CrossRef]

J. Peřina, O. Haderka, and J. Soubusta, “Quantum cryptography using a photon source based on postselection from entangled two-photon states,” Phys. Rev. A64, 052305 (2001).
[CrossRef]

2000 (2)

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett.84, 4729–4732 (2000).
[CrossRef] [PubMed]

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett.85, 290–293 (2000).
[CrossRef] [PubMed]

1999 (2)

C. Brunel, B. Lounis, P. Tamarat, and M. Orrit, “Triggered source of single photons based on controlled single molecule fluorescence,” Phys. Rev. Lett.83, 2722–2725 (1999).
[CrossRef]

A. Migdall, “Correlated-photon metrology without absolute standards,” Physics Today52, 41–46 (1999).
[CrossRef]

1998 (1)

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett.81, 5039–5043 (1998).
[CrossRef]

1997 (1)

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature390, 575–579 (1997).
[CrossRef]

1993 (1)

M. Koashi, K. Kono, T. Hirano, and M. Matsuoka, “Photon antibunching in pulsed squeezed light generated via parametric amplification,” Phys. Rev. Lett.71, 1164–1167 (1993).
[CrossRef] [PubMed]

1990 (1)

J. Mertz, A. Heidmann, C. Fabre, E. Giacobino, and S. Reynaud, “Observation of high-intensity sub-Poissonian light using an optical parametric oscillator,” Phys. Rev. Lett.64, 2897–2900 (1990).
[CrossRef] [PubMed]

1987 (2)

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

B. E. A. Saleh and M. C. Teich, “Can the channel capacity of a light-wave communication system be increased by the use of photon-number-squeezed light?” Phys. Rev. Lett.58, 2656–2659 (1987).
[CrossRef] [PubMed]

1986 (1)

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

1985 (1)

1983 (1)

R. Short and L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett.51, 384–387 (1983).
[CrossRef]

1818 (1)

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, M. V. Chekhova, A. Aiello, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Comm.4, 1818 (2013).

Abouraddy, A. F.

Achilles, D.

Aiello, A.

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, M. V. Chekhova, A. Aiello, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Comm.4, 1818 (2013).

Alibart, O.

Allevi, A.

A. Allevi, M. Bondani, and A. Andreoni, “Photon-number correlations by photon-number resolving detectors,” Opt. Lett.35, 1707–1709 (2010).
[CrossRef] [PubMed]

M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B27, 852–862 (2010).
[CrossRef]

J. Peřina, J. Křepelka, J. Peřina, M. Bondani, A. Allevi, and A. Andreoni, “Correlations in photon-numbers and integrated intensities in parametric processes involving three optical fields,” Eur. Phys. J. D53, 373–382 (2009).
[CrossRef]

J. Peřina, J. Křepelka, J. Peřina, M. Bondani, A. Allevi, and A. Andreoni, “Experimental joint signal-idler quasidistributions and photon-number statistics for mesoscopic twin beams,” Phys. Rev. A76, 043806 (2007).
[CrossRef]

Amemiya, K.

Andreoni, A.

A. Allevi, M. Bondani, and A. Andreoni, “Photon-number correlations by photon-number resolving detectors,” Opt. Lett.35, 1707–1709 (2010).
[CrossRef] [PubMed]

M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B27, 852–862 (2010).
[CrossRef]

J. Peřina, J. Křepelka, J. Peřina, M. Bondani, A. Allevi, and A. Andreoni, “Correlations in photon-numbers and integrated intensities in parametric processes involving three optical fields,” Eur. Phys. J. D53, 373–382 (2009).
[CrossRef]

J. Peřina, J. Křepelka, J. Peřina, M. Bondani, A. Allevi, and A. Andreoni, “Experimental joint signal-idler quasidistributions and photon-number statistics for mesoscopic twin beams,” Phys. Rev. A76, 043806 (2007).
[CrossRef]

Aspect, A.

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

Bahgat Shehata, A.

G. Brida, I. P. Degiovanni, M. Genovese, F. Piacentini, P. Traina, A. Della Frera, A. Tosi, A. Bahgat Shehata, C. Scarcella, A. Gulinatti, M. Ghioni, S. V. Polyakov, A. Migdall, and A. Giudice, “An extremely low-noise heralded single-photon source: A breakthrough for quantum technologies,” Appl. Phys. Lett.101, 221112 (2012).
[CrossRef]

Baldi, P.

Banaszek, K.

Barclay, P. E.

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Phot.5, 301–305 (2011).
[CrossRef]

Beausoleil, R. G.

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Phot.5, 301–305 (2011).
[CrossRef]

Benkahoul, M.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Goltsman, K. G. Lagoudakis, M. Benkahoul, F. Levy, and A. Fiore, “Superconducting nanowire photonnumber-resolving detector at telecommunication wavelengths,” Nat. Phot.2, 302–306 (2008).
[CrossRef]

Bitauld, D.

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L. Lolli, G. Brida, I. P. Degiovanni, M. Gramegna, E. Monticone, F. Piacentini, C. Portesi, M. Rajteri, I. Ruo-Berchera, E. Taralli, and P. Traina, “Ti/Au TES as superconducting detector for quantum technologies,” Int. J. Quant. Inf.9, 405–413 (2011).
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P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-Poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett.4, 293–299 (1987).
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A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Goltsman, K. G. Lagoudakis, M. Benkahoul, F. Levy, and A. Fiore, “Superconducting nanowire photonnumber-resolving detector at telecommunication wavelengths,” Nat. Phot.2, 302–306 (2008).
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A. J. Miller, S. W. Nam, J. M. Martinis, and A. V. Sergienko, “Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination,” Appl. Phys. Lett.83, 791–793 (2003).
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A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon ellipsometry,” J. Opt. Soc. Am. B19, 656–662 (2002).
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L. Lolli, G. Brida, I. P. Degiovanni, M. Gramegna, E. Monticone, F. Piacentini, C. Portesi, M. Rajteri, I. Ruo-Berchera, E. Taralli, and P. Traina, “Ti/Au TES as superconducting detector for quantum technologies,” Int. J. Quant. Inf.9, 405–413 (2011).
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A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon ellipsometry,” J. Opt. Soc. Am. B19, 656–662 (2002).
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B. E. A. Saleh and M. C. Teich, “Can the channel capacity of a light-wave communication system be increased by the use of photon-number-squeezed light?” Phys. Rev. Lett.58, 2656–2659 (1987).
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B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74, 145–195 (2011).
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G. Brida, I. P. Degiovanni, M. Genovese, F. Piacentini, P. Traina, A. Della Frera, A. Tosi, A. Bahgat Shehata, C. Scarcella, A. Gulinatti, M. Ghioni, S. V. Polyakov, A. Migdall, and A. Giudice, “An extremely low-noise heralded single-photon source: A breakthrough for quantum technologies,” Appl. Phys. Lett.101, 221112 (2012).
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Toussaint, K. C.

Traina, P.

G. Brida, I. P. Degiovanni, M. Genovese, F. Piacentini, P. Traina, A. Della Frera, A. Tosi, A. Bahgat Shehata, C. Scarcella, A. Gulinatti, M. Ghioni, S. V. Polyakov, A. Migdall, and A. Giudice, “An extremely low-noise heralded single-photon source: A breakthrough for quantum technologies,” Appl. Phys. Lett.101, 221112 (2012).
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L. Lolli, G. Brida, I. P. Degiovanni, M. Gramegna, E. Monticone, F. Piacentini, C. Portesi, M. Rajteri, I. Ruo-Berchera, E. Taralli, and P. Traina, “Ti/Au TES as superconducting detector for quantum technologies,” Int. J. Quant. Inf.9, 405–413 (2011).
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T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett.84, 4729–4732 (2000).
[CrossRef] [PubMed]

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C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett.85, 290–293 (2000).
[CrossRef] [PubMed]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett.84, 4729–4732 (2000).
[CrossRef] [PubMed]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett.81, 5039–5043 (1998).
[CrossRef]

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[CrossRef]

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M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, M. V. Chekhova, A. Aiello, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Comm.4, 1818 (2013).

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C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, “Single-photon generation with InAs quantum dots,” New. J. Phys.6, 89 (2004).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74, 145–195 (2011).
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T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett.84, 4729–4732 (2000).
[CrossRef] [PubMed]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett.81, 5039–5043 (1998).
[CrossRef]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature390, 575–579 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

G. Brida, I. P. Degiovanni, M. Genovese, F. Piacentini, P. Traina, A. Della Frera, A. Tosi, A. Bahgat Shehata, C. Scarcella, A. Gulinatti, M. Ghioni, S. V. Polyakov, A. Migdall, and A. Giudice, “An extremely low-noise heralded single-photon source: A breakthrough for quantum technologies,” Appl. Phys. Lett.101, 221112 (2012).
[CrossRef]

A. J. Miller, S. W. Nam, J. M. Martinis, and A. V. Sergienko, “Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination,” Appl. Phys. Lett.83, 791–793 (2003).
[CrossRef]

Eur. Phys. J. D (3)

J. Peřina, J. Křepelka, J. Peřina, M. Bondani, A. Allevi, and A. Andreoni, “Correlations in photon-numbers and integrated intensities in parametric processes involving three optical fields,” Eur. Phys. J. D53, 373–382 (2009).
[CrossRef]

O. Haderka, M. Hamar, and J. Peřina, “Experimental multi-photon-resolving detector using a single avalanche photodiode,” Eur. Phys. J. D28, 149–154 (2004).
[CrossRef]

J. Peřina and J. Křepelka, “Joint probability distributions of stimulated parametric down-conversion for controllable nonclassical fluctuations,” Eur. Phys. J. D281, 4705–4711 (2008).

Europhys. Lett. (2)

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

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

Int. J. Quant. Inf. (1)

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Figures (4)

Fig. 1
Fig. 1

Scheme of the experiment. An output of a femtosecond cavity dumped Ti:sapphire laser is converted to its third harmonics (THG, 280 nm) and used to pump a BaB2O4 nonlinear crystal. Nearly degenerate signal and idler (steered by high-reflectivity mirror HR) beams are selected using 14 nm wide bandpass filter IF and detected using an iCCD. Long-pass (above 490 nm) filter diminishes the noise. The intensity of the pumping beam is actively stabilized (rms below 0.3%) using motorized half-wave plate HWP and polarizer P based on the remnant UV intensity read by detector D.

Fig. 2
Fig. 2

(a) Fano factor Fi and (b) mean photon number 〈nc,i〉 [photocount 〈ci〉] of conditional idler photon-number [photocount] distribution as they depend on the number cs of signal photocounts. (c) Marginal signal-field photocount distributions fs(cs) = ∑ci f(cs, ci) and f s t ( c s ) = n s , n i T s ( c s , n s ) p s i ( n s , n i ). Asterisks give experimental values, triangles mark values obtained in the maximum-likelihood reconstruction and solid curves arise from the theory. In plots (b) and (c) experimental errors are smaller than symbol sizes.

Fig. 3
Fig. 3

(a) Sub-Poissonian idler-field CPNDs pc,i(ni) revealed by the maximum-likelihood reconstruction (▴) and the theoretical CPND (plain curve) for cs = 4. (b) Corresponding QDs Pc,i of integrated intensity Wi for the symmetric operator ordering (▴ → dash-dot curve). Poissonian PND (○) and its distribution of integrated intensity (dashed curve) are shown for comparison.

Fig. 4
Fig. 4

The least available value F i l of idler-field Fano factor (plain curve) and the most probable value F i m of Fano factor (dashed curve) for the conditional idler field ps(cs) as they depend on (a) mean photon-pair number 〈np〉 [Mp = 180], (b) QDE ηηs = ηi, and (c) mean number of noise signal photons 〈ns〉 [Ms = 0.012]; values of parameters are taken from the experiment.

Equations (4)

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p c , i ( n + 1 ) ( n i ; c s ) = p c , i ( n ) ( n i ; c s ) c i f i ( c i ; c s ) T i ( c i , n i ) n i T i ( c i , n i ) p c , i ( n ) ( n i ; c s ) .
T i ( c i , n i ) = ( N i c i ) ( 1 D i ) N i ( 1 η i ) n i ( 1 ) c i l = 0 c i ( c i l ) ( 1 ) l ( 1 D i ) l ( 1 + l N i η i 1 η i ) n i .
p c , i t ( n i ; c s ) = n s T s ( c s , n s ) p s i ( n s , n i ) .
p s i ( n s , n i ) = n = 0 min [ n s , n i ] p ( n s n ; M s , b s ) p ( n i n ; M i , b i ) p ( n ; M p , b p ) ;

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