Abstract

The realization of large-scale photonic circuits for quantum optics experiments at telecom wavelengths requires an increasing number of integrated detectors. Superconducting nanowire single photon detectors (SNSPDs) can be easily integrated onchip, and they can efficiently detect the light propagating inside waveguides. The thermal budget of cryostats poses a limit on the maximum number of elements that can be integrated on the same chip due to the thermal impact of the readout electronics. In this paper, we propose and implement a novel amplitude-multiplexing scheme allowing the efficient reading of several SNSPDs with only one readout port, thus enabling the realization of photonic circuits with a large number of modes.

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

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  31. Rth=Vn/IB, with vn=(4 kBTBRout)1/2 given by the Johnson noise of the amplifier resistance at T=300  K and IB=17  μA.
  32. This value have been derived from the ΔRth considering at least a broadening similar to the case at 300 K.
  33. http://www.caltechmicrowave.org/amplifiers .
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  36. In general, N=∑n=1Ch(Chn)=Ch+(Ch2)+(Ch3)+…=Ch+Ch(Ch−1)2+Ch(Ch−1)(Ch−2)6+…=2Ch−1 is the number of levels necessary to discriminate n photons. In Table 1N=Ch, as we are discussing the case n=1, i.e., the single photon regime.
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  39. In the single photon regime (see Table 1), with amplitude multiplexing the number of coax lines NAM required to encode NSNSPDs detectors is NAM=NSNSPD/Ch, while in the case of the row–column readout, the number of coax lines needed is NRC=2√NSNSPD. The condition NAM<NRC is satisfied for NSNSPDs≤4  Ch2. For example, for Ch6σ=35, amplitude multiplexing is still superior up to NSNSPD=4900 because it uses fewer coax lines. The advantage is even more evident in the 2σ case, where the readable channel Ch is larger.
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    [Crossref]

2019 (1)

2018 (4)

D. Zhu, Q. Y. Zhao, H. Choi, T. J. Lu, A. E. Dane, D. Englund, and K. Berggren, “A scalable multi-photon coincidence detector based on superconducting nanowires,” Nat. Nanotechnology 13, 596–601(2018).
[Crossref]

M. Schwartz, E. Schmidt, U. Rengstl, F. Hornung, S. Hepp, S. L. Portalupi, K. Llin, M. Jetter, M. Siegel, and P. Michler, “Fully on-chip single-photon Hanbury-Brown and Twiss experiment on a monolithic semiconductor-superconductor platform,” Nano Lett. 18, 6892–6897 (2018).
[Crossref]

R. Cernansky, F. Martini, and A. Politi, “Complementary metal-oxide semiconductor compatible source of single photons at near-visible wavelengths,” Opt. Lett. 43, 855 (2018).
[Crossref]

L. Zhang, L. You, X. Yang, J. Wu, C. Lv, Q. Guo, W. Zhang, H. Li, W. Peng, Z. Wang, and X. Xie, “Hotspot relaxation time of NbN superconducting nanowire single-photon detectors on various substrates,” Sci. Rep. 8, 1486 (2018).
[Crossref]

2017 (2)

S. Doerner, A. Kuzmin, S. Wuensch, I. Charaev, F. Boes, T. Zwick, and M. Siegel, “Frequency-multiplexed bias and readout of a 16-pixel superconducting nanowire single-photon detector array,” Appl. Phys. Lett. 111, 032603 (2017).
[Crossref]

Q. Y. Zhao, D. Zhu, N. Calandri, A. E. Dane, A. N. McCaughan, F. Bellei, H. Z. Wang, D. F. Santavicca, and K. K. Berggren, “Single-photon imager based on a superconducting nanowire delay line,” Nat. Photonics 11, 247–251 (2017).
[Crossref]

2016 (2)

F. Mattioli, Z. Zhou, A. Gaggero, R. Gaudio, R. Leoni, and A. Fiore, “Photon-counting and analog operation of a 24-pixel photon number resolving detector based on superconducting nanowires,” Opt. Express 24, 9067 (2016).
[Crossref]

A. Vetter, S. Ferrari, P. Rath, R. Alaee, O. Kah, V. Kovalyuk, S. Diewald, G. N. Goltsman, A. Korneev, C. Rockstuh, and W. H. P. Pernice, “Cavity-enhanced and ultrafast superconducting single-photon detectors,” Nano Lett. 16, 7085–7092 (2016).
[Crossref]

2015 (4)

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106, 192601 (2015).
[Crossref]

G. Reithmaier, M. Kaniber, F. Flassig, S. Lichtmannecker, K. Müller, A. Andrejew, J. Vuckovic, R. Gross, and J. J. Finley, “On-chip generation, routing, and detection of resonance fluorescence,” Nano Lett. 15, 5208–5213 (2015).
[Crossref]

P. Rath, O. Kahl, S. Ferrari, F. Sproll, G. Lewes-Malandrakis, D. Brink, K. Ilin, M. Siegel, C. Nebel, and W. Pernice, “Superconducting single photon detectors integrated with diamond nanophotonic circuits,” Light Sci. Appl. 4, e338 (2015).
[Crossref]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, W. J. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2015).
[Crossref]

2014 (2)

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

J. J. Renema, R. Gaudio, Q. Wang, Z. Zhou, A. Gaggero, F. Mattioli, R. Leoni, D. Sahin, M. J. A. de Dood, A. Fiore, and M. P. van Exter, “Experimental test of theories of the detection mechanism in a nanowire superconducting single photon detector,” Phys. Rev. Lett. 112, 117604 (2014).
[Crossref]

2013 (8)

D. Sahin, A. Gaggero, T. B. Hoang, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, and A. Fiore, “Integrated autocorrelator based on superconducting nanowires,” Opt. Express 21, 11162 (2013).
[Crossref]

J. J. Renema, G. Frucci, Z. Zhou, F. Mattioli, A. Gaggero, R. Leoni, M. J. A. de Dood, A. Fiore, and M. P. van Exter, “Universal response curve for nanowire superconducting single-photon detectors,” Phys. Rev. B 87, 174526 (2013).
[Crossref]

M. Hofherr, M. Arndt, K. Il’in, D. Henrich, M. Siegel, J. Toussaint, T. May, and H. G. Meyer, “Time-tagged multiplexing of serially biased superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. 23, 2501205 (2013).
[Crossref]

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, De. F. Nicola, F. Sciarrino, and P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
[Crossref]

C. Schuck, W. H. P. Pernice, and H. X. Tang, “Waveguide integrated low noise NbTiN nanowire single-photon detectors with milli-Hz dark count rate,” Sci. Rep. 3, 1893 (2013).
[Crossref]

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

F. Najafi, J. Mower, N. C. Harris, F. Bellei, A. Dane, C. Lee, X. Hu, P. Kharel, F. Marsili, S. Assefa, K. K. Berggren, and D. Englund, “On-chip detection of non-classical light by scalable integration of single-photon detectors,” Nat. Commun. 6, 5873 (2013).
[Crossref]

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

2012 (4)

W. H. P. Pernice, C. Schuck, O. Minaeva, M. Li, G. Goltsman, A. V. Sergienko, and H. X. Tang, “High-speed and high-efficiency travelling wave single-photon detectors embedded in nanophotonic circuits,” Nat. Commun. 3, 1325 (2012).
[Crossref]

A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Phys. 8, 285–291 (2012).
[Crossref]

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

S. Jahanmirinejad and A. Fiore, “Proposal for a superconducting photon number resolving detector with large dynamic range,” Opt. Express 20, 5017–5028 (2012).
[Crossref]

2011 (2)

F. Marsili, F. Najafi, E. Dauler, F. Bellei, X. Hu, M. Csete, R. J. Molnar, and K. K. Berggren, “Single-photon detectors based on ultranarrow superconducting nanowires,” Nano Lett. 11, 2048–2053 (2011).
[Crossref]

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

2009 (2)

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2009).
[Crossref]

R. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3, 696–705 (2009).
[Crossref]

2008 (2)

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (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. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2, 302–306 (2008).
[Crossref]

2007 (1)

M. Ejrnaes, R. Cristiano, O. Quaranta, S. Pagano, A. Gaggero, F. Mattioli, R. Leoni, B. Voronov, and G. Gol’tsman, “A cascade switching superconducting single photon detector,” Appl. Phys. Lett. 91, 262509 (2007).
[Crossref]

2006 (1)

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

2001 (1)

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

Acín, A.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, W. J. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2015).
[Crossref]

Alaee, R.

A. Vetter, S. Ferrari, P. Rath, R. Alaee, O. Kah, V. Kovalyuk, S. Diewald, G. N. Goltsman, A. Korneev, C. Rockstuh, and W. H. P. Pernice, “Cavity-enhanced and ultrafast superconducting single-photon detectors,” Nano Lett. 16, 7085–7092 (2016).
[Crossref]

Allman, M. S.

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106, 192601 (2015).
[Crossref]

Andrejew, A.

G. Reithmaier, M. Kaniber, F. Flassig, S. Lichtmannecker, K. Müller, A. Andrejew, J. Vuckovic, R. Gross, and J. J. Finley, “On-chip generation, routing, and detection of resonance fluorescence,” Nano Lett. 15, 5208–5213 (2015).
[Crossref]

Arndt, M.

M. Hofherr, M. Arndt, K. Il’in, D. Henrich, M. Siegel, J. Toussaint, T. May, and H. G. Meyer, “Time-tagged multiplexing of serially biased superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. 23, 2501205 (2013).
[Crossref]

Aspuru-Guzik, A.

A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Phys. 8, 285–291 (2012).
[Crossref]

Assefa, S.

F. Najafi, J. Mower, N. C. Harris, F. Bellei, A. Dane, C. Lee, X. Hu, P. Kharel, F. Marsili, S. Assefa, K. K. Berggren, and D. Englund, “On-chip detection of non-classical light by scalable integration of single-photon detectors,” Nat. Commun. 6, 5873 (2013).
[Crossref]

Augusiak, R.

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J. J. Renema, R. Gaudio, Q. Wang, Z. Zhou, A. Gaggero, F. Mattioli, R. Leoni, D. Sahin, M. J. A. de Dood, A. Fiore, and M. P. van Exter, “Experimental test of theories of the detection mechanism in a nanowire superconducting single photon detector,” Phys. Rev. Lett. 112, 117604 (2014).
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J. J. Renema, G. Frucci, Z. Zhou, F. Mattioli, A. Gaggero, R. Leoni, M. J. A. de Dood, A. Fiore, and M. P. van Exter, “Universal response curve for nanowire superconducting single-photon detectors,” Phys. Rev. B 87, 174526 (2013).
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D. Sahin, A. Gaggero, T. B. Hoang, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, and A. Fiore, “Integrated autocorrelator based on superconducting nanowires,” Opt. Express 21, 11162 (2013).
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D. Sahin, A. Gaggero, Z. Zhou, S. Jahanmirinejad, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, and A. Fiore, “Waveguide photon-number-resolving detectors for quantum photonic integrated circuits,” Appl. Phys. Lett. 103, 111116 (2013).
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S. Jahanmirinejad, G. Frucci, F. Mattioli, D. Sahin, A. Gaggero, R. Leoni, and A. Fiore, “Photon-number resolving detector based on a series array of superconducting nanowires,” Appl. Phys. Lett. 101, 072602 (2012).
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S. Jahanmirinejad and A. Fiore, “Proposal for a superconducting photon number resolving detector with large dynamic range,” Opt. Express 20, 5017–5028 (2012).
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J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
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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. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2, 302–306 (2008).
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J. J. Renema, G. Frucci, Z. Zhou, F. Mattioli, A. Gaggero, R. Leoni, M. J. A. de Dood, A. Fiore, and M. P. van Exter, “Universal response curve for nanowire superconducting single-photon detectors,” Phys. Rev. B 87, 174526 (2013).
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D. Sahin, A. Gaggero, T. B. Hoang, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, and A. Fiore, “Integrated autocorrelator based on superconducting nanowires,” Opt. Express 21, 11162 (2013).
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S. Jahanmirinejad, G. Frucci, F. Mattioli, D. Sahin, A. Gaggero, R. Leoni, and A. Fiore, “Photon-number resolving detector based on a series array of superconducting nanowires,” Appl. Phys. Lett. 101, 072602 (2012).
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J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
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F. Mattioli, Z. Zhou, A. Gaggero, R. Gaudio, R. Leoni, and A. Fiore, “Photon-counting and analog operation of a 24-pixel photon number resolving detector based on superconducting nanowires,” Opt. Express 24, 9067 (2016).
[Crossref]

J. J. Renema, R. Gaudio, Q. Wang, Z. Zhou, A. Gaggero, F. Mattioli, R. Leoni, D. Sahin, M. J. A. de Dood, A. Fiore, and M. P. van Exter, “Experimental test of theories of the detection mechanism in a nanowire superconducting single photon detector,” Phys. Rev. Lett. 112, 117604 (2014).
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D. Sahin, A. Gaggero, T. B. Hoang, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, and A. Fiore, “Integrated autocorrelator based on superconducting nanowires,” Opt. Express 21, 11162 (2013).
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J. J. Renema, G. Frucci, Z. Zhou, F. Mattioli, A. Gaggero, R. Leoni, M. J. A. de Dood, A. Fiore, and M. P. van Exter, “Universal response curve for nanowire superconducting single-photon detectors,” Phys. Rev. B 87, 174526 (2013).
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D. Sahin, A. Gaggero, Z. Zhou, S. Jahanmirinejad, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, and A. Fiore, “Waveguide photon-number-resolving detectors for quantum photonic integrated circuits,” Appl. Phys. Lett. 103, 111116 (2013).
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S. Jahanmirinejad, G. Frucci, F. Mattioli, D. Sahin, A. Gaggero, R. Leoni, and A. Fiore, “Photon-number resolving detector based on a series array of superconducting nanowires,” Appl. Phys. Lett. 101, 072602 (2012).
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J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[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. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2, 302–306 (2008).
[Crossref]

M. Ejrnaes, R. Cristiano, O. Quaranta, S. Pagano, A. Gaggero, F. Mattioli, R. Leoni, B. Voronov, and G. Gol’tsman, “A cascade switching superconducting single photon detector,” Appl. Phys. Lett. 91, 262509 (2007).
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N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
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F. Mattioli, Z. Zhou, A. Gaggero, R. Gaudio, R. Leoni, and A. Fiore, “Photon-counting and analog operation of a 24-pixel photon number resolving detector based on superconducting nanowires,” Opt. Express 24, 9067 (2016).
[Crossref]

J. J. Renema, R. Gaudio, Q. Wang, Z. Zhou, A. Gaggero, F. Mattioli, R. Leoni, D. Sahin, M. J. A. de Dood, A. Fiore, and M. P. van Exter, “Experimental test of theories of the detection mechanism in a nanowire superconducting single photon detector,” Phys. Rev. Lett. 112, 117604 (2014).
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M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106, 192601 (2015).
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F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
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Appl. Phys. Lett. (7)

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
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IEEE Trans. Appl. Supercond. (1)

M. Hofherr, M. Arndt, K. Il’in, D. Henrich, M. Siegel, J. Toussaint, T. May, and H. G. Meyer, “Time-tagged multiplexing of serially biased superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. 23, 2501205 (2013).
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Light Sci. Appl. (1)

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Nano Lett. (4)

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Other (5)

In general, N=∑n=1Ch(Chn)=Ch+(Ch2)+(Ch3)+…=Ch+Ch(Ch−1)2+Ch(Ch−1)(Ch−2)6+…=2Ch−1 is the number of levels necessary to discriminate n photons. In Table 1N=Ch, as we are discussing the case n=1, i.e., the single photon regime.

Rth=Vn/IB, with vn=(4 kBTBRout)1/2 given by the Johnson noise of the amplifier resistance at T=300  K and IB=17  μA.

This value have been derived from the ΔRth considering at least a broadening similar to the case at 300 K.

http://www.caltechmicrowave.org/amplifiers .

In the single photon regime (see Table 1), with amplitude multiplexing the number of coax lines NAM required to encode NSNSPDs detectors is NAM=NSNSPD/Ch, while in the case of the row–column readout, the number of coax lines needed is NRC=2√NSNSPD. The condition NAM<NRC is satisfied for NSNSPDs≤4  Ch2. For example, for Ch6σ=35, amplitude multiplexing is still superior up to NSNSPD=4900 because it uses fewer coax lines. The advantage is even more evident in the 2σ case, where the readable channel Ch is larger.

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Figures (4)

Fig. 1.
Fig. 1. (a) Sketch of the electrical scheme used to read the pulsed signal at the output of an N -element array. Each element of the array is made by a SNSPD (represented in the sketch with a switch, the normal resistance r n , and the wire kinetic inductance L k ) with an on-chip AuPd resistance R i in parallel (see text). A bias-tee is used to bias and read out the array. (b) Integrated experiment scheme, consisting of an array of two SNSPDs and a PIC made of two 50:50 Y splitters and input/output ports.
Fig. 2.
Fig. 2. (a) Scanning electron micrograph of the SNSPD array consisting of two detectors ( D 1 and D 2 ) integrated on top of a PIC made of two 50:50 Y splitters and input/output ports realized with grating couplers; the scale bar corresponds to 125 μm. Enlarged views of (b)  D 1 and (c)  D 2 . The scale bars are 30 μm. In green are highlighted the parallel resistance R 1 and R 2 , respectively.
Fig. 3.
Fig. 3. (a) Single trace of the array output signal showing peaks with three different heights due to the firing of D 1 (with R 1 in parallel, red squares), D 2 (with R 2 in parallel, yellow squares), and the simultaneous firing of D 1 and D 2 (purple squares) at I B = 17 μA . The exponential fit of the decay time provides a value of τ 1 = 11.81 ns and τ 2 = 6.10 ns for the peaks due to D 1 and D 2 , respectively. (b) Persistence map of the transient response of the array under the illumination of a 10 ps pulsed laser with 10 MHz repetition rate and an average photon number per pulse μ = 1 . (c) Histogram of pulse counts as a function of voltage, obtained from the persistence plot using data of the slice taken at 700 ps [green vertical line in (b)] and its fits with three Gaussian curves (continuous lines).
Fig. 4.
Fig. 4. (a) Pulse count rate of the array versus trigger voltage level of the counter measured at different bias currents for 10 5 photons / s photon flux coupled to the input of the second Y splitter. Inset: ODE of the array (red squares) and DCR (black squares) as a function of the bias current, taken at T = 2.9 K . (b) ODE and DCR of individual D 1 and D 2 , respectively.

Tables (1)

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Table 1. Figures of Merit Regarding the Array Readout Scalability in Single Photon Regime a

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