Abstract

Typically, transition edge sensors resolve photon number of up to 10 or 20 photons, depending on the wavelength and TES design. We extend that dynamic range up to 1000 photons, while maintaining sub-shot noise detection process uncertainty of the number of detected photons and beyond that show a monotonic response up to ≈ 6 · 106 photons in a single light pulse. This mode of operation, which heats the sensor far beyond its transition edge into the normal conductive regime, offers a technique for connecting single-photon-counting measurements to radiant-power measurements at picowatt levels. Connecting these two usually incompatible operating regimes in a single detector offers significant potential for directly tying photon counting measurements to conventional cryogenic radiometric standards. In addition, our measurements highlight the advantages of a photon-number state source over a coherent pulse source as a tool for characterizing such a detector.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Eppeldauer and J. E. Hardis, “Fourteen-decade photocurrent measurements with large-area silicon photodiodes at room temperature,” Appl. Opt.30, 3091–3099 (1991).
    [CrossRef] [PubMed]
  2. J. Mountford, G. Porrovecchio, M. Smid, and R. Smid, “Development of a switched integrator amplifier for high-accuracy optical measurements,” Appl. Opt.47, 5821–5828 (2008).
    [CrossRef]
  3. R. J. McIntyre, “Theory of microplasma instability in silicon,” J. Appl. Phys.32, 983–995 (1961).
    [CrossRef]
  4. H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-db channel loss using superconducting single-photon detectors,” Nat. Photonics1, 343–348 (2007).
    [CrossRef]
  5. T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82, 031802 (2010).
    [CrossRef]
  6. E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
    [CrossRef]
  7. N. Namekata, S. Adachi, and S. Inoue, “1.5 GHz single-photon detection at telecommunication wavelengths using sinusoidally gated ingaas/inp avalanche photodiode,” Opt. Express17, 6275–6282 (2009).
    [CrossRef] [PubMed]
  8. M. A. Krainak, G. Yanga, W. Lu, and X. Sun,“Photon-counting detectors for space-based applications” Detectors and Imaging Devices: Infrared, Focal Plane, SPIE Proc. 7780, 77801J (2010).
  9. P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature429, 158–161 (2004).
    [CrossRef] [PubMed]
  10. M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature429, 161–164 (2004).
    [CrossRef] [PubMed]
  11. K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express18, 8107–8114 (2010).
    [CrossRef] [PubMed]
  12. A. Garg and N.D. Mermin, “Detector inefficiencies in the Einstein-Podolsky-Rosen experiment,” Phys. Rev. D35, 3831–3835 (1987).
    [CrossRef]
  13. A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon-photon counting community,” Nucl. Instrum. Meth. A610, 183–187 (2009).
    [CrossRef]
  14. G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo-Berchera, “Absolute calibration of analog detectors using stimulated parametric down conversion,” J. Mod. Optic.56, 401–404 (2009).
    [CrossRef]
  15. J. A. Chervenak, E. N. Grossman, C. D. Reintsema, K. D. Irwin, S. H. Moseley, and C. A. Allen, “Sub-picowatt precision radiometry using superconducting transition edge sensor bolometers,” IEEE Trans. Appl. Supercond., 11, 593–596 (2001).
    [CrossRef]
  16. S. I. Woods, S. M. Carr, A. C. Carter, T. M. Jung, and R. U. Datla, “Calibration of ultra-low infrared power at NIST,” SPIE Proc.7742, 77421P (2010).
    [CrossRef]
  17. R. Klein, R. Thornagel, and G. Ulm, “From single photons to milliwatt radiant power-electron storage rings as radiation sources with a high dynamic range,” Metrologia47, R33–R40 (2010).
    [CrossRef]
  18. G. P. Eppeldauer and D. C. Lynch, “Opto-mechanical and electronic mesign of a tunnel-trap Si radiometer,” J. Res. Natl. Inst. Stan.105, 813–828 (2000).
    [CrossRef]
  19. J. Y. Cheung, C. J. Chunnilall, G. Porrovecchio, M. Smid, and E. Theocharous, “Low optical power reference detector implemented in the validation of two independent techniques for calibrating photon-counting detectors,” Opt. Express19, 20347–20363 (2011).
    [CrossRef] [PubMed]
  20. A. R. Dixon, Z. L. Yuan, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate,” Opt. Express16, 18790–18979 (2008).
    [CrossRef]
  21. D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98% detection efficiency with index-matched small-gap fiber coupling,” Opt. Express19, 870–875 (2011).
    [CrossRef] [PubMed]
  22. R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics3, 696–705 (2009).
    [CrossRef]
  23. M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
    [CrossRef] [PubMed]
  24. P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The crosstalk problem in sipms and their use as light sensors for imaging atmospheric cherenkov telescopes,”Nucl. Instrum. Meth. A610, 131–134 (2009).
    [CrossRef]
  25. 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]
  26. A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express16, 3032–3040 (2008).
    [CrossRef] [PubMed]
  27. 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, 735–737 (1998).
    [CrossRef]
  28. A. G. Kozorezov, J. K. Wigmore, D. Martin, P. Verhoeve, and A. Peacock, “Electron energy down-conversion in thin superconducting films,” Phys. Rev. B75, 094513 (2007).
    [CrossRef]
  29. A. Lamas-Linares, T. Gerrits, N. A. Tomlin, A. Lita, B. Calkins, J. Beyer, R. Mirin, and S. W. Nam, “Transition edge sensors with low timing jitter at 1550 nm,” CLEO conference2012 http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2012-QTu3E.1
  30. A. J. Miller, A. E. Lita, B. Calkins, I. Vayshenker, S. M. Gruber, and S. W. Nam, “Compact cryogenic self-aligning fiber-to-detector coupling with losses below one percent,” Opt. Express19, 9102–9110 (2011).
    [CrossRef] [PubMed]
  31. P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A44, 3266–3269 (1991).
    [CrossRef] [PubMed]
  32. G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall, M. G. Mingolla, M. G. A. Paris, F. Piacentini, and S. V. Polyakov, “Ancilla-assisted calibration of a measuring apparatus”, Phys. Rev. Lett., 108, 253601 (2012).
    [CrossRef]
  33. K. D. Irwin and G. C. Hilton, “Transition-edge sensors,” Cryogenic Particle Detection, Top. Appl. Phys.99, 63–152 (2005).
  34. K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” Appl. Phys. Lett.66, 1998–2000 (1995).
    [CrossRef]
  35. E. Figueroa-Feliciano, B. Cabrera, A. Miller, S. Powell, T. Saab, and A. Walker, “Optimal filter analysis of energy-dependent pulse shapes and its application to TES detectors,” Nucl. Instrum. Meth. A444, 453–456 (2000).
    [CrossRef]
  36. D. Fixsen, S. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Meth. A520, 555–558 (2004).
    [CrossRef]
  37. Z. H. Levine, T. Gerrits, A. L. Migdall, D. V. Samarov, B. Calkins, A. E. Lita, and S. W. Nam, “An algorithm for finding clusters with a known distribution and its application to photon-number resolution using a superconducting transition-edge sensor,” J. Opt. Soc. Am. B29, 2066–2073 (2012).
    [CrossRef]
  38. T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express19, 24434–24447 (2011).
    [CrossRef] [PubMed]

2012 (2)

G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall, M. G. Mingolla, M. G. A. Paris, F. Piacentini, and S. V. Polyakov, “Ancilla-assisted calibration of a measuring apparatus”, Phys. Rev. Lett., 108, 253601 (2012).
[CrossRef]

Z. H. Levine, T. Gerrits, A. L. Migdall, D. V. Samarov, B. Calkins, A. E. Lita, and S. W. Nam, “An algorithm for finding clusters with a known distribution and its application to photon-number resolution using a superconducting transition-edge sensor,” J. Opt. Soc. Am. B29, 2066–2073 (2012).
[CrossRef]

2011 (5)

2010 (5)

S. I. Woods, S. M. Carr, A. C. Carter, T. M. Jung, and R. U. Datla, “Calibration of ultra-low infrared power at NIST,” SPIE Proc.7742, 77421P (2010).
[CrossRef]

R. Klein, R. Thornagel, and G. Ulm, “From single photons to milliwatt radiant power-electron storage rings as radiation sources with a high dynamic range,” Metrologia47, R33–R40 (2010).
[CrossRef]

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express18, 8107–8114 (2010).
[CrossRef] [PubMed]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82, 031802 (2010).
[CrossRef]

M. A. Krainak, G. Yanga, W. Lu, and X. Sun,“Photon-counting detectors for space-based applications” Detectors and Imaging Devices: Infrared, Focal Plane, SPIE Proc. 7780, 77801J (2010).

2009 (5)

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon-photon counting community,” Nucl. Instrum. Meth. A610, 183–187 (2009).
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo-Berchera, “Absolute calibration of analog detectors using stimulated parametric down conversion,” J. Mod. Optic.56, 401–404 (2009).
[CrossRef]

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The crosstalk problem in sipms and their use as light sensors for imaging atmospheric cherenkov telescopes,”Nucl. Instrum. Meth. A610, 131–134 (2009).
[CrossRef]

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics3, 696–705 (2009).
[CrossRef]

N. Namekata, S. Adachi, and S. Inoue, “1.5 GHz single-photon detection at telecommunication wavelengths using sinusoidally gated ingaas/inp avalanche photodiode,” Opt. Express17, 6275–6282 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (3)

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-db channel loss using superconducting single-photon detectors,” Nat. Photonics1, 343–348 (2007).
[CrossRef]

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

A. G. Kozorezov, J. K. Wigmore, D. Martin, P. Verhoeve, and A. Peacock, “Electron energy down-conversion in thin superconducting films,” Phys. Rev. B75, 094513 (2007).
[CrossRef]

2005 (1)

K. D. Irwin and G. C. Hilton, “Transition-edge sensors,” Cryogenic Particle Detection, Top. Appl. Phys.99, 63–152 (2005).

2004 (3)

D. Fixsen, S. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Meth. A520, 555–558 (2004).
[CrossRef]

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature429, 158–161 (2004).
[CrossRef] [PubMed]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature429, 161–164 (2004).
[CrossRef] [PubMed]

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]

2001 (1)

J. A. Chervenak, E. N. Grossman, C. D. Reintsema, K. D. Irwin, S. H. Moseley, and C. A. Allen, “Sub-picowatt precision radiometry using superconducting transition edge sensor bolometers,” IEEE Trans. Appl. Supercond., 11, 593–596 (2001).
[CrossRef]

2000 (2)

G. P. Eppeldauer and D. C. Lynch, “Opto-mechanical and electronic mesign of a tunnel-trap Si radiometer,” J. Res. Natl. Inst. Stan.105, 813–828 (2000).
[CrossRef]

E. Figueroa-Feliciano, B. Cabrera, A. Miller, S. Powell, T. Saab, and A. Walker, “Optimal filter analysis of energy-dependent pulse shapes and its application to TES detectors,” Nucl. Instrum. Meth. A444, 453–456 (2000).
[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, 735–737 (1998).
[CrossRef]

1995 (1)

K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” Appl. Phys. Lett.66, 1998–2000 (1995).
[CrossRef]

1991 (2)

P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A44, 3266–3269 (1991).
[CrossRef] [PubMed]

G. Eppeldauer and J. E. Hardis, “Fourteen-decade photocurrent measurements with large-area silicon photodiodes at room temperature,” Appl. Opt.30, 3091–3099 (1991).
[CrossRef] [PubMed]

1987 (1)

A. Garg and N.D. Mermin, “Detector inefficiencies in the Einstein-Podolsky-Rosen experiment,” Phys. Rev. D35, 3831–3835 (1987).
[CrossRef]

1961 (1)

R. J. McIntyre, “Theory of microplasma instability in silicon,” J. Appl. Phys.32, 983–995 (1961).
[CrossRef]

Adachi, S.

Allen, C. A.

J. A. Chervenak, E. N. Grossman, C. D. Reintsema, K. D. Irwin, S. H. Moseley, and C. A. Allen, “Sub-picowatt precision radiometry using superconducting transition edge sensor bolometers,” IEEE Trans. Appl. Supercond., 11, 593–596 (2001).
[CrossRef]

Amemiya, K.

Aspelmeyer, M.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature429, 158–161 (2004).
[CrossRef] [PubMed]

Baek, B.

Beaumont, A. R.

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon-photon counting community,” Nucl. Instrum. Meth. A610, 183–187 (2009).
[CrossRef]

Bennink, R. S.

Brida, G.

G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall, M. G. Mingolla, M. G. A. Paris, F. Piacentini, and S. V. Polyakov, “Ancilla-assisted calibration of a measuring apparatus”, Phys. Rev. Lett., 108, 253601 (2012).
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo-Berchera, “Absolute calibration of analog detectors using stimulated parametric down conversion,” J. Mod. Optic.56, 401–404 (2009).
[CrossRef]

Buzhan, P.

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The crosstalk problem in sipms and their use as light sensors for imaging atmospheric cherenkov telescopes,”Nucl. Instrum. Meth. A610, 131–134 (2009).
[CrossRef]

Cabrera, B.

D. Fixsen, S. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Meth. A520, 555–558 (2004).
[CrossRef]

E. Figueroa-Feliciano, B. Cabrera, A. Miller, S. Powell, T. Saab, and A. Walker, “Optimal filter analysis of energy-dependent pulse shapes and its application to TES detectors,” Nucl. Instrum. Meth. A444, 453–456 (2000).
[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, 735–737 (1998).
[CrossRef]

Calkins, B.

Carr, S. M.

S. I. Woods, S. M. Carr, A. C. Carter, T. M. Jung, and R. U. Datla, “Calibration of ultra-low infrared power at NIST,” SPIE Proc.7742, 77421P (2010).
[CrossRef]

Carter, A. C.

S. I. Woods, S. M. Carr, A. C. Carter, T. M. Jung, and R. U. Datla, “Calibration of ultra-low infrared power at NIST,” SPIE Proc.7742, 77421P (2010).
[CrossRef]

Chekhova, M.

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo-Berchera, “Absolute calibration of analog detectors using stimulated parametric down conversion,” J. Mod. Optic.56, 401–404 (2009).
[CrossRef]

Chervenak, J. A.

J. A. Chervenak, E. N. Grossman, C. D. Reintsema, K. D. Irwin, S. H. Moseley, and C. A. Allen, “Sub-picowatt precision radiometry using superconducting transition edge sensor bolometers,” IEEE Trans. Appl. Supercond., 11, 593–596 (2001).
[CrossRef]

Cheung, J. Y.

J. Y. Cheung, C. J. Chunnilall, G. Porrovecchio, M. Smid, and E. Theocharous, “Low optical power reference detector implemented in the validation of two independent techniques for calibrating photon-counting detectors,” Opt. Express19, 20347–20363 (2011).
[CrossRef] [PubMed]

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon-photon counting community,” Nucl. Instrum. Meth. A610, 183–187 (2009).
[CrossRef]

Chulkova, G.

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Chunnilall, C. J.

J. Y. Cheung, C. J. Chunnilall, G. Porrovecchio, M. Smid, and E. Theocharous, “Low optical power reference detector implemented in the validation of two independent techniques for calibrating photon-counting detectors,” Opt. Express19, 20347–20363 (2011).
[CrossRef] [PubMed]

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon-photon counting community,” Nucl. Instrum. Meth. A610, 183–187 (2009).
[CrossRef]

Ciavarella, L.

G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall, M. G. Mingolla, M. G. A. Paris, F. Piacentini, and S. V. Polyakov, “Ancilla-assisted calibration of a measuring apparatus”, Phys. Rev. Lett., 108, 253601 (2012).
[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, 735–737 (1998).
[CrossRef]

Clement, T. S.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82, 031802 (2010).
[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, 735–737 (1998).
[CrossRef]

Datla, R. U.

S. I. Woods, S. M. Carr, A. C. Carter, T. M. Jung, and R. U. Datla, “Calibration of ultra-low infrared power at NIST,” SPIE Proc.7742, 77421P (2010).
[CrossRef]

Degiovanni, I. P.

G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall, M. G. Mingolla, M. G. A. Paris, F. Piacentini, and S. V. Polyakov, “Ancilla-assisted calibration of a measuring apparatus”, Phys. Rev. Lett., 108, 253601 (2012).
[CrossRef]

Dixon, A. R.

Dolgoshein, B.

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The crosstalk problem in sipms and their use as light sensors for imaging atmospheric cherenkov telescopes,”Nucl. Instrum. Meth. A610, 131–134 (2009).
[CrossRef]

Dorenbos, S.

T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express19, 24434–24447 (2011).
[CrossRef] [PubMed]

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Dynes, J. F.

Eisaman, M. D.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
[CrossRef] [PubMed]

Eppeldauer, G.

Eppeldauer, G. P.

G. P. Eppeldauer and D. C. Lynch, “Opto-mechanical and electronic mesign of a tunnel-trap Si radiometer,” J. Res. Natl. Inst. Stan.105, 813–828 (2000).
[CrossRef]

Fan, J.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
[CrossRef] [PubMed]

Figueroa-Feliciano, E.

D. Fixsen, S. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Meth. A520, 555–558 (2004).
[CrossRef]

E. Figueroa-Feliciano, B. Cabrera, A. Miller, S. Powell, T. Saab, and A. Walker, “Optimal filter analysis of energy-dependent pulse shapes and its application to TES detectors,” Nucl. Instrum. Meth. A444, 453–456 (2000).
[CrossRef]

Fixsen, D.

D. Fixsen, S. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Meth. A520, 555–558 (2004).
[CrossRef]

Fujii, G.

Fujino, H.

Fujiwara, M.

Fukuda, D.

Garg, A.

A. Garg and N.D. Mermin, “Detector inefficiencies in the Einstein-Podolsky-Rosen experiment,” Phys. Rev. D35, 3831–3835 (1987).
[CrossRef]

Gasparoni, S.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature429, 158–161 (2004).
[CrossRef] [PubMed]

Genovese, M.

G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall, M. G. Mingolla, M. G. A. Paris, F. Piacentini, and S. V. Polyakov, “Ancilla-assisted calibration of a measuring apparatus”, Phys. Rev. Lett., 108, 253601 (2012).
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo-Berchera, “Absolute calibration of analog detectors using stimulated parametric down conversion,” J. Mod. Optic.56, 401–404 (2009).
[CrossRef]

Gerrits, T.

Glancy, S.

T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express19, 24434–24447 (2011).
[CrossRef] [PubMed]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82, 031802 (2010).
[CrossRef]

Gol’tsman, G.

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Grice, W. P.

Grossman, E. N.

J. A. Chervenak, E. N. Grossman, C. D. Reintsema, K. D. Irwin, S. H. Moseley, and C. A. Allen, “Sub-picowatt precision radiometry using superconducting transition edge sensor bolometers,” IEEE Trans. Appl. Supercond., 11, 593–596 (2001).
[CrossRef]

Gruber, S. M.

Hadfield, R. H.

T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express19, 24434–24447 (2011).
[CrossRef] [PubMed]

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics3, 696–705 (2009).
[CrossRef]

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-db channel loss using superconducting single-photon detectors,” Nat. Photonics1, 343–348 (2007).
[CrossRef]

Hardis, J. E.

Hilton, G. C.

K. D. Irwin and G. C. Hilton, “Transition-edge sensors,” Cryogenic Particle Detection, Top. Appl. Phys.99, 63–152 (2005).

Honjo, T.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-db channel loss using superconducting single-photon detectors,” Nat. Photonics1, 343–348 (2007).
[CrossRef]

Ilyin, A.

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The crosstalk problem in sipms and their use as light sensors for imaging atmospheric cherenkov telescopes,”Nucl. Instrum. Meth. A610, 131–134 (2009).
[CrossRef]

Inoue, S.

Ireland, J.

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon-photon counting community,” Nucl. Instrum. Meth. A610, 183–187 (2009).
[CrossRef]

Irwin, K. D.

K. D. Irwin and G. C. Hilton, “Transition-edge sensors,” Cryogenic Particle Detection, Top. Appl. Phys.99, 63–152 (2005).

J. A. Chervenak, E. N. Grossman, C. D. Reintsema, K. D. Irwin, S. H. Moseley, and C. A. Allen, “Sub-picowatt precision radiometry using superconducting transition edge sensor bolometers,” IEEE Trans. Appl. Supercond., 11, 593–596 (2001).
[CrossRef]

K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” Appl. Phys. Lett.66, 1998–2000 (1995).
[CrossRef]

Ishii, H.

Itatani, T.

Jukna, A.

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Jung, T. M.

S. I. Woods, S. M. Carr, A. C. Carter, T. M. Jung, and R. U. Datla, “Calibration of ultra-low infrared power at NIST,” SPIE Proc.7742, 77421P (2010).
[CrossRef]

Kaplin, V.

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The crosstalk problem in sipms and their use as light sensors for imaging atmospheric cherenkov telescopes,”Nucl. Instrum. Meth. A610, 131–134 (2009).
[CrossRef]

Kitaygorsky, J.

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Klapwijk, T.

Klein, R.

R. Klein, R. Thornagel, and G. Ulm, “From single photons to milliwatt radiant power-electron storage rings as radiation sources with a high dynamic range,” Metrologia47, R33–R40 (2010).
[CrossRef]

Klemin, S.

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The crosstalk problem in sipms and their use as light sensors for imaging atmospheric cherenkov telescopes,”Nucl. Instrum. Meth. A610, 131–134 (2009).
[CrossRef]

Knill, E.

T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express19, 24434–24447 (2011).
[CrossRef] [PubMed]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82, 031802 (2010).
[CrossRef]

Korneev, A.

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Kozorezov, A. G.

A. G. Kozorezov, J. K. Wigmore, D. Martin, P. Verhoeve, and A. Peacock, “Electron energy down-conversion in thin superconducting films,” Phys. Rev. B75, 094513 (2007).
[CrossRef]

Krainak, M. A.

M. A. Krainak, G. Yanga, W. Lu, and X. Sun,“Photon-counting detectors for space-based applications” Detectors and Imaging Devices: Infrared, Focal Plane, SPIE Proc. 7780, 77801J (2010).

Levine, Z. H.

Lita, A.

Lita, A. E.

Lu, W.

M. A. Krainak, G. Yanga, W. Lu, and X. Sun,“Photon-counting detectors for space-based applications” Detectors and Imaging Devices: Infrared, Focal Plane, SPIE Proc. 7780, 77801J (2010).

Lundeen, J. S.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature429, 161–164 (2004).
[CrossRef] [PubMed]

Lynch, D. C.

G. P. Eppeldauer and D. C. Lynch, “Opto-mechanical and electronic mesign of a tunnel-trap Si radiometer,” J. Res. Natl. Inst. Stan.105, 813–828 (2000).
[CrossRef]

Martin, D.

A. G. Kozorezov, J. K. Wigmore, D. Martin, P. Verhoeve, and A. Peacock, “Electron energy down-conversion in thin superconducting films,” Phys. Rev. B75, 094513 (2007).
[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]

McIntyre, R. J.

R. J. McIntyre, “Theory of microplasma instability in silicon,” J. Appl. Phys.32, 983–995 (1961).
[CrossRef]

Mermin, N.D.

A. Garg and N.D. Mermin, “Detector inefficiencies in the Einstein-Podolsky-Rosen experiment,” Phys. Rev. D35, 3831–3835 (1987).
[CrossRef]

Migdall, A.

G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall, M. G. Mingolla, M. G. A. Paris, F. Piacentini, and S. V. Polyakov, “Ancilla-assisted calibration of a measuring apparatus”, Phys. Rev. Lett., 108, 253601 (2012).
[CrossRef]

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
[CrossRef] [PubMed]

Migdall, A. L.

Z. H. Levine, T. Gerrits, A. L. Migdall, D. V. Samarov, B. Calkins, A. E. Lita, and S. W. Nam, “An algorithm for finding clusters with a known distribution and its application to photon-number resolution using a superconducting transition-edge sensor,” J. Opt. Soc. Am. B29, 2066–2073 (2012).
[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82, 031802 (2010).
[CrossRef]

Miller, A.

E. Figueroa-Feliciano, B. Cabrera, A. Miller, S. Powell, T. Saab, and A. Walker, “Optimal filter analysis of energy-dependent pulse shapes and its application to TES detectors,” Nucl. Instrum. Meth. A444, 453–456 (2000).
[CrossRef]

Miller, A. J.

A. J. Miller, A. E. Lita, B. Calkins, I. Vayshenker, S. M. Gruber, and S. W. Nam, “Compact cryogenic self-aligning fiber-to-detector coupling with losses below one percent,” Opt. Express19, 9102–9110 (2011).
[CrossRef] [PubMed]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82, 031802 (2010).
[CrossRef]

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express16, 3032–3040 (2008).
[CrossRef] [PubMed]

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

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, 735–737 (1998).
[CrossRef]

Milostnaya, I.

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Minaeva, O.

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Mingolla, M. G.

G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall, M. G. Mingolla, M. G. A. Paris, F. Piacentini, and S. V. Polyakov, “Ancilla-assisted calibration of a measuring apparatus”, Phys. Rev. Lett., 108, 253601 (2012).
[CrossRef]

Mirin, R. P.

T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express19, 24434–24447 (2011).
[CrossRef] [PubMed]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82, 031802 (2010).
[CrossRef]

Mirzoyan, R.

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The crosstalk problem in sipms and their use as light sensors for imaging atmospheric cherenkov telescopes,”Nucl. Instrum. Meth. A610, 131–134 (2009).
[CrossRef]

Mitchell, M. W.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature429, 161–164 (2004).
[CrossRef] [PubMed]

Moseley, S.

D. Fixsen, S. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Meth. A520, 555–558 (2004).
[CrossRef]

Moseley, S. H.

J. A. Chervenak, E. N. Grossman, C. D. Reintsema, K. D. Irwin, S. H. Moseley, and C. A. Allen, “Sub-picowatt precision radiometry using superconducting transition edge sensor bolometers,” IEEE Trans. Appl. Supercond., 11, 593–596 (2001).
[CrossRef]

Mountford, J.

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, 735–737 (1998).
[CrossRef]

Nam, S. W.

Z. H. Levine, T. Gerrits, A. L. Migdall, D. V. Samarov, B. Calkins, A. E. Lita, and S. W. Nam, “An algorithm for finding clusters with a known distribution and its application to photon-number resolution using a superconducting transition-edge sensor,” J. Opt. Soc. Am. B29, 2066–2073 (2012).
[CrossRef]

A. J. Miller, A. E. Lita, B. Calkins, I. Vayshenker, S. M. Gruber, and S. W. Nam, “Compact cryogenic self-aligning fiber-to-detector coupling with losses below one percent,” Opt. Express19, 9102–9110 (2011).
[CrossRef] [PubMed]

T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express19, 24434–24447 (2011).
[CrossRef] [PubMed]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82, 031802 (2010).
[CrossRef]

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express16, 3032–3040 (2008).
[CrossRef] [PubMed]

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-db channel loss using superconducting single-photon detectors,” Nat. Photonics1, 343–348 (2007).
[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]

Namekata, N.

Numata, T.

Pan, D.

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Pan, J. W.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature429, 158–161 (2004).
[CrossRef] [PubMed]

Paris, M. G. A.

G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall, M. G. Mingolla, M. G. A. Paris, F. Piacentini, and S. V. Polyakov, “Ancilla-assisted calibration of a measuring apparatus”, Phys. Rev. Lett., 108, 253601 (2012).
[CrossRef]

Peacock, A.

A. G. Kozorezov, J. K. Wigmore, D. Martin, P. Verhoeve, and A. Peacock, “Electron energy down-conversion in thin superconducting films,” Phys. Rev. B75, 094513 (2007).
[CrossRef]

Piacentini, F.

G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall, M. G. Mingolla, M. G. A. Paris, F. Piacentini, and S. V. Polyakov, “Ancilla-assisted calibration of a measuring apparatus”, Phys. Rev. Lett., 108, 253601 (2012).
[CrossRef]

Polyakov, S. V.

G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall, M. G. Mingolla, M. G. A. Paris, F. Piacentini, and S. V. Polyakov, “Ancilla-assisted calibration of a measuring apparatus”, Phys. Rev. Lett., 108, 253601 (2012).
[CrossRef]

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
[CrossRef] [PubMed]

Popova, E.

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The crosstalk problem in sipms and their use as light sensors for imaging atmospheric cherenkov telescopes,”Nucl. Instrum. Meth. A610, 131–134 (2009).
[CrossRef]

Porrovecchio, G.

Powell, S.

E. Figueroa-Feliciano, B. Cabrera, A. Miller, S. Powell, T. Saab, and A. Walker, “Optimal filter analysis of energy-dependent pulse shapes and its application to TES detectors,” Nucl. Instrum. Meth. A444, 453–456 (2000).
[CrossRef]

Rarity, J. G.

P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A44, 3266–3269 (1991).
[CrossRef] [PubMed]

Rastello, M. L.

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo-Berchera, “Absolute calibration of analog detectors using stimulated parametric down conversion,” J. Mod. Optic.56, 401–404 (2009).
[CrossRef]

Reiger, E.

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Reintsema, C. D.

J. A. Chervenak, E. N. Grossman, C. D. Reintsema, K. D. Irwin, S. H. Moseley, and C. A. Allen, “Sub-picowatt precision radiometry using superconducting transition edge sensor bolometers,” IEEE Trans. Appl. Supercond., 11, 593–596 (2001).
[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, 735–737 (1998).
[CrossRef]

Ruo-Berchera, I.

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo-Berchera, “Absolute calibration of analog detectors using stimulated parametric down conversion,” J. Mod. Optic.56, 401–404 (2009).
[CrossRef]

Saab, T.

E. Figueroa-Feliciano, B. Cabrera, A. Miller, S. Powell, T. Saab, and A. Walker, “Optimal filter analysis of energy-dependent pulse shapes and its application to TES detectors,” Nucl. Instrum. Meth. A444, 453–456 (2000).
[CrossRef]

Samarov, D. V.

Sasaki, M.

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]

Seward, S. F.

P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A44, 3266–3269 (1991).
[CrossRef] [PubMed]

Sharpe, A. W.

Shields, A. J.

Smid, M.

Smid, R.

Sobolewski, R.

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Steinberg, A. M.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature429, 161–164 (2004).
[CrossRef] [PubMed]

Stevens, M. J.

Sun, X.

M. A. Krainak, G. Yanga, W. Lu, and X. Sun,“Photon-counting detectors for space-based applications” Detectors and Imaging Devices: Infrared, Focal Plane, SPIE Proc. 7780, 77801J (2010).

Sysz, W.

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Takeoka, M.

Takesue, H.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-db channel loss using superconducting single-photon detectors,” Nat. Photonics1, 343–348 (2007).
[CrossRef]

Tamaki, K.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-db channel loss using superconducting single-photon detectors,” Nat. Photonics1, 343–348 (2007).
[CrossRef]

Tapster, P. R.

P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A44, 3266–3269 (1991).
[CrossRef] [PubMed]

Teshima, M.

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The crosstalk problem in sipms and their use as light sensors for imaging atmospheric cherenkov telescopes,”Nucl. Instrum. Meth. A610, 131–134 (2009).
[CrossRef]

Theocharous, E.

Thornagel, R.

R. Klein, R. Thornagel, and G. Ulm, “From single photons to milliwatt radiant power-electron storage rings as radiation sources with a high dynamic range,” Metrologia47, R33–R40 (2010).
[CrossRef]

Tsuchida, H.

Tsujino, K.

Ulm, G.

R. Klein, R. Thornagel, and G. Ulm, “From single photons to milliwatt radiant power-electron storage rings as radiation sources with a high dynamic range,” Metrologia47, R33–R40 (2010).
[CrossRef]

Ursin, R.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature429, 158–161 (2004).
[CrossRef] [PubMed]

Vayshenker, I.

Verhoeve, P.

A. G. Kozorezov, J. K. Wigmore, D. Martin, P. Verhoeve, and A. Peacock, “Electron energy down-conversion in thin superconducting films,” Phys. Rev. B75, 094513 (2007).
[CrossRef]

Walker, A.

E. Figueroa-Feliciano, B. Cabrera, A. Miller, S. Powell, T. Saab, and A. Walker, “Optimal filter analysis of energy-dependent pulse shapes and its application to TES detectors,” Nucl. Instrum. Meth. A444, 453–456 (2000).
[CrossRef]

Walther, P.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature429, 158–161 (2004).
[CrossRef] [PubMed]

White, M. G.

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon-photon counting community,” Nucl. Instrum. Meth. A610, 183–187 (2009).
[CrossRef]

Wigmore, J. K.

A. G. Kozorezov, J. K. Wigmore, D. Martin, P. Verhoeve, and A. Peacock, “Electron energy down-conversion in thin superconducting films,” Phys. Rev. B75, 094513 (2007).
[CrossRef]

Woods, S. I.

S. I. Woods, S. M. Carr, A. C. Carter, T. M. Jung, and R. U. Datla, “Calibration of ultra-low infrared power at NIST,” SPIE Proc.7742, 77421P (2010).
[CrossRef]

Yamamoto, Y.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-db channel loss using superconducting single-photon detectors,” Nat. Photonics1, 343–348 (2007).
[CrossRef]

Yanga, G.

M. A. Krainak, G. Yanga, W. Lu, and X. Sun,“Photon-counting detectors for space-based applications” Detectors and Imaging Devices: Infrared, Focal Plane, SPIE Proc. 7780, 77801J (2010).

Yoshizawa, A.

Yuan, Z. L.

Zama, T.

Zeilinger, A.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature429, 158–161 (2004).
[CrossRef] [PubMed]

Zhang, Q.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-db channel loss using superconducting single-photon detectors,” Nat. Photonics1, 343–348 (2007).
[CrossRef]

Zijlstra, T.

Zwiller, V.

T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express19, 24434–24447 (2011).
[CrossRef] [PubMed]

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

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, 735–737 (1998).
[CrossRef]

K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” Appl. Phys. Lett.66, 1998–2000 (1995).
[CrossRef]

Cryogenic Particle Detection, Top. Appl. Phys. (1)

K. D. Irwin and G. C. Hilton, “Transition-edge sensors,” Cryogenic Particle Detection, Top. Appl. Phys.99, 63–152 (2005).

Detectors and Imaging Devices: Infrared, Focal Plane, SPIE Proc (1)

M. A. Krainak, G. Yanga, W. Lu, and X. Sun,“Photon-counting detectors for space-based applications” Detectors and Imaging Devices: Infrared, Focal Plane, SPIE Proc. 7780, 77801J (2010).

IEEE J. Sel. Topics Quantum Electron. Journal of (1)

E. Reiger, S. Dorenbos, V. Zwiller, A. Korneev, G. Chulkova, I. Milostnaya, O. Minaeva, G. Gol’tsman, J. Kitaygorsky, D. Pan, W. Sysz, A. Jukna, and R. Sobolewski, “Spectroscopy with nanostructured superconducting single photon detectors,” IEEE J. Sel. Topics Quantum Electron. Journal of13, 934 –943 (2007).
[CrossRef]

IEEE Trans. Appl. Supercond. (1)

J. A. Chervenak, E. N. Grossman, C. D. Reintsema, K. D. Irwin, S. H. Moseley, and C. A. Allen, “Sub-picowatt precision radiometry using superconducting transition edge sensor bolometers,” IEEE Trans. Appl. Supercond., 11, 593–596 (2001).
[CrossRef]

J. Appl. Phys. (1)

R. J. McIntyre, “Theory of microplasma instability in silicon,” J. Appl. Phys.32, 983–995 (1961).
[CrossRef]

J. Mod. Optic. (1)

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo-Berchera, “Absolute calibration of analog detectors using stimulated parametric down conversion,” J. Mod. Optic.56, 401–404 (2009).
[CrossRef]

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

J. Res. Natl. Inst. Stan. (1)

G. P. Eppeldauer and D. C. Lynch, “Opto-mechanical and electronic mesign of a tunnel-trap Si radiometer,” J. Res. Natl. Inst. Stan.105, 813–828 (2000).
[CrossRef]

Metrologia (1)

R. Klein, R. Thornagel, and G. Ulm, “From single photons to milliwatt radiant power-electron storage rings as radiation sources with a high dynamic range,” Metrologia47, R33–R40 (2010).
[CrossRef]

Nat. Photonics (2)

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics3, 696–705 (2009).
[CrossRef]

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-db channel loss using superconducting single-photon detectors,” Nat. Photonics1, 343–348 (2007).
[CrossRef]

Nature (2)

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature429, 158–161 (2004).
[CrossRef] [PubMed]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature429, 161–164 (2004).
[CrossRef] [PubMed]

Nucl. Instrum. Meth. A (4)

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon-photon counting community,” Nucl. Instrum. Meth. A610, 183–187 (2009).
[CrossRef]

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The crosstalk problem in sipms and their use as light sensors for imaging atmospheric cherenkov telescopes,”Nucl. Instrum. Meth. A610, 131–134 (2009).
[CrossRef]

E. Figueroa-Feliciano, B. Cabrera, A. Miller, S. Powell, T. Saab, and A. Walker, “Optimal filter analysis of energy-dependent pulse shapes and its application to TES detectors,” Nucl. Instrum. Meth. A444, 453–456 (2000).
[CrossRef]

D. Fixsen, S. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Meth. A520, 555–558 (2004).
[CrossRef]

Opt. Express (8)

T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express19, 24434–24447 (2011).
[CrossRef] [PubMed]

A. J. Miller, A. E. Lita, B. Calkins, I. Vayshenker, S. M. Gruber, and S. W. Nam, “Compact cryogenic self-aligning fiber-to-detector coupling with losses below one percent,” Opt. Express19, 9102–9110 (2011).
[CrossRef] [PubMed]

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express16, 3032–3040 (2008).
[CrossRef] [PubMed]

N. Namekata, S. Adachi, and S. Inoue, “1.5 GHz single-photon detection at telecommunication wavelengths using sinusoidally gated ingaas/inp avalanche photodiode,” Opt. Express17, 6275–6282 (2009).
[CrossRef] [PubMed]

J. Y. Cheung, C. J. Chunnilall, G. Porrovecchio, M. Smid, and E. Theocharous, “Low optical power reference detector implemented in the validation of two independent techniques for calibrating photon-counting detectors,” Opt. Express19, 20347–20363 (2011).
[CrossRef] [PubMed]

A. R. Dixon, Z. L. Yuan, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate,” Opt. Express16, 18790–18979 (2008).
[CrossRef]

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

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express18, 8107–8114 (2010).
[CrossRef] [PubMed]

Phys. Rev. A (2)

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82, 031802 (2010).
[CrossRef]

P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A44, 3266–3269 (1991).
[CrossRef] [PubMed]

Phys. Rev. B (1)

A. G. Kozorezov, J. K. Wigmore, D. Martin, P. Verhoeve, and A. Peacock, “Electron energy down-conversion in thin superconducting films,” Phys. Rev. B75, 094513 (2007).
[CrossRef]

Phys. Rev. D (1)

A. Garg and N.D. Mermin, “Detector inefficiencies in the Einstein-Podolsky-Rosen experiment,” Phys. Rev. D35, 3831–3835 (1987).
[CrossRef]

Phys. Rev. Lett. (1)

G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall, M. G. Mingolla, M. G. A. Paris, F. Piacentini, and S. V. Polyakov, “Ancilla-assisted calibration of a measuring apparatus”, Phys. Rev. Lett., 108, 253601 (2012).
[CrossRef]

Rev. Sci. Instrum. (1)

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
[CrossRef] [PubMed]

SPIE Proc. (1)

S. I. Woods, S. M. Carr, A. C. Carter, T. M. Jung, and R. U. Datla, “Calibration of ultra-low infrared power at NIST,” SPIE Proc.7742, 77421P (2010).
[CrossRef]

Other (1)

A. Lamas-Linares, T. Gerrits, N. A. Tomlin, A. Lita, B. Calkins, J. Beyer, R. Mirin, and S. W. Nam, “Transition edge sensors with low timing jitter at 1550 nm,” CLEO conference2012 http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2012-QTu3E.1

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) TES output signal time response (blue line) and fit (red line) after illumination with a coherent laser pulse with N̄ = 4.8 · 106 photons. (b) Thermal relaxation time (TRT) of the TES (crosses), as a function of mean input photon number. The numerical integration of Eq. (2) for each input mean photon number: model with cumulative heating (solid line), model with no cumulative heating (dashed line).

Fig. 2
Fig. 2

(a) Standard deviations of photon-number determinations as a function of input mean photon number. Total measured uncertainty, as determined by the matched filter analysis (red stars). Uncertainty associated with detection process, i.e. read-out plus detector, as determined by the matched filter analysis (red squares) or the fitting routine (black squares). Fit uncertainty representing a 1σ confidence interval determined from each fit to an individual response (black crosses). Input state shot noise (blue dashed line). (b)–(e). Families of raw response curves for four different input mean photon numbers N ̄ as labeled.

Fig. 3
Fig. 3

(a) Simulation of photon-number statistics for different input states. The red bars show the anticipated TES photon number response when illuminating the TES with an NF = 1, 20, and 80 Fock states. The black bars show the TES response when illuminating with a coherent state with N̄ = 1, 20, and 80. (b) Data for a heralded photon state from parametric down-conversion (PDC).

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

σ F ( η ) = N F η ( 1 η ) ,
C e ( T e ) d T e d t = κ e p ( T e 5 T p 5 ) + P J + η γ δ ( t ) P γ C p ( T p ) d T p d t = κ p b ( T p 4 T b 4 ) + κ e p ( T e 5 T p 5 ) + ( 1 η γ ) δ ( t ) P γ ,
η γ E p = T c T e ( 0 ) C e d T = T c T e ( 0 ) 𝒞 e V T d T ,
( 1 η γ ) E p = T b T p ( 0 ) C p d T = T b T p ( 0 ) 𝒞 p V T 3 d T ,
σ N ¯ = [ ¯ P N ] 1 σ P ,
σ N ¯ 2 = ( N ¯ + σ d 2 ) ,
p k = μ k k ! e μ ,
G k ( x ) = 1 σ x 2 π exp [ ( x ( k ) ) 2 2 σ x 2 ] ,
G ( x , k ) = 1 σ x 2 π k = 0 μ k k ! e μ exp [ ( x ( k ) ) 2 2 σ x 2 ] .
σ ε 2 = + [ x ¯ ] 2 G ( x , k ) d x ,
σ 2 = e μ k = 0 μ k k ! [ ( ( k ) μ 2 ) + σ x 2 ] ,
¯ = k = 0 k = p k ( k ) = e μ k = 0 k = μ k k ! ( k ) .
σ N 2 = | ¯ μ | 2 σ 2 ¯ μ = e μ k = 0 μ k 1 k ! ( k ) [ k μ ] .
σ N 2 = k = 0 μ k k ! [ ( ( k ) μ ) 2 + σ x 2 ] e μ [ k = 0 μ k 1 k ! ( k ) [ k μ ] ] 2 .
lim μ 0 σ N 2 = k = 0 μ k k ! [ ( ( k ε ) μ ) 2 + σ x 2 ] e μ [ k = 0 μ k 1 k ! ( k ε ) [ k μ ] ] 2 = ε 2 + μ + σ x 2 1 > μ + σ x 2 ,
lim μ σ N 2 = k = 0 μ k k ! [ ( C μ ) 2 + σ x 2 ] e μ [ k = 0 μ k 1 k ! C [ k μ ] ] 2 = ( C μ ) 2 + σ x 2 e μ [ k = 0 μ k 1 k ! C [ k μ ] ] 2 ,

Metrics