Abstract

We demonstrate a superconducting photon-number-resolving detector capable of resolving up to twelve photons at telecommunication wavelengths. It is based on a series array of twelve superconducting NbN nanowire elements, each connected in parallel with an integrated resistor. The photon-induced voltage signals from the twelve elements are summed up into a single readout pulse with a height proportional to the detected photon number. Thirteen distinct output levels corresponding to the detection of n = 0-12 photons are observed experimentally. A detailed analysis of the linearity and of the excess noise shows the potential of scaling to an even larger dynamic range.

© 2014 Optical Society of America

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2013 (3)

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. Shaw, R. Mirin, S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7(3), 210–214 (2013).
[CrossRef]

Z. Zhou, G. Frucci, F. Mattioli, A. Gaggero, R. Leoni, S. Jahanmirinejad, T. B. Hoang, A. Fiore, “Ultrasensitive N-photon interferometric autocorrelator,” Phys. Rev. Lett. 110(13), 133605 (2013).
[CrossRef] [PubMed]

D. Sahin, A. Gaggero, Z. Zhou, S. Jahanmirinejad, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Hofling, A. Fiore, “Waveguide photon-number-resolving detectors for quantum photonic integrated circuits,” Appl. Phys. Lett. 103(11), 111116 (2013).
[CrossRef]

2012 (4)

2010 (3)

D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. 10(8), 2977–2981 (2010).
[CrossRef] [PubMed]

M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B 27(5), 852–862 (2010).
[CrossRef]

A. Gaggero, S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Notzel, R. Sanjines, A. Fiore, “Nanowire superconducting single-photon detectors on GaAs for integrated quantum photonic applications,” Appl. Phys. Lett. 97(15), 151108 (2010).
[CrossRef]

2009 (3)

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Gol’tsman, S. A. Hamilton, K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2–3), 364–373 (2009).
[CrossRef]

F. Marsili, D. Bitauld, A. Gaggero, S. Jahanmirinejad, R. Leoni, F. Mattioli, A. Fiore, “Physics and application of photon number resolving detectors based on superconducting parallel nanowires,” New J. Phys. 11(4), 045022 (2009).
[CrossRef]

J. Kitaygorsky, S. Dorenbos, E. Reiger, R. Schouten, V. Zwiller, R. Sobolewski, “HEMT-based readout technique for dark- and photon-count studies in NbN superconducting single-photon detectors,” IEEE Trans. Appl. Supercond. 19(3), 346–349 (2009).
[CrossRef]

2008 (4)

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. Benkhaoul, F. Lévy, A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[CrossRef]

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

A. E. Lita, A. J. Miller, S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16(5), 3032–3040 (2008).
[CrossRef] [PubMed]

V. Anant, A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, K. K. Berggren, “Optical properties of superconducting nanowire single-photon detectors,” Opt. Express 16(14), 10750–10761 (2008).
[CrossRef] [PubMed]

2007 (8)

M. Fujiwara, M. Sasaki, “Direct measurement of photon number statistics at telecom wavelengths using a charge integration photon detector,” Appl. Opt. 46(16), 3069–3074 (2007).
[CrossRef] [PubMed]

A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, V. Anant, K. K. Berggren, G. N. Gol’tsman, B. M. Voronov, “Constriction-limited detection efficiency of superconducting nanowire single-photon detectors,” Appl. Phys. Lett. 90(10), 101110 (2007).
[CrossRef]

F. Mattioli, R. Leoni, A. Gaggero, M. G. Castellano, P. Carelli, F. Marsili, A. Fiore, “Electrical characterization of superconducting single-photon detectors,” J. Appl. Phys. 101(5), 054302 (2007).
[CrossRef]

J. K. W. Yang, A. J. Kerman, E. A. Dauler, V. Anant, K. M. Rosfjord, K. K. Berggren, “Modeling the electrical and thermal response of superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. 17(2), 581–585 (2007).
[CrossRef]

N. Sangouard, C. Simon, J. Minář, H. Zbinden, H. de Riedmatten, N. Gisin, “Long-distance entanglement distribution with single-photon sources,” Phys. Rev. A 76(5), 050301 (2007).
[CrossRef]

L. A. Jiang, E. A. Dauler, J. T. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A 75(6), 062325 (2007).
[CrossRef]

E. A. Dauler, B. S. Robinson, A. J. Kerman, J. K. W. Yang, K. M. Rosfjord, V. Anant, B. Voronov, G. Gol’tsman, K. K. Berggren, “Multi-element superconducting nanowire single-photon detector,” IEEE Trans Appl. Supercond. 17(2), 279–284 (2007).

M. Bell, A. Antipov, B. Karasik, A. Sergeev, V. Mitin, A. Verevkin, “Photon number-resolved detection with sequentially connected nanowires,” IEEE Trans. Appl. Supercond. 17(2), 289–292 (2007).
[CrossRef]

2006 (1)

2003 (2)

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1502–1511 (2003).
[CrossRef]

M. J. Fitch, B. C. Jacobs, T. B. Pittman, J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003).
[CrossRef]

2001 (2)

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

E. Knill, R. Laflamme, G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[CrossRef] [PubMed]

1971 (1)

Allevi, A.

Anant, V.

V. Anant, A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, K. K. Berggren, “Optical properties of superconducting nanowire single-photon detectors,” Opt. Express 16(14), 10750–10761 (2008).
[CrossRef] [PubMed]

J. K. W. Yang, A. J. Kerman, E. A. Dauler, V. Anant, K. M. Rosfjord, K. K. Berggren, “Modeling the electrical and thermal response of superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. 17(2), 581–585 (2007).
[CrossRef]

E. A. Dauler, B. S. Robinson, A. J. Kerman, J. K. W. Yang, K. M. Rosfjord, V. Anant, B. Voronov, G. Gol’tsman, K. K. Berggren, “Multi-element superconducting nanowire single-photon detector,” IEEE Trans Appl. Supercond. 17(2), 279–284 (2007).

A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, V. Anant, K. K. Berggren, G. N. Gol’tsman, B. M. Voronov, “Constriction-limited detection efficiency of superconducting nanowire single-photon detectors,” Appl. Phys. Lett. 90(10), 101110 (2007).
[CrossRef]

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

Andreoni, A.

Antipov, A.

M. Bell, A. Antipov, B. Karasik, A. Sergeev, V. Mitin, A. Verevkin, “Photon number-resolved detection with sequentially connected nanowires,” IEEE Trans. Appl. Supercond. 17(2), 289–292 (2007).
[CrossRef]

Arnaud, J. A.

Baek, B.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. Shaw, R. Mirin, S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7(3), 210–214 (2013).
[CrossRef]

Beetz, J.

D. Sahin, A. Gaggero, Z. Zhou, S. Jahanmirinejad, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Hofling, A. Fiore, “Waveguide photon-number-resolving detectors for quantum photonic integrated circuits,” Appl. Phys. Lett. 103(11), 111116 (2013).
[CrossRef]

Bell, M.

M. Bell, A. Antipov, B. Karasik, A. Sergeev, V. Mitin, A. Verevkin, “Photon number-resolved detection with sequentially connected nanowires,” IEEE Trans. Appl. Supercond. 17(2), 289–292 (2007).
[CrossRef]

Benkhaoul, 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. Benkhaoul, F. Lévy, A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[CrossRef]

Berggren, K. K.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Gol’tsman, S. A. Hamilton, K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2–3), 364–373 (2009).
[CrossRef]

V. Anant, A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, K. K. Berggren, “Optical properties of superconducting nanowire single-photon detectors,” Opt. Express 16(14), 10750–10761 (2008).
[CrossRef] [PubMed]

J. K. W. Yang, A. J. Kerman, E. A. Dauler, V. Anant, K. M. Rosfjord, K. K. Berggren, “Modeling the electrical and thermal response of superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. 17(2), 581–585 (2007).
[CrossRef]

A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, V. Anant, K. K. Berggren, G. N. Gol’tsman, B. M. Voronov, “Constriction-limited detection efficiency of superconducting nanowire single-photon detectors,” Appl. Phys. Lett. 90(10), 101110 (2007).
[CrossRef]

E. A. Dauler, B. S. Robinson, A. J. Kerman, J. K. W. Yang, K. M. Rosfjord, V. Anant, B. Voronov, G. Gol’tsman, K. K. Berggren, “Multi-element superconducting nanowire single-photon detector,” IEEE Trans Appl. Supercond. 17(2), 279–284 (2007).

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

Bitauld, D.

D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. 10(8), 2977–2981 (2010).
[CrossRef] [PubMed]

A. Gaggero, S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Notzel, R. Sanjines, A. Fiore, “Nanowire superconducting single-photon detectors on GaAs for integrated quantum photonic applications,” Appl. Phys. Lett. 97(15), 151108 (2010).
[CrossRef]

F. Marsili, D. Bitauld, A. Gaggero, S. Jahanmirinejad, R. Leoni, F. Mattioli, A. Fiore, “Physics and application of photon number resolving detectors based on superconducting parallel nanowires,” New J. Phys. 11(4), 045022 (2009).
[CrossRef]

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. Benkhaoul, F. Lévy, A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[CrossRef]

Bondani, M.

Caccia, M.

Carelli, P.

F. Mattioli, R. Leoni, A. Gaggero, M. G. Castellano, P. Carelli, F. Marsili, A. Fiore, “Electrical characterization of superconducting single-photon detectors,” J. Appl. Phys. 101(5), 054302 (2007).
[CrossRef]

Castellano, M. G.

F. Mattioli, R. Leoni, A. Gaggero, M. G. Castellano, P. Carelli, F. Marsili, A. Fiore, “Electrical characterization of superconducting single-photon detectors,” J. Appl. Phys. 101(5), 054302 (2007).
[CrossRef]

Chang, J. T.

L. A. Jiang, E. A. Dauler, J. T. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A 75(6), 062325 (2007).
[CrossRef]

Chmill, V.

Chulkova, G.

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

Dauler, E. A.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Gol’tsman, S. A. Hamilton, K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2–3), 364–373 (2009).
[CrossRef]

V. Anant, A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, K. K. Berggren, “Optical properties of superconducting nanowire single-photon detectors,” Opt. Express 16(14), 10750–10761 (2008).
[CrossRef] [PubMed]

A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, V. Anant, K. K. Berggren, G. N. Gol’tsman, B. M. Voronov, “Constriction-limited detection efficiency of superconducting nanowire single-photon detectors,” Appl. Phys. Lett. 90(10), 101110 (2007).
[CrossRef]

J. K. W. Yang, A. J. Kerman, E. A. Dauler, V. Anant, K. M. Rosfjord, K. K. Berggren, “Modeling the electrical and thermal response of superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. 17(2), 581–585 (2007).
[CrossRef]

E. A. Dauler, B. S. Robinson, A. J. Kerman, J. K. W. Yang, K. M. Rosfjord, V. Anant, B. Voronov, G. Gol’tsman, K. K. Berggren, “Multi-element superconducting nanowire single-photon detector,” IEEE Trans Appl. Supercond. 17(2), 279–284 (2007).

L. A. Jiang, E. A. Dauler, J. T. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A 75(6), 062325 (2007).
[CrossRef]

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

de Dood, M. J. A.

de la Clavière, B.

de Riedmatten, H.

N. Sangouard, C. Simon, J. Minář, H. Zbinden, H. de Riedmatten, N. Gisin, “Long-distance entanglement distribution with single-photon sources,” Phys. Rev. A 76(5), 050301 (2007).
[CrossRef]

Diamanti, E.

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F. Marsili, D. Bitauld, A. Gaggero, S. Jahanmirinejad, R. Leoni, F. Mattioli, A. Fiore, “Physics and application of photon number resolving detectors based on superconducting parallel nanowires,” New J. Phys. 11(4), 045022 (2009).
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K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, K. K. Berggren, “Nanowire Single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express 14(2), 527–534 (2006).
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J. Kitaygorsky, S. Dorenbos, E. Reiger, R. Schouten, V. Zwiller, R. Sobolewski, “HEMT-based readout technique for dark- and photon-count studies in NbN superconducting single-photon detectors,” IEEE Trans. Appl. Supercond. 19(3), 346–349 (2009).
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[CrossRef]

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[CrossRef]

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[CrossRef] [PubMed]

F. Marsili, D. Bitauld, A. Gaggero, S. Jahanmirinejad, R. Leoni, F. Mattioli, A. Fiore, “Physics and application of photon number resolving detectors based on superconducting parallel nanowires,” New J. Phys. 11(4), 045022 (2009).
[CrossRef]

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F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. Shaw, R. Mirin, S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7(3), 210–214 (2013).
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[CrossRef] [PubMed]

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[CrossRef]

F. Marsili, D. Bitauld, A. Gaggero, S. Jahanmirinejad, R. Leoni, F. Mattioli, A. Fiore, “Physics and application of photon number resolving detectors based on superconducting parallel nanowires,” New J. Phys. 11(4), 045022 (2009).
[CrossRef]

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. Benkhaoul, F. Lévy, A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[CrossRef]

F. Mattioli, R. Leoni, A. Gaggero, M. G. Castellano, P. Carelli, F. Marsili, A. Fiore, “Electrical characterization of superconducting single-photon detectors,” J. Appl. Phys. 101(5), 054302 (2007).
[CrossRef]

Mattioli, F.

Z. Zhou, G. Frucci, F. Mattioli, A. Gaggero, R. Leoni, S. Jahanmirinejad, T. B. Hoang, A. Fiore, “Ultrasensitive N-photon interferometric autocorrelator,” Phys. Rev. Lett. 110(13), 133605 (2013).
[CrossRef] [PubMed]

D. Sahin, A. Gaggero, Z. Zhou, S. Jahanmirinejad, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Hofling, A. Fiore, “Waveguide photon-number-resolving detectors for quantum photonic integrated circuits,” Appl. Phys. Lett. 103(11), 111116 (2013).
[CrossRef]

S. Jahanmirinejad, G. Frucci, F. Mattioli, D. Sahin, A. Gaggero, R. Leoni, A. Fiore, “Photon-number resolving detector based on a series array of superconducting nanowires,” Appl. Phys. Lett. 101(7), 072602 (2012).
[CrossRef]

J. J. Renema, G. Frucci, Z. Zhou, F. Mattioli, A. Gaggero, R. Leoni, M. J. A. de Dood, A. Fiore, M. P. van Exter, “Modified detector tomography technique applied to a superconducting multiphoton nanodetector,” Opt. Express 20(3), 2806–2813 (2012).
[CrossRef] [PubMed]

A. Gaggero, S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Notzel, R. Sanjines, A. Fiore, “Nanowire superconducting single-photon detectors on GaAs for integrated quantum photonic applications,” Appl. Phys. Lett. 97(15), 151108 (2010).
[CrossRef]

D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. 10(8), 2977–2981 (2010).
[CrossRef] [PubMed]

F. Marsili, D. Bitauld, A. Gaggero, S. Jahanmirinejad, R. Leoni, F. Mattioli, A. Fiore, “Physics and application of photon number resolving detectors based on superconducting parallel nanowires,” New J. Phys. 11(4), 045022 (2009).
[CrossRef]

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. Benkhaoul, F. Lévy, A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[CrossRef]

F. Mattioli, R. Leoni, A. Gaggero, M. G. Castellano, P. Carelli, F. Marsili, A. Fiore, “Electrical characterization of superconducting single-photon detectors,” J. Appl. Phys. 101(5), 054302 (2007).
[CrossRef]

Milburn, G. J.

E. Knill, R. Laflamme, G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[CrossRef] [PubMed]

Miller, A. J.

Minaeva, O.

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. Benkhaoul, F. Lévy, A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[CrossRef]

Minár, J.

N. Sangouard, C. Simon, J. Minář, H. Zbinden, H. de Riedmatten, N. Gisin, “Long-distance entanglement distribution with single-photon sources,” Phys. Rev. A 76(5), 050301 (2007).
[CrossRef]

Mirin, R.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. Shaw, R. Mirin, S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7(3), 210–214 (2013).
[CrossRef]

Mitin, V.

M. Bell, A. Antipov, B. Karasik, A. Sergeev, V. Mitin, A. Verevkin, “Photon number-resolved detection with sequentially connected nanowires,” IEEE Trans. Appl. Supercond. 17(2), 289–292 (2007).
[CrossRef]

Nam, S. W.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. Shaw, R. Mirin, S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7(3), 210–214 (2013).
[CrossRef]

A. E. Lita, A. J. Miller, S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16(5), 3032–3040 (2008).
[CrossRef] [PubMed]

Nejad, S. J.

D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. 10(8), 2977–2981 (2010).
[CrossRef] [PubMed]

A. Gaggero, S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Notzel, R. Sanjines, A. Fiore, “Nanowire superconducting single-photon detectors on GaAs for integrated quantum photonic applications,” Appl. Phys. Lett. 97(15), 151108 (2010).
[CrossRef]

Notzel, R.

A. Gaggero, S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Notzel, R. Sanjines, A. Fiore, “Nanowire superconducting single-photon detectors on GaAs for integrated quantum photonic applications,” Appl. Phys. Lett. 97(15), 151108 (2010).
[CrossRef]

Okunev, O.

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

Oliver, W. D.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1502–1511 (2003).
[CrossRef]

Pittman, T. B.

M. J. Fitch, B. C. Jacobs, T. B. Pittman, J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003).
[CrossRef]

Ramilli, M.

Reiger, E.

J. Kitaygorsky, S. Dorenbos, E. Reiger, R. Schouten, V. Zwiller, R. Sobolewski, “HEMT-based readout technique for dark- and photon-count studies in NbN superconducting single-photon detectors,” IEEE Trans. Appl. Supercond. 19(3), 346–349 (2009).
[CrossRef]

Renema, J. J.

Robinson, B. S.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Gol’tsman, S. A. Hamilton, K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2–3), 364–373 (2009).
[CrossRef]

E. A. Dauler, B. S. Robinson, A. J. Kerman, J. K. W. Yang, K. M. Rosfjord, V. Anant, B. Voronov, G. Gol’tsman, K. K. Berggren, “Multi-element superconducting nanowire single-photon detector,” IEEE Trans Appl. Supercond. 17(2), 279–284 (2007).

Rosfjord, K. M.

V. Anant, A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, K. K. Berggren, “Optical properties of superconducting nanowire single-photon detectors,” Opt. Express 16(14), 10750–10761 (2008).
[CrossRef] [PubMed]

A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, V. Anant, K. K. Berggren, G. N. Gol’tsman, B. M. Voronov, “Constriction-limited detection efficiency of superconducting nanowire single-photon detectors,” Appl. Phys. Lett. 90(10), 101110 (2007).
[CrossRef]

J. K. W. Yang, A. J. Kerman, E. A. Dauler, V. Anant, K. M. Rosfjord, K. K. Berggren, “Modeling the electrical and thermal response of superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. 17(2), 581–585 (2007).
[CrossRef]

E. A. Dauler, B. S. Robinson, A. J. Kerman, J. K. W. Yang, K. M. Rosfjord, V. Anant, B. Voronov, G. Gol’tsman, K. K. Berggren, “Multi-element superconducting nanowire single-photon detector,” IEEE Trans Appl. Supercond. 17(2), 279–284 (2007).

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

Sahin, D.

D. Sahin, A. Gaggero, Z. Zhou, S. Jahanmirinejad, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Hofling, A. Fiore, “Waveguide photon-number-resolving detectors for quantum photonic integrated circuits,” Appl. Phys. Lett. 103(11), 111116 (2013).
[CrossRef]

S. Jahanmirinejad, G. Frucci, F. Mattioli, D. Sahin, A. Gaggero, R. Leoni, A. Fiore, “Photon-number resolving detector based on a series array of superconducting nanowires,” Appl. Phys. Lett. 101(7), 072602 (2012).
[CrossRef]

A. Gaggero, S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Notzel, R. Sanjines, A. Fiore, “Nanowire superconducting single-photon detectors on GaAs for integrated quantum photonic applications,” Appl. Phys. Lett. 97(15), 151108 (2010).
[CrossRef]

Sangouard, N.

N. Sangouard, C. Simon, J. Minář, H. Zbinden, H. de Riedmatten, N. Gisin, “Long-distance entanglement distribution with single-photon sources,” Phys. Rev. A 76(5), 050301 (2007).
[CrossRef]

Sanjines, R.

A. Gaggero, S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Notzel, R. Sanjines, A. Fiore, “Nanowire superconducting single-photon detectors on GaAs for integrated quantum photonic applications,” Appl. Phys. Lett. 97(15), 151108 (2010).
[CrossRef]

Sasaki, M.

Schouten, R.

J. Kitaygorsky, S. Dorenbos, E. Reiger, R. Schouten, V. Zwiller, R. Sobolewski, “HEMT-based readout technique for dark- and photon-count studies in NbN superconducting single-photon detectors,” IEEE Trans. Appl. Supercond. 19(3), 346–349 (2009).
[CrossRef]

Seleznev, V.

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. Benkhaoul, F. Lévy, A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[CrossRef]

Semenov, A.

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

Sergeev, A.

M. Bell, A. Antipov, B. Karasik, A. Sergeev, V. Mitin, A. Verevkin, “Photon number-resolved detection with sequentially connected nanowires,” IEEE Trans. Appl. Supercond. 17(2), 289–292 (2007).
[CrossRef]

Shaw, M.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. Shaw, R. Mirin, S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7(3), 210–214 (2013).
[CrossRef]

Shields, A. J.

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

Simon, C.

N. Sangouard, C. Simon, J. Minář, H. Zbinden, H. de Riedmatten, N. Gisin, “Long-distance entanglement distribution with single-photon sources,” Phys. Rev. A 76(5), 050301 (2007).
[CrossRef]

Smirnov, K.

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

Sobolewski, R.

J. Kitaygorsky, S. Dorenbos, E. Reiger, R. Schouten, V. Zwiller, R. Sobolewski, “HEMT-based readout technique for dark- and photon-count studies in NbN superconducting single-photon detectors,” IEEE Trans. Appl. Supercond. 19(3), 346–349 (2009).
[CrossRef]

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

Stern, J.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. Shaw, R. Mirin, S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7(3), 210–214 (2013).
[CrossRef]

Tan, S. H.

van Exter, M. P.

Vayshenker, I.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. Shaw, R. Mirin, S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7(3), 210–214 (2013).
[CrossRef]

Verevkin, A.

M. Bell, A. Antipov, B. Karasik, A. Sergeev, V. Mitin, A. Verevkin, “Photon number-resolved detection with sequentially connected nanowires,” IEEE Trans. Appl. Supercond. 17(2), 289–292 (2007).
[CrossRef]

Verma, V.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. Shaw, R. Mirin, S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7(3), 210–214 (2013).
[CrossRef]

Voronov, B.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Gol’tsman, S. A. Hamilton, K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2–3), 364–373 (2009).
[CrossRef]

E. A. Dauler, B. S. Robinson, A. J. Kerman, J. K. W. Yang, K. M. Rosfjord, V. Anant, B. Voronov, G. Gol’tsman, K. K. Berggren, “Multi-element superconducting nanowire single-photon detector,” IEEE Trans Appl. Supercond. 17(2), 279–284 (2007).

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

Voronov, B. M.

A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, V. Anant, K. K. Berggren, G. N. Gol’tsman, B. M. Voronov, “Constriction-limited detection efficiency of superconducting nanowire single-photon detectors,” Appl. Phys. Lett. 90(10), 101110 (2007).
[CrossRef]

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

Waks, E.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1502–1511 (2003).
[CrossRef]

Williams, C.

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

Yamamoto, Y.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1502–1511 (2003).
[CrossRef]

Yang, J. K. W.

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Gol’tsman, S. A. Hamilton, K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2–3), 364–373 (2009).
[CrossRef]

V. Anant, A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, K. K. Berggren, “Optical properties of superconducting nanowire single-photon detectors,” Opt. Express 16(14), 10750–10761 (2008).
[CrossRef] [PubMed]

J. K. W. Yang, A. J. Kerman, E. A. Dauler, V. Anant, K. M. Rosfjord, K. K. Berggren, “Modeling the electrical and thermal response of superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. 17(2), 581–585 (2007).
[CrossRef]

A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, V. Anant, K. K. Berggren, G. N. Gol’tsman, B. M. Voronov, “Constriction-limited detection efficiency of superconducting nanowire single-photon detectors,” Appl. Phys. Lett. 90(10), 101110 (2007).
[CrossRef]

E. A. Dauler, B. S. Robinson, A. J. Kerman, J. K. W. Yang, K. M. Rosfjord, V. Anant, B. Voronov, G. Gol’tsman, K. K. Berggren, “Multi-element superconducting nanowire single-photon detector,” IEEE Trans Appl. Supercond. 17(2), 279–284 (2007).

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

Yuan, Z. L.

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

Zbinden, H.

N. Sangouard, C. Simon, J. Minář, H. Zbinden, H. de Riedmatten, N. Gisin, “Long-distance entanglement distribution with single-photon sources,” Phys. Rev. A 76(5), 050301 (2007).
[CrossRef]

Zhou, Z.

D. Sahin, A. Gaggero, Z. Zhou, S. Jahanmirinejad, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Hofling, A. Fiore, “Waveguide photon-number-resolving detectors for quantum photonic integrated circuits,” Appl. Phys. Lett. 103(11), 111116 (2013).
[CrossRef]

Z. Zhou, G. Frucci, F. Mattioli, A. Gaggero, R. Leoni, S. Jahanmirinejad, T. B. Hoang, A. Fiore, “Ultrasensitive N-photon interferometric autocorrelator,” Phys. Rev. Lett. 110(13), 133605 (2013).
[CrossRef] [PubMed]

J. J. Renema, G. Frucci, Z. Zhou, F. Mattioli, A. Gaggero, R. Leoni, M. J. A. de Dood, A. Fiore, M. P. van Exter, “Modified detector tomography technique applied to a superconducting multiphoton nanodetector,” Opt. Express 20(3), 2806–2813 (2012).
[CrossRef] [PubMed]

Zwiller, V.

J. Kitaygorsky, S. Dorenbos, E. Reiger, R. Schouten, V. Zwiller, R. Sobolewski, “HEMT-based readout technique for dark- and photon-count studies in NbN superconducting single-photon detectors,” IEEE Trans. Appl. Supercond. 19(3), 346–349 (2009).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (5)

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

S. Jahanmirinejad, G. Frucci, F. Mattioli, D. Sahin, A. Gaggero, R. Leoni, A. Fiore, “Photon-number resolving detector based on a series array of superconducting nanowires,” Appl. Phys. Lett. 101(7), 072602 (2012).
[CrossRef]

D. Sahin, A. Gaggero, Z. Zhou, S. Jahanmirinejad, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Hofling, A. Fiore, “Waveguide photon-number-resolving detectors for quantum photonic integrated circuits,” Appl. Phys. Lett. 103(11), 111116 (2013).
[CrossRef]

A. Gaggero, S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Notzel, R. Sanjines, A. Fiore, “Nanowire superconducting single-photon detectors on GaAs for integrated quantum photonic applications,” Appl. Phys. Lett. 97(15), 151108 (2010).
[CrossRef]

A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, V. Anant, K. K. Berggren, G. N. Gol’tsman, B. M. Voronov, “Constriction-limited detection efficiency of superconducting nanowire single-photon detectors,” Appl. Phys. Lett. 90(10), 101110 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1502–1511 (2003).
[CrossRef]

IEEE Trans Appl. Supercond. (1)

E. A. Dauler, B. S. Robinson, A. J. Kerman, J. K. W. Yang, K. M. Rosfjord, V. Anant, B. Voronov, G. Gol’tsman, K. K. Berggren, “Multi-element superconducting nanowire single-photon detector,” IEEE Trans Appl. Supercond. 17(2), 279–284 (2007).

IEEE Trans. Appl. Supercond. (3)

J. K. W. Yang, A. J. Kerman, E. A. Dauler, V. Anant, K. M. Rosfjord, K. K. Berggren, “Modeling the electrical and thermal response of superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. 17(2), 581–585 (2007).
[CrossRef]

M. Bell, A. Antipov, B. Karasik, A. Sergeev, V. Mitin, A. Verevkin, “Photon number-resolved detection with sequentially connected nanowires,” IEEE Trans. Appl. Supercond. 17(2), 289–292 (2007).
[CrossRef]

J. Kitaygorsky, S. Dorenbos, E. Reiger, R. Schouten, V. Zwiller, R. Sobolewski, “HEMT-based readout technique for dark- and photon-count studies in NbN superconducting single-photon detectors,” IEEE Trans. Appl. Supercond. 19(3), 346–349 (2009).
[CrossRef]

J. Appl. Phys. (1)

F. Mattioli, R. Leoni, A. Gaggero, M. G. Castellano, P. Carelli, F. Marsili, A. Fiore, “Electrical characterization of superconducting single-photon detectors,” J. Appl. Phys. 101(5), 054302 (2007).
[CrossRef]

J. Mod. Opt. (1)

E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Gol’tsman, S. A. Hamilton, K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. 56(2–3), 364–373 (2009).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nano Lett. (1)

D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. 10(8), 2977–2981 (2010).
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Nat. Photonics (3)

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Nature (1)

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G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, New York, 2002), Chap. 4.5.

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Figures (13)

Fig. 1
Fig. 1

(a) Schematic diagram of the 12-SND (not to scale). (b) SEM image of the 12-SND. The twelve active nanowires are highlighted in colors. The twelve Rps, the signal (S) and ground (G) contact pads, and the direction of IB are marked. The white scale bar in the upper-left corner of the image indicates a length of 10 μm.

Fig. 2
Fig. 2

IV characterization of the 12-SND at T = 1.2 K with the amplifier connected to the device. The value of 12 × Rp is determined by calculating the reciprocal of the slope using a linear fit (dashed blue line). The inset presents an enlarged view on the IV curve. The IC of the device was 13.4 μA.

Fig. 3
Fig. 3

The histograms of the output signals obtained in a light power range of 0-64 nW. Thirteen distinct output levels corresponding to the detections of 0-12 photons (marked by red numbers) were obtained. The device was biased with an IB of 13.0 μA.

Fig. 4
Fig. 4

The measured CR plotted as a function of the light power by setting different trigger levels of the counter, corresponding to the detections of ‘≥n-photons’ (n = 1-12). The slopes of the curves at lower powers agree well with the ( η μ ¯ ) n dependence (indicated by solid black lines), providing a proof for the 12-SND’s PNR functionality.

Fig. 5
Fig. 5

Device quantum efficiency as a function of IB, reaching a maximum value of ~0.17% at IB = 13.2 μA. Inset: photoresponse pulse for the 12-photon detection recorded by the 40-GHz sampling oscilloscope. The dashed blue line is the calculated photoresponse pulse for the 12-photon detection event, giving a fall time τfall of ~11.3 ns. After applying a band-pass filter (0.02-3 GHz, corresponding to the passband of the amplifiers) to the simulation, the result (solid red line) shows a good agreement with the measurement.

Fig. 6
Fig. 6

Two profiles (grey dots) of Fig. 3 at two different light powers of 5.33 nW (a) and 20.59 nW (b). They are fitted using a sum of Gaussian peaks, corresponding to the detections of n = 0-6 (a) and n = 3-10 (b) photons, respectively. The single Gaussian fits (Fit_n) are shown as solid blue lines and their sum (Fit_tot) is depicted as a dashed red line.

Fig. 7
Fig. 7

The value of P η N ( n| μ ¯ ) (black dots) at different light powers extracted from Fig. 3 and the fitting (red stars) based on Eq. (1) using a single fitting parameter η. Inset: the value of η obtained from the fitting is plotted as a function of the light power.

Fig. 8
Fig. 8

The calculated value of Iuf (solid blue lines) as a function of time in the cases of detecting n = 1-11 photons, for RL = 50 Ω (a) and RL = 1 MΩ (b), respectively. The inset provides an enlarged view of Iuf where the temporal profile of the incident pulse (τp = 100 ps, dashed red line) is also indicated.

Fig. 9
Fig. 9

(a) The value of H extracted from Fig. 3 plotted as a function of light power for different n. (b) The value of ΔH, defined as the value of H at different powers subtracted by the value of H at the lowest power for the same n, as a function of power for a few n in the 0-10 range.

Fig. 10
Fig. 10

(a) The value of H averaged for different powers (namely H ¯ ) plotted as a function of n (black dots). A power-law fit (red line) to H ¯ , defined as H ¯ =A n α , is also plotted, giving α = 0.81. Inset of (a): The value of Δ H ¯ , defined as Δ H ¯ = H ¯ ( n ) H ¯ ( n1 ) , is plotted as a function of n. Inset of (b): the calculated Vout plotted as a function of time for n = 1-12 using the electro-thermal model [21, 30]. Main panel of (b): the value of H (black dots) extracted from the inset of (b), plotted as a function of n together with a power-law fit (red line), giving α = 0.98.

Fig. 11
Fig. 11

(a) The value of VN plotted as a function of the light power for a few n in the 0-10 range. (b) The value of VEN plotted as a function of n for different light powers.

Fig. 12
Fig. 12

The distribution of Nelement (H1) and the corresponding distribution of P1 (H1) are shown as histogram (grey bars) in (a) to the right and to the left axis, respectively. The distribution of Pn (Hn) for n = 0-12 is calculated based on P1 (H1) assuming a uniform distribution of the elements’ efficiency. The examples for n = 4, 6 and 11 are plotted as histograms (grey bars) in (b), (c) and (d), respectively. Each Pn (Hn) distribution is fitted by a Gaussian peak (red lines). The FWHM of the fitting Gaussian peak, which represents VEN, is plotted as a function of n in (e) for n = 0-12. The VEN for the examples of n = 1, 4, 6 and 11 is marked in (a)-(d), respectively.

Fig. 13
Fig. 13

The ratio of ΔH/VN plotted as a function of n for different powers.

Equations (1)

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P η N ( n| μ ¯ )= m=n N! n!( Nn )! ( η μ ¯ ) m e η μ ¯ m! × j=0 n ( 1 ) j n! j!( nj )! [ 1η+ ( nj )η N ] m

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