Abstract

A nonclassical light source is used to demonstrate experimentally the absolute efficiency calibration of a photon-number-resolving detector. The photon-pair detector calibration method developed by Klyshko for single-photon detectors is generalized to take advantage of the higher dynamic range and additional information provided by photon-number-resolving detectors. This enables the use of brighter twin-beam sources including amplified pulse pumped sources, which increases the relevant signal and provides measurement redundancy, making the calibration more robust.

© 2009 Optical Society of America

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2009 (1)

J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, C. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, "Tomography of quantum detectors," Nature Phys. 5, 27-30 (2009).
[CrossRef]

2008 (4)

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] [PubMed]

M. Avenhaus, H. B. Coldenstrodt-Ronge, K. Laiho, W. Mauerer, I. A. Walmsley, and C. Silberhorn," Photon number statistics of multimode parametric down conversion," Phys. Rev. Lett. 101, 053601 (2008).
[CrossRef] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J. Smith, and I. A. Walmsley, "Conditional Preparation of Single Photons Using Parametric Downconversion: A recipe for Purity," New J. Phys. 10, 093011 (2008).
[CrossRef]

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
[CrossRef]

2007 (4)

L. A. Jiang, E. A. Dauler, and J. T. Chang, "Photon-number-resolving detector with 10 bits of resolution," Phys. Rev. A 75, 062325 (2007).
[CrossRef]

B. E. Kardynal, S. S. Hees, A. J. Shields, C. Nicoll, I. Farrer, and D. A. Ritchie, "Photon number resolving detector based on a quantum dot field effect transistor," Appl. Phys. Lett. 90, 181114 (2007).
[CrossRef]

H. B. Coldenstrodt-Ronge, and C. Silberhorn, "Avalanche photo-detection for high data rate applications," J. Phys. B 40, 3909-3921 (2007).
[CrossRef]

J. Y. Cheung, C. J. Chunnilall, E. R. Woolliams, N. P. Fox, J. R. Mountford, J. Wang and P. J. Thomas, "The quantum candela: a re-definition of the standard units for optical radiation," J. Mod. Opt. 54, 373-396 (2007).
[CrossRef]

2006 (3)

D. Achilles, C. Silberhorn, and I. A. Walmsley, "Direct, Loss-Tolerant Characterization of Nonclassical Photon Statistics," Phys. Rev. Lett. 97, 043642 (2006).
[CrossRef]

E. Waks, B. C. Sanders, E. Diamanti, and Y. Yamamoto, "Highly nonclassical photon statistics in parametric down-conversion," Phys. Rev. A 73, 033814 (2006).
[CrossRef]

M. Fujiwara, and M. Sasaki, "Photon-number-resolving detection at a telecommunications wavelength with a charge-integration photon detector," Opt. Lett. 31, 691-693 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (3)

V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum-Enhanced Measurements: Beating the Standard Quantum Limit," Science 306, 1330-1336 (2004).
[CrossRef] [PubMed]

O. Haderka, M. Hamar, and J. PerinaJr., "Experimental multi-photon-resolving detector using a single avalanche photodiode," Eur. Phys. J. D 28, 149-154 (2004).
[CrossRef]

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing," J. Mod. Opt. 51, 1499-1515 (2004).

2003 (1)

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]

2000 (1)

A. J. Shields, M. P. O’Sullivan, I. Farrer, D. A. Ritchie, R. A. Hogg, M. L. Leadbeater, C. E. Norman, and M. Pepper, "Detection of single photons using a field-effect transistor gated by a layer of quantum dots," Appl. Phys. Lett. 76, 3673-3675 (2000).
[CrossRef]

1999 (1)

J. S. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, "Multiphoton detection using visible light photon counter," Appl. Phys. Lett. 74, 902-904 (1999).
[CrossRef]

1998 (1)

B. Cabrera, R. M. Clarke, P. Colling, A. J. Miller, S. Nam, and R. W. Romani, "Detection of single infrared, optical, and ultraviolet photons using superconducting transition edge sensors," Appl. Phys. Lett. 73, 735 (1998).
[CrossRef]

1997 (1)

Y. Ohno, "Improved Photometric Standards and Calibration Procedures at NIST," J. Res. Natl. Inst. Stand. Technol. 102, 323 (1997).

1996 (2)

T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, and A. C. Parr, "National Institute of Standards and Technology high-accuracy cryogenic radiometer," Appl. Opt. 35, 1056-1068 (1996).
[CrossRef] [PubMed]

A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih,"Absolute detector quantum efficiency measurements using correlated photons," Metrologia 32, 479-483 (1996).
[CrossRef]

1993 (1)

P. G. Kwiat, A. M. Steinberg, R. Y. Chao, P. H. Eberhard, and M. D. Petroff, "High-efficiency single-photon detectors," Phys. Rev. A 48, R867-R870 (1993).
[CrossRef] [PubMed]

1991 (1)

1987 (1)

1980 (1)

D. N. Klyshko, "Use of two-photon light for absolute calibration of photoelectric detectors," Sov. J. Quantum Electron. 10, 1112-1117 (1980).
[CrossRef]

1959 (1)

L. Mandel, "Fluctuations of Photon Beams: The Distribution of the Photo-Electrons," Proc. Phys. Soc. London 74, 233-243 (1959).
[CrossRef]

Achilles, D.

D. Achilles, C. Silberhorn, and I. A. Walmsley, "Direct, Loss-Tolerant Characterization of Nonclassical Photon Statistics," Phys. Rev. Lett. 97, 043642 (2006).
[CrossRef]

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing," J. Mod. Opt. 51, 1499-1515 (2004).

Avenhaus, M.

M. Avenhaus, H. B. Coldenstrodt-Ronge, K. Laiho, W. Mauerer, I. A. Walmsley, and C. Silberhorn," Photon number statistics of multimode parametric down conversion," Phys. Rev. Lett. 101, 053601 (2008).
[CrossRef] [PubMed]

Banaszek, K.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing," J. Mod. Opt. 51, 1499-1515 (2004).

Benkhaoul, M.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
[CrossRef]

Bitauld, D.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
[CrossRef]

Cabrera, B.

B. Cabrera, R. M. Clarke, P. Colling, A. J. Miller, S. Nam, and R. W. Romani, "Detection of single infrared, optical, and ultraviolet photons using superconducting transition edge sensors," Appl. Phys. Lett. 73, 735 (1998).
[CrossRef]

Chang, J. T.

L. A. Jiang, E. A. Dauler, and J. T. Chang, "Photon-number-resolving detector with 10 bits of resolution," Phys. Rev. A 75, 062325 (2007).
[CrossRef]

Chao, R. Y.

P. G. Kwiat, A. M. Steinberg, R. Y. Chao, P. H. Eberhard, and M. D. Petroff, "High-efficiency single-photon detectors," Phys. Rev. A 48, R867-R870 (1993).
[CrossRef] [PubMed]

Cheung, J. Y.

J. Y. Cheung, C. J. Chunnilall, E. R. Woolliams, N. P. Fox, J. R. Mountford, J. Wang and P. J. Thomas, "The quantum candela: a re-definition of the standard units for optical radiation," J. Mod. Opt. 54, 373-396 (2007).
[CrossRef]

Chunnilall, C. J.

J. Y. Cheung, C. J. Chunnilall, E. R. Woolliams, N. P. Fox, J. R. Mountford, J. Wang and P. J. Thomas, "The quantum candela: a re-definition of the standard units for optical radiation," J. Mod. Opt. 54, 373-396 (2007).
[CrossRef]

Clarke, R. M.

B. Cabrera, R. M. Clarke, P. Colling, A. J. Miller, S. Nam, and R. W. Romani, "Detection of single infrared, optical, and ultraviolet photons using superconducting transition edge sensors," Appl. Phys. Lett. 73, 735 (1998).
[CrossRef]

Coldenstrodt-Ronge, H.

J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, C. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, "Tomography of quantum detectors," Nature Phys. 5, 27-30 (2009).
[CrossRef]

Coldenstrodt-Ronge, H. B.

M. Avenhaus, H. B. Coldenstrodt-Ronge, K. Laiho, W. Mauerer, I. A. Walmsley, and C. Silberhorn," Photon number statistics of multimode parametric down conversion," Phys. Rev. Lett. 101, 053601 (2008).
[CrossRef] [PubMed]

H. B. Coldenstrodt-Ronge, and C. Silberhorn, "Avalanche photo-detection for high data rate applications," J. Phys. B 40, 3909-3921 (2007).
[CrossRef]

Colling, P.

B. Cabrera, R. M. Clarke, P. Colling, A. J. Miller, S. Nam, and R. W. Romani, "Detection of single infrared, optical, and ultraviolet photons using superconducting transition edge sensors," Appl. Phys. Lett. 73, 735 (1998).
[CrossRef]

Cromer, C. L.

Datla, R. U.

A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih,"Absolute detector quantum efficiency measurements using correlated photons," Metrologia 32, 479-483 (1996).
[CrossRef]

Dauler, E. A.

L. A. Jiang, E. A. Dauler, and J. T. Chang, "Photon-number-resolving detector with 10 bits of resolution," Phys. Rev. A 75, 062325 (2007).
[CrossRef]

Diamanti, E.

E. Waks, B. C. Sanders, E. Diamanti, and Y. Yamamoto, "Highly nonclassical photon statistics in parametric down-conversion," Phys. Rev. A 73, 033814 (2006).
[CrossRef]

Divochiy, A.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
[CrossRef]

Eberhard, P. H.

P. G. Kwiat, A. M. Steinberg, R. Y. Chao, P. H. Eberhard, and M. D. Petroff, "High-efficiency single-photon detectors," Phys. Rev. A 48, R867-R870 (1993).
[CrossRef] [PubMed]

Eisert, J.

J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, C. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, "Tomography of quantum detectors," Nature Phys. 5, 27-30 (2009).
[CrossRef]

Farrer, I.

B. E. Kardynal, S. S. Hees, A. J. Shields, C. Nicoll, I. Farrer, and D. A. Ritchie, "Photon number resolving detector based on a quantum dot field effect transistor," Appl. Phys. Lett. 90, 181114 (2007).
[CrossRef]

A. J. Shields, M. P. O’Sullivan, I. Farrer, D. A. Ritchie, R. A. Hogg, M. L. Leadbeater, C. E. Norman, and M. Pepper, "Detection of single photons using a field-effect transistor gated by a layer of quantum dots," Appl. Phys. Lett. 76, 3673-3675 (2000).
[CrossRef]

Feito, A.

J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, C. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, "Tomography of quantum detectors," Nature Phys. 5, 27-30 (2009).
[CrossRef]

Fiore, A.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
[CrossRef]

Fitch, M. J.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing," J. Mod. Opt. 51, 1499-1515 (2004).

Fox, N. P.

J. Y. Cheung, C. J. Chunnilall, E. R. Woolliams, N. P. Fox, J. R. Mountford, J. Wang and P. J. Thomas, "The quantum candela: a re-definition of the standard units for optical radiation," J. Mod. Opt. 54, 373-396 (2007).
[CrossRef]

Franson, J. D.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing," J. Mod. Opt. 51, 1499-1515 (2004).

Fujiwara, M.

Gaggero, A.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
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Gentile, T. R.

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum-Enhanced Measurements: Beating the Standard Quantum Limit," Science 306, 1330-1336 (2004).
[CrossRef] [PubMed]

Gol’tsman, G.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
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Gruber, S. S.

Haderka, O.

O. Haderka, M. Hamar, and J. PerinaJr., "Experimental multi-photon-resolving detector using a single avalanche photodiode," Eur. Phys. J. D 28, 149-154 (2004).
[CrossRef]

Hadfield, R. H.

Hamar, M.

O. Haderka, M. Hamar, and J. PerinaJr., "Experimental multi-photon-resolving detector using a single avalanche photodiode," Eur. Phys. J. D 28, 149-154 (2004).
[CrossRef]

Hardis, J. E.

Hees, S. S.

B. E. Kardynal, S. S. Hees, A. J. Shields, C. Nicoll, I. Farrer, and D. A. Ritchie, "Photon number resolving detector based on a quantum dot field effect transistor," Appl. Phys. Lett. 90, 181114 (2007).
[CrossRef]

Hogg, R. A.

A. J. Shields, M. P. O’Sullivan, I. Farrer, D. A. Ritchie, R. A. Hogg, M. L. Leadbeater, C. E. Norman, and M. Pepper, "Detection of single photons using a field-effect transistor gated by a layer of quantum dots," Appl. Phys. Lett. 76, 3673-3675 (2000).
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Hogue, H. H.

J. S. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, "Multiphoton detection using visible light photon counter," Appl. Phys. Lett. 74, 902-904 (1999).
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Houston, J. M.

Jacobs, B. C.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing," J. Mod. Opt. 51, 1499-1515 (2004).

Jiang, L. A.

L. A. Jiang, E. A. Dauler, and J. T. Chang, "Photon-number-resolving detector with 10 bits of resolution," Phys. Rev. A 75, 062325 (2007).
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Kardynal, B. E.

B. E. Kardynal, S. S. Hees, A. J. Shields, C. Nicoll, I. Farrer, and D. A. Ritchie, "Photon number resolving detector based on a quantum dot field effect transistor," Appl. Phys. Lett. 90, 181114 (2007).
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Kaurova, N.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
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Kim, J. S.

J. S. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, "Multiphoton detection using visible light photon counter," Appl. Phys. Lett. 74, 902-904 (1999).
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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. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
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Kwiat, P. G.

P. G. Kwiat, A. M. Steinberg, R. Y. Chao, P. H. Eberhard, and M. D. Petroff, "High-efficiency single-photon detectors," Phys. Rev. A 48, R867-R870 (1993).
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Lagoudakis, K. G.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
[CrossRef]

Laiho, K.

M. Avenhaus, H. B. Coldenstrodt-Ronge, K. Laiho, W. Mauerer, I. A. Walmsley, and C. Silberhorn," Photon number statistics of multimode parametric down conversion," Phys. Rev. Lett. 101, 053601 (2008).
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Leadbeater, M. L.

A. J. Shields, M. P. O’Sullivan, I. Farrer, D. A. Ritchie, R. A. Hogg, M. L. Leadbeater, C. E. Norman, and M. Pepper, "Detection of single photons using a field-effect transistor gated by a layer of quantum dots," Appl. Phys. Lett. 76, 3673-3675 (2000).
[CrossRef]

Leoni, R.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
[CrossRef]

Lita, A. E.

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, "Noise-free high-efficiency photon-number-resolving detectors," Phys. Rev. A 72, 019901 (2005).
[CrossRef]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum-Enhanced Measurements: Beating the Standard Quantum Limit," Science 306, 1330-1336 (2004).
[CrossRef] [PubMed]

Lundeen, J. S.

J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, C. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, "Tomography of quantum detectors," Nature Phys. 5, 27-30 (2009).
[CrossRef]

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] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J. Smith, and I. A. Walmsley, "Conditional Preparation of Single Photons Using Parametric Downconversion: A recipe for Purity," New J. Phys. 10, 093011 (2008).
[CrossRef]

Lvy, F.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
[CrossRef]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum-Enhanced Measurements: Beating the Standard Quantum Limit," Science 306, 1330-1336 (2004).
[CrossRef] [PubMed]

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L. Mandel, "Fluctuations of Photon Beams: The Distribution of the Photo-Electrons," Proc. Phys. Soc. London 74, 233-243 (1959).
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Marsili, F.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
[CrossRef]

Martinis, J. M.

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]

Mattioli, F.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
[CrossRef]

Mauerer, W.

M. Avenhaus, H. B. Coldenstrodt-Ronge, K. Laiho, W. Mauerer, I. A. Walmsley, and C. Silberhorn," Photon number statistics of multimode parametric down conversion," Phys. Rev. Lett. 101, 053601 (2008).
[CrossRef] [PubMed]

Migdall, A. L.

A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih,"Absolute detector quantum efficiency measurements using correlated photons," Metrologia 32, 479-483 (1996).
[CrossRef]

Miller, A. J.

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, 10846-10853 (2005).
[CrossRef] [PubMed]

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, "Noise-free high-efficiency photon-number-resolving detectors," Phys. Rev. A 72, 019901 (2005).
[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]

B. Cabrera, R. M. Clarke, P. Colling, A. J. Miller, S. Nam, and R. W. Romani, "Detection of single infrared, optical, and ultraviolet photons using superconducting transition edge sensors," Appl. Phys. Lett. 73, 735 (1998).
[CrossRef]

Minaeva, O.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
[CrossRef]

Mirin, R. P.

Mosley, P. J.

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] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J. Smith, and I. A. Walmsley, "Conditional Preparation of Single Photons Using Parametric Downconversion: A recipe for Purity," New J. Phys. 10, 093011 (2008).
[CrossRef]

Mountford, J. R.

J. Y. Cheung, C. J. Chunnilall, E. R. Woolliams, N. P. Fox, J. R. Mountford, J. Wang and P. J. Thomas, "The quantum candela: a re-definition of the standard units for optical radiation," J. Mod. Opt. 54, 373-396 (2007).
[CrossRef]

Nam, S.

B. Cabrera, R. M. Clarke, P. Colling, A. J. Miller, S. Nam, and R. W. Romani, "Detection of single infrared, optical, and ultraviolet photons using superconducting transition edge sensors," Appl. Phys. Lett. 73, 735 (1998).
[CrossRef]

Nam, S. W.

Nam, S.W.

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]

Nicoll, C.

B. E. Kardynal, S. S. Hees, A. J. Shields, C. Nicoll, I. Farrer, and D. A. Ritchie, "Photon number resolving detector based on a quantum dot field effect transistor," Appl. Phys. Lett. 90, 181114 (2007).
[CrossRef]

Norman, C. E.

A. J. Shields, M. P. O’Sullivan, I. Farrer, D. A. Ritchie, R. A. Hogg, M. L. Leadbeater, C. E. Norman, and M. Pepper, "Detection of single photons using a field-effect transistor gated by a layer of quantum dots," Appl. Phys. Lett. 76, 3673-3675 (2000).
[CrossRef]

O’Sullivan, M. P.

A. J. Shields, M. P. O’Sullivan, I. Farrer, D. A. Ritchie, R. A. Hogg, M. L. Leadbeater, C. E. Norman, and M. Pepper, "Detection of single photons using a field-effect transistor gated by a layer of quantum dots," Appl. Phys. Lett. 76, 3673-3675 (2000).
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Ohno, Y.

Y. Ohno, "Improved Photometric Standards and Calibration Procedures at NIST," J. Res. Natl. Inst. Stand. Technol. 102, 323 (1997).

Orszak, J. S.

A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih,"Absolute detector quantum efficiency measurements using correlated photons," Metrologia 32, 479-483 (1996).
[CrossRef]

Parr, A. C.

Penin, A. N.

Pepper, M.

A. J. Shields, M. P. O’Sullivan, I. Farrer, D. A. Ritchie, R. A. Hogg, M. L. Leadbeater, C. E. Norman, and M. Pepper, "Detection of single photons using a field-effect transistor gated by a layer of quantum dots," Appl. Phys. Lett. 76, 3673-3675 (2000).
[CrossRef]

Perina, J.

O. Haderka, M. Hamar, and J. PerinaJr., "Experimental multi-photon-resolving detector using a single avalanche photodiode," Eur. Phys. J. D 28, 149-154 (2004).
[CrossRef]

Petroff, M. D.

P. G. Kwiat, A. M. Steinberg, R. Y. Chao, P. H. Eberhard, and M. D. Petroff, "High-efficiency single-photon detectors," Phys. Rev. A 48, R867-R870 (1993).
[CrossRef] [PubMed]

Pittman, T. B.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing," J. Mod. Opt. 51, 1499-1515 (2004).

Plenio, M. B.

J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, C. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, "Tomography of quantum detectors," Nature Phys. 5, 27-30 (2009).
[CrossRef]

Pregnell, K. L.

J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, C. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, "Tomography of quantum detectors," Nature Phys. 5, 27-30 (2009).
[CrossRef]

Ralph, T. C.

J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, C. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, "Tomography of quantum detectors," Nature Phys. 5, 27-30 (2009).
[CrossRef]

Rarity, J. G.

Ridley, K. D.

Ritchie, D. A.

B. E. Kardynal, S. S. Hees, A. J. Shields, C. Nicoll, I. Farrer, and D. A. Ritchie, "Photon number resolving detector based on a quantum dot field effect transistor," Appl. Phys. Lett. 90, 181114 (2007).
[CrossRef]

A. J. Shields, M. P. O’Sullivan, I. Farrer, D. A. Ritchie, R. A. Hogg, M. L. Leadbeater, C. E. Norman, and M. Pepper, "Detection of single photons using a field-effect transistor gated by a layer of quantum dots," Appl. Phys. Lett. 76, 3673-3675 (2000).
[CrossRef]

Romani, R. W.

B. Cabrera, R. M. Clarke, P. Colling, A. J. Miller, S. Nam, and R. W. Romani, "Detection of single infrared, optical, and ultraviolet photons using superconducting transition edge sensors," Appl. Phys. Lett. 73, 735 (1998).
[CrossRef]

Rosenberg, D.

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, "Noise-free high-efficiency photon-number-resolving detectors," Phys. Rev. A 72, 019901 (2005).
[CrossRef]

Sanders, B. C.

E. Waks, B. C. Sanders, E. Diamanti, and Y. Yamamoto, "Highly nonclassical photon statistics in parametric down-conversion," Phys. Rev. A 73, 033814 (2006).
[CrossRef]

Sasaki, M.

Schwall, R. E.

Seleznev, V.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photon. 2, 302-306 (2008).
[CrossRef]

Sergienko, A.

A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih,"Absolute detector quantum efficiency measurements using correlated photons," Metrologia 32, 479-483 (1996).
[CrossRef]

Sergienko, A. V.

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]

A. N. Penin, and A. V. Sergienko, "Absolute standardless calibration of photodetectors based on quantum twophoton fields," Appl. Opt. 30, 3582-3588 (1991).
[CrossRef] [PubMed]

Shields, A. J.

B. E. Kardynal, S. S. Hees, A. J. Shields, C. Nicoll, I. Farrer, and D. A. Ritchie, "Photon number resolving detector based on a quantum dot field effect transistor," Appl. Phys. Lett. 90, 181114 (2007).
[CrossRef]

A. J. Shields, M. P. O’Sullivan, I. Farrer, D. A. Ritchie, R. A. Hogg, M. L. Leadbeater, C. E. Norman, and M. Pepper, "Detection of single photons using a field-effect transistor gated by a layer of quantum dots," Appl. Phys. Lett. 76, 3673-3675 (2000).
[CrossRef]

Shih, Y. H.

A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih,"Absolute detector quantum efficiency measurements using correlated photons," Metrologia 32, 479-483 (1996).
[CrossRef]

Silberhorn, C.

J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, C. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, "Tomography of quantum detectors," Nature Phys. 5, 27-30 (2009).
[CrossRef]

M. Avenhaus, H. B. Coldenstrodt-Ronge, K. Laiho, W. Mauerer, I. A. Walmsley, and C. Silberhorn," Photon number statistics of multimode parametric down conversion," Phys. Rev. Lett. 101, 053601 (2008).
[CrossRef] [PubMed]

H. B. Coldenstrodt-Ronge, and C. Silberhorn, "Avalanche photo-detection for high data rate applications," J. Phys. B 40, 3909-3921 (2007).
[CrossRef]

D. Achilles, C. Silberhorn, and I. A. Walmsley, "Direct, Loss-Tolerant Characterization of Nonclassical Photon Statistics," Phys. Rev. Lett. 97, 043642 (2006).
[CrossRef]

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing," J. Mod. Opt. 51, 1499-1515 (2004).

Sliwa, C.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing," J. Mod. Opt. 51, 1499-1515 (2004).

Smith, B. J.

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] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J. Smith, and I. A. Walmsley, "Conditional Preparation of Single Photons Using Parametric Downconversion: A recipe for Purity," New J. Phys. 10, 093011 (2008).
[CrossRef]

Steinberg, A. M.

P. G. Kwiat, A. M. Steinberg, R. Y. Chao, P. H. Eberhard, and M. D. Petroff, "High-efficiency single-photon detectors," Phys. Rev. A 48, R867-R870 (1993).
[CrossRef] [PubMed]

Stevens, M. J.

Takeuchi, S.

J. S. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, "Multiphoton detection using visible light photon counter," Appl. Phys. Lett. 74, 902-904 (1999).
[CrossRef]

Tapster, P. R.

Thomas, P. J.

J. Y. Cheung, C. J. Chunnilall, E. R. Woolliams, N. P. Fox, J. R. Mountford, J. Wang and P. J. Thomas, "The quantum candela: a re-definition of the standard units for optical radiation," J. Mod. Opt. 54, 373-396 (2007).
[CrossRef]

Waks, E.

E. Waks, B. C. Sanders, E. Diamanti, and Y. Yamamoto, "Highly nonclassical photon statistics in parametric down-conversion," Phys. Rev. A 73, 033814 (2006).
[CrossRef]

Walmsley, I. A.

J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, C. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, "Tomography of quantum detectors," Nature Phys. 5, 27-30 (2009).
[CrossRef]

M. Avenhaus, H. B. Coldenstrodt-Ronge, K. Laiho, W. Mauerer, I. A. Walmsley, and C. Silberhorn," Photon number statistics of multimode parametric down conversion," Phys. Rev. Lett. 101, 053601 (2008).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1.
Fig. 1.

A typical optimization residual (F) for simulated joint outcome statistics as a function of the two PNRD efficiencies η 1 and η 2. There is only one minimum, suggesting that the problem is convex.

Fig. 2.
Fig. 2.

The experimental setup. A KDP crystal two-beam source is pumped by an amplified Ti:Sapph laser. The two generated beams propagate collinearly and are orthogonally polarized. Each beam is measured by a time-multiplexed photon number resolving detector. Details are given in the text.

Fig. 3.
Fig. 3.

The estimated detector efficiencies for TMD1 (oe-17-6-4397-i001) and TMD2 (oe-17-6-4397-i002) as a function of the average SHG power pumping the SPDC. Three distinct regimes (regions 1, 2, and 3) are indicated by shading.

Fig. 4.
Fig. 4.

The reconstructed photon statistics σ for n 1 and n 2 photons in beam 1 and 2, respectively, measured at a pump power of (a) 1.5 mW and (b) 30 mW. The presence of significant off-diagonal elements indicate that the input state is corrupted by background.

Fig. 5.
Fig. 5.

The loss l in beam 1 of a twin-beam state σB that results in the same joint outcome statistics as the addition of a Poissonian background, with average photon number 〈nB 〉, to beam 2 of another twin-beam state, σA , for some σA and σB . M is the photon number range of PNRDs in beams 1 and 2.

Fig. 6.
Fig. 6.

The reconstructed photon statistics σ for n 1 and n 2 photons in beam 1 and 2, respectively, after subtracting an independently measured background. For pump powers (a) 1.5 mW and (b) 30 mW, as in Fig. 4. The reduction of significant off-diagonal elements indicates that the background subtraction method works.

Fig. 7.
Fig. 7.

The estimated detector efficiencies for TMD1 (oe-17-6-4397-i003) and TMD2 (oe-17-6-4397-i004) determined from background subtracted outcome statistics, plotted as a function of the average pump power. Also plotted is the Klyshko efficiencies that would have been estimated for single photon detector 1 (oe-17-6-4397-i005) and 2 (oe-17-6-4397-i006). The standard Klyshko method overestimates the efficiencies for high powers. The dotted lines indicate the average efficiencies of the two PNRDs.

Fig. 8.
Fig. 8.

The reconstructed average photon number (+) as a function of the pump power. SPDC theory predicts a linear relationship. The line is a linear fit.

Equations (18)

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η s = R c R i ,
P n = Tr [ ρ ̂ ̂ n ] ,
̂ n = m [ F · L ( η ) ] n , m m m ,
L i , j ( η ) = { j i η i ( 1 η ) j i if j i 0 otherwise .
p = C · L ( η ) · σ ,
P = C 1 · L ( η 1 ) · σ · L T ( η 2 ) · C 2 T ,
η ˜ s = R ˜ c R ˜ i = σ 1,1 + ( η s η i 2 η s 2 η i + 4 ) σ 2,2 σ 1,1 + ( 2 η i ) σ 2,2 η s .
ψ = 1 λ 2 n λ n n s n i ,
σ m , n = c m · δ m , n ,
G = R C 1 · L ( η 1 ) · σ · L T ( η 2 ) · C 2 T .
σ ˜ k , l A = m = 0 k d ( m ) · σ k m , l A .
σ ˜ A = D ( n B ) · σ A ,
D ( n B ) · σ A = σ B · L T ( η ) .
P M P S P B .
P M = C 1 1 P M ( C 2 T ) 1 ,
P B = C 1 1 P B ( C 2 T ) 1 ,
P M = [ C 1 1 P S ( C 2 T ) 1 ] P B .
P S = C 1 1 { { P M } { P B } } C 2 T ,

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