## Self consistent, absolute calibration technique for photon number resolving detectors |

Optics Express, Vol. 19, Issue 23, pp. 23249-23257 (2011)

http://dx.doi.org/10.1364/OE.19.023249

Acrobat PDF (813 KB)

### Abstract

Well characterized photon number resolving detectors are a requirement for many applications ranging from quantum information and quantum metrology to the foundations of quantum mechanics. This prompts the necessity for reliable calibration techniques at the single photon level. In this paper we propose an innovative absolute calibration technique for photon number resolving detectors, using a pulsed heralded photon source based on parametric down conversion. The technique, being absolute, does not require reference standards and is independent upon the performances of the heralding detector. The method provides the results of quantum efficiency for the heralded detector as a function of detected photon numbers. Furthermore, we prove its validity by performing the calibration of a Transition Edge Sensor based detector, a real photon number resolving detector that has recently demonstrated its effectiveness in various quantum information protocols.

© 2011 OSA

## 1. Introduction

1. R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nature Photon. **3**, 696–705 (2009) *and ref.s therein*. [CrossRef]

2. C. Silberhorn, “Detecting quantum light,” Contemp. Phys. **48**, 143–156 (2007) *and ref.s therein*. [CrossRef]

3. J. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and ’the candela’: evolution in the classical and quantum world,” Metrologia **47**, R15–R32 (2010). [CrossRef]

4. Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J.Opt. Soc. Am. B **27**, A170–A174 (2010). [CrossRef]

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

6. G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon. **4**, 227–230 (2010). [CrossRef]

7. T. Laenger and G. Lenhart, “Standardization of quantum key distribution and the ETSI standardization initiative ISG-QKD,” New J. Phys. **11**, 055051 (2009) *and ref.s therein*. [CrossRef]

8. J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nature Photon. **3**, 687–695 (2009) *and ref.s therein*. [CrossRef]

9. N. Gisin and R. Thew, “Quantum communication,” Nature Photon. **1**, 165–171 (2007) *and ref.s therein*. [CrossRef]

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

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

12. D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. **28**, 2387–2389 (2003). [CrossRef] [PubMed]

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

1. R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nature Photon. **3**, 696–705 (2009) *and ref.s therein*. [CrossRef]

2. C. Silberhorn, “Detecting quantum light,” Contemp. Phys. **48**, 143–156 (2007) *and ref.s therein*. [CrossRef]

14. G. Zambra, M. Bondani, A. S. Spinelli, F. Paleari, and A. Andreoni, “Counting photoelectrons in the response of a photomultiplier tube to single picosecond light pulses,” Rev. Sci. Instrum. **75**, 2762 (2004). [CrossRef]

15. M. Bondani, A. Allevi, and A. Andreoni, “Light Statistics by Non-Calibrated Linear Photodetectors,” Advanced Science Letters **2**, 463–468 (2009). [CrossRef]

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

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

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

21. A. J. Pearlman, A. Ling, E. A. Goldschmidt, C. F. Wildfeuer, J. Fan, and A. Migdall, “Enhancing image contrast using coherent states and photon number resolving detectors,” Opt. Express **18**, 6033–6039 (2010). [CrossRef] [PubMed]

22. 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. A **82**, 031802 (2010). [CrossRef]

23. 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. Express **18**, 8107–8114 (2010). [CrossRef] [PubMed]

24. A. Migdall, “Correlated-photon metrology without absolute standards,” Phys. Today **52**, 41–46 (1999) *and ref.s therein*. [CrossRef]

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

26. S. V. Polyakov and A. L. Migdall, “Quantum radiometry,” J. Mod. Opt. **56**, 1045–1052 (2009) *and ref.s therein*. [CrossRef]

27. D. C. Burnham and D. L. Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett. **25**, 84–87 (1970). [CrossRef]

28. D. N. Klyshko, “Utilization of vacuum fluctuations as an optical brightness standard,” Sov. J. Quantum Electron. **7**, 591 (1977). [CrossRef]

29. P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “Absolute efficiency and time-response measurement of single-photon detectors,” Appl. Opt. **33**, 1844–1853 (1994). [CrossRef] [PubMed]

30. E. Dauler, A. L. Migdall, N. Boeuf, R. U. Datla, A. Muller, and A. Sergienko, “Measuring absolute infrared spectral radiance with correlated photons: new arrangements for improved uncertainty and extended IR range,” Metrologia **35**, 295 (1998). [CrossRef]

31. G. Brida, S. Castelletto, I. P. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Towards an uncertainty budget in quantum-efficiency measurements with parametric fluorescence,” Metrologia **37**, 629 (2000). [CrossRef]

32. J. G. Rarity, K. D. Ridley, and P. R. Tapster, “Absolute measurement of detector quantum efficiency using parametric downconversion,” Appl. Opt. **26**, 4616–4619 (1987). [CrossRef] [PubMed]

33. S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Evaluation of statistical noise in measurements based on correlated photons,” J. Opt. Soc. Am. B **19**, 1247–1258 (2002). [CrossRef]

34. A. Ghazi-Bellouati, A. Razet, J. Bastie, M. E. Himbert, I. P. Degiovanni, S. Castelletto, and M. L. Rastello, “Radiometric reference for weak radiations: comparison of methods,” Metrologia **42**, 271 (2005). [CrossRef]

35. A. L. Migdall, S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Intercomparison of a Correlated-Photon-Based Method to Measure Detector Quantum Efficiency,” Appl. Opt. **41**, 2914–2922 (2002). [CrossRef] [PubMed]

36. S.V. Polyakov and A.L. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express **15**, 1390–1407 (2007). [CrossRef] [PubMed]

37. 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. Express (*submitted*). [PubMed]

38. G. Brida, M. Genovese, I. Ruo-Berchera, M. Chekhova, and A. Penin, “Possibility of absolute calibration of analog detectors by using parametric downconversion: a systematic study,” J. Opt. Soc. Am. B **23**, 2185–2193 (2006). [CrossRef]

39. G. Brida, M. Chekhova, M. Genovese, and I. Ruo-Berchera, “Analysis of the possibility of analog detectors calibration by exploiting stimulated parametric down conversion,” Opt. Express **16**, 12550–12558 (2008). [CrossRef] [PubMed]

40. G. Brida, I. P. Degiovanni, M. Genovese, M. L. Rastello, and I. Ruo Berchera, “Detection of multimode spatial correlation in PDC and application to the absolute calibration of a CCD camera,” Opt. Express **18**, 20572–20584 (2010). [CrossRef] [PubMed]

41. A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express **17**, 4397–4411 (2009). [CrossRef] [PubMed]

^{3}[36

36. S.V. Polyakov and A.L. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express **15**, 1390–1407 (2007). [CrossRef] [PubMed]

37. 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. Express (*submitted*). [PubMed]

41. A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express **17**, 4397–4411 (2009). [CrossRef] [PubMed]

42. 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. Express **19**, 870–875 (2011). [CrossRef] [PubMed]

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

## 2. Our method

*i*photons per heralding count in the presence and in the absence of the heralded photon,

*P*(

*i*) and 𝒫(

*i*) respectively. Furthermore, we account for the presence of false heralding counts due to stray light and dark counts. As

*ξ*is the probability of having a true heralding count (i.e. not due to stray light and dark counts), the probability of observing no photons on the PNR detector is the sum of the probability of non-detection of the heralded photons multiplied by the probability of having no accidental counts in the presence of a true heralding count and the probability of having no accidental counts in the presence of a heralding count due to stray light or dark counts: hereafter

*γ*is the TES “total” quantum efficiency, i.e.

*γ*=

*τη*where

*τ*is the optical and coupling losses from the crystal to the fibre end ((a) in Fig. 1), and

*η*is the quantum efficiency of the TES detector. According to Fig. 1, we consider the TES detector as the system from the fibre end (b) to the sensitive area, since this represents the real detector for applications. This means that

*η*accounts also for the losses of the fibre in the fridge and the geometrical coupling of the light from the fibre to the TES sensitive area.

*i*counts is with i=1,2,..., i.e. the sum of the joint probability of non-detection of the heralded photons and the probability of having

*i*accidental counts, and the joint probability of detection of the heralded photons and the probability of having

*i*– 1 accidental counts both in the presence of a true heralding count, and the probability of having

*i*accidental counts in the presence of a heralding count due to stray light or dark counts.

*i*we obtain an estimation for

*γ*allowing a test of consistency for the estimation model.

## 3. Method implementation and discussion

45. C. Portesi, E. Taralli, R. Rocci, M. Rajteri, and E. Monticone, “Fabrication of Au/Ti TESs for Optical Photon Counting,” J. Low Temp. Phys. **151**, 261–265 (2008). [CrossRef]

46. E. Taralli, C. Portesi, L. Lolli, E. Monticone, M. Rajteri, I. Novikov, and J. Beyer, “Impedance measurements on a fast transition-edge sensor for optical and near-infrared range,” Supercond. Sci. Technol. **23**, 105012 (2010). [CrossRef]

*T*=121 mK with Δ

_{c}*T*=2 mK. It is voltage biased [47] and mounted inside a dilution refrigerator at a bath temperature of 40 mK. The TES active area is 20

_{c}*μ*m x 20

*μ*m and is illuminated with a single mode, 9.5

*μ*m core, optical fibre. The fibre is aligned on the TES using a stereomicroscope [48

48. L. Lolli, E. Taralli, C. Portesi, D. Alberto, M. Rajteri, and E. Monticone, “Ti/Au Transition-Edge Sensors Coupled to Single Mode Optical Fibers Aligned by Si V-Groove,” IEEE Trans. Appl. Supercond. **21**215–218 (2011). [CrossRef]

*μ*m. The read out is based on a dc-SQUID array [49

49. D. Drung, C. Assmann, J. Beyer, A. Kirste, M. Peters, F. Ruede, and T. Schurig, “Highly Sensitive and Easy-to-Use SQUID Sensors,” IEEE Trans. Appl. Supercond. **17**, 699–704 (2007). [CrossRef]

*E*=0.4 eV (64 zJ), with a response time of 10.4

_{FWHM}*μ*s [48

48. L. Lolli, E. Taralli, C. Portesi, D. Alberto, M. Rajteri, and E. Monticone, “Ti/Au Transition-Edge Sensors Coupled to Single Mode Optical Fibers Aligned by Si V-Groove,” IEEE Trans. Appl. Supercond. **21**215–218 (2011). [CrossRef]

24. A. Migdall, “Correlated-photon metrology without absolute standards,” Phys. Today **52**, 41–46 (1999) *and ref.s therein*. [CrossRef]

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

26. S. V. Polyakov and A. L. Migdall, “Quantum radiometry,” J. Mod. Opt. **56**, 1045–1052 (2009) *and ref.s therein*. [CrossRef]

24. A. Migdall, “Correlated-photon metrology without absolute standards,” Phys. Today **52**, 41–46 (1999) *and ref.s therein*. [CrossRef]

37. 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. Express (*submitted*). [PubMed]

50. S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Theoretical aspects of photon number measurement,” Metrologia **37**, 613–616 (2000). [CrossRef]

*P*(

*i*) and 𝒫(

*i*) in terms of events

*C*(

*i*) and 𝒞(

*i*) counted by the TES. In particular

*C*(

*i*) (𝒞(

*i*)) is the number of events observed by the TES counting

*i*photons in the presence (absence) of the heralding photon, where

*P*(

*i*) =

*C*(

*i*)/Σ

*(*

_{i}C*i*) and 𝒫(

*i*) = 𝒞(

*i*)/Σ

*𝒞(*

_{i}*i*).

*A*, the centres

_{i}*x*and the widths

_{i}*σ*of the Gaussian curves. The agreement between the experimental data and the fitting is excellent, as stated from the ratio between the reduced

_{i}*χ*-square value and the reduced total sum of square that is lower than 10

^{−4}. The integrals of the gaussian curves fitted to the histogram peaks provide an estimate for the parameters

*C*(

*i*) and 𝒞(

*i*). The probability of having true heralding counts

*ξ*= 0.98793 ± 0.00007 is obtained as

*ξ*= 1 –

*n*/

_{OFF}*n*, where

_{ON}*n*and

_{ON}*n*are the number of events triggered by the laser pulses and counted by DET1 in the presence and in the absence of PDC emission, respectively. They correspond in one case to true heralded counts, or stray light and dark counts, while in the other case only to stray light and dark counts and they are obtained by means of pump polarization rotation. The PDC extinction provided by the pump polarization rotation was almost perfect at our pump regime.The measured value for stray light and dark counts on DET1, are compatible with the values measured with the pump laser blocked before the crystal. The uncertainty on

_{OFF}*ξ*is evaluated by standard uncertainty propagation on the measured counts in the presence and in the absence of PDC.

*γ*

_{0}= (0.709 ± 0.003)%,

*γ*

_{1}= (0.709 ± 0.003)%, and

*γ*

_{2}= (0.65 ± 0.05)%. In Table 1 can be found the full analysis of the uncertainty contributions [51]. All the uncertainties are given with coverage factor

*k*= 1, obtained from six repeated measurements, each measurement being five hours long, corresponding to approximately 11 × 10

^{6}heralding counts. The system was very stable during this long run of measurements. We note that the large uncertainty (derived from standard uncertainty propagation) in the estimation of

*γ*

_{2}is essentially due to the poor statistics. For the same reason, i.e. negligible amount of counted events, it was impossible to obtain estimates of

*γ*for

*i*> 2. Nevertheless, within its large uncertainty

*γ*

_{2}is compatible with

*γ*

_{0}and

*γ*

_{1}estimates, which are themselves within very good agreement. This is consistent with the fact that

*γ*

_{0}=

*γ*

_{1}=

*γ*

_{2}is expected, since the TES detector has been recently proved to be a linear detector [52

52. G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, L. Lolli, M. G. Mingolla, F. Piacentini, M. Rajteri, E. Taralli, and M. G. A. Paris, “Full quantum characterization of superconducting photon counters,” http://arxiv.org/pdf/1103.2991.

1. R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nature Photon. **3**, 696–705 (2009) *and ref.s therein*. [CrossRef]

2. C. Silberhorn, “Detecting quantum light,” Contemp. Phys. **48**, 143–156 (2007) *and ref.s therein*. [CrossRef]

28. D. N. Klyshko, “Utilization of vacuum fluctuations as an optical brightness standard,” Sov. J. Quantum Electron. **7**, 591 (1977). [CrossRef]

36. S.V. Polyakov and A.L. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express **15**, 1390–1407 (2007). [CrossRef] [PubMed]

*submitted*). [PubMed]

*γ*’s we evaluate the “total” efficiency in the case of the Klyshko’s technique, obtaining

_{i}*γ*= (0.707 ± 0.003)%. The result is in perfect agreement with that obtained from the proposed new technique as implemented in the work reported here.

_{Klyshko}*γ*, instead of

*η*, allows us a better comparison between the results obtained from the two techniques, as the additional independent measurement of

*τ*is common to the two techniques. For this reason, in the context of the comparison, it only provides an additional and somewhat misleading common uncertainty contribution [53

53. Incidentally, if one wants to provide a precise estimate of the naked TES based detector quantum efficiency *η* it is necessary a careful estimation of the optical transmittance *τ*, accounting for the coupling efficiency in the optical fiber and the optical losses in the non-linear crystal. According to the results of Ref.s [S.V. Polyakov, A.L. Migdall, Opt. Express **15**, 1390 (2007); J. Y. Cheung *et al*., Appl. Opt. (*submitted*)], one could provide an estimate of this parameter with a less than 1% uncertainty.

42. 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. Express **19**, 870–875 (2011). [CrossRef] [PubMed]

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

*τ*is estimated to be 10%. The geometrical and optical losses inside the refrigerator contribute to lower the value of

*η*to 7%.

## 4. Conclusions

^{−3}, that does not rely on reference standards. Considering the importance of PNR detectors in advancing quantum technologies, this result represents an important step in their precise characterisation, paving the way to metrological applications of this absolute method.

## Acknowledgments

## References and links

1. | R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nature Photon. |

2. | C. Silberhorn, “Detecting quantum light,” Contemp. Phys. |

3. | J. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and ’the candela’: evolution in the classical and quantum world,” Metrologia |

4. | Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J.Opt. Soc. Am. B |

5. | M. Genovese, “Research on hidden variable theories: A review of recent progresses,” Phys. Rep. |

6. | G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon. |

7. | T. Laenger and G. Lenhart, “Standardization of quantum key distribution and the ETSI standardization initiative ISG-QKD,” New J. Phys. |

8. | J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nature Photon. |

9. | N. Gisin and R. Thew, “Quantum communication,” Nature Photon. |

10. | L. A. Jiang, E. A. Dauler, and J. T. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A |

11. | A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nature Photon. |

12. | D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. |

13. | M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A |

14. | G. Zambra, M. Bondani, A. S. Spinelli, F. Paleari, and A. Andreoni, “Counting photoelectrons in the response of a photomultiplier tube to single picosecond light pulses,” Rev. Sci. Instrum. |

15. | M. Bondani, A. Allevi, and A. Andreoni, “Light Statistics by Non-Calibrated Linear Photodetectors,” Advanced Science Letters |

16. | G. A. Morton, RCA Rev. |

17. | M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B |

18. | J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. , |

19. | E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron |

20. | K. D. Irwin and G. C. Hilton, “Transition-Edge Sensors,” in |

21. | A. J. Pearlman, A. Ling, E. A. Goldschmidt, C. F. Wildfeuer, J. Fan, and A. Migdall, “Enhancing image contrast using coherent states and photon number resolving detectors,” Opt. Express |

22. | 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. A |

23. | 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. Express |

24. | A. Migdall, “Correlated-photon metrology without absolute standards,” Phys. Today |

25. | G. Brida, M. Genovese, and M. Gramegna, “Twin-photon techniques for photo-detector calibration,” Laser Physics Lett. |

26. | S. V. Polyakov and A. L. Migdall, “Quantum radiometry,” J. Mod. Opt. |

27. | D. C. Burnham and D. L. Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett. |

28. | D. N. Klyshko, “Utilization of vacuum fluctuations as an optical brightness standard,” Sov. J. Quantum Electron. |

29. | P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “Absolute efficiency and time-response measurement of single-photon detectors,” Appl. Opt. |

30. | E. Dauler, A. L. Migdall, N. Boeuf, R. U. Datla, A. Muller, and A. Sergienko, “Measuring absolute infrared spectral radiance with correlated photons: new arrangements for improved uncertainty and extended IR range,” Metrologia |

31. | G. Brida, S. Castelletto, I. P. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Towards an uncertainty budget in quantum-efficiency measurements with parametric fluorescence,” Metrologia |

32. | J. G. Rarity, K. D. Ridley, and P. R. Tapster, “Absolute measurement of detector quantum efficiency using parametric downconversion,” Appl. Opt. |

33. | S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Evaluation of statistical noise in measurements based on correlated photons,” J. Opt. Soc. Am. B |

34. | A. Ghazi-Bellouati, A. Razet, J. Bastie, M. E. Himbert, I. P. Degiovanni, S. Castelletto, and M. L. Rastello, “Radiometric reference for weak radiations: comparison of methods,” Metrologia |

35. | A. L. Migdall, S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Intercomparison of a Correlated-Photon-Based Method to Measure Detector Quantum Efficiency,” Appl. Opt. |

36. | S.V. Polyakov and A.L. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express |

37. | 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. Express ( |

38. | G. Brida, M. Genovese, I. Ruo-Berchera, M. Chekhova, and A. Penin, “Possibility of absolute calibration of analog detectors by using parametric downconversion: a systematic study,” J. Opt. Soc. Am. B |

39. | G. Brida, M. Chekhova, M. Genovese, and I. Ruo-Berchera, “Analysis of the possibility of analog detectors calibration by exploiting stimulated parametric down conversion,” Opt. Express |

40. | G. Brida, I. P. Degiovanni, M. Genovese, M. L. Rastello, and I. Ruo Berchera, “Detection of multimode spatial correlation in PDC and application to the absolute calibration of a CCD camera,” Opt. Express |

41. | A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express |

42. | 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. Express |

43. | A.E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express |

44. | A. C. Parr, R. U. Datla, and J. L. Gardner, |

45. | C. Portesi, E. Taralli, R. Rocci, M. Rajteri, and E. Monticone, “Fabrication of Au/Ti TESs for Optical Photon Counting,” J. Low Temp. Phys. |

46. | E. Taralli, C. Portesi, L. Lolli, E. Monticone, M. Rajteri, I. Novikov, and J. Beyer, “Impedance measurements on a fast transition-edge sensor for optical and near-infrared range,” Supercond. Sci. Technol. |

47. | K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” |

48. | L. Lolli, E. Taralli, C. Portesi, D. Alberto, M. Rajteri, and E. Monticone, “Ti/Au Transition-Edge Sensors Coupled to Single Mode Optical Fibers Aligned by Si V-Groove,” IEEE Trans. Appl. Supercond. |

49. | D. Drung, C. Assmann, J. Beyer, A. Kirste, M. Peters, F. Ruede, and T. Schurig, “Highly Sensitive and Easy-to-Use SQUID Sensors,” IEEE Trans. Appl. Supercond. |

50. | S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Theoretical aspects of photon number measurement,” Metrologia |

51. | Guide to the Expression of Uncertainty in Measurement, ISO (1995). |

52. | G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, L. Lolli, M. G. Mingolla, F. Piacentini, M. Rajteri, E. Taralli, and M. G. A. Paris, “Full quantum characterization of superconducting photon counters,” http://arxiv.org/pdf/1103.2991. |

53. | Incidentally, if one wants to provide a precise estimate of the naked TES based detector quantum efficiency |

**OCIS Codes**

(030.5260) Coherence and statistical optics : Photon counting

(030.5630) Coherence and statistical optics : Radiometry

(270.5570) Quantum optics : Quantum detectors

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: July 29, 2011

Revised Manuscript: August 31, 2011

Manuscript Accepted: September 6, 2011

Published: November 1, 2011

**Citation**

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, "Self consistent, absolute calibration technique for photon number resolving detectors," Opt. Express **19**, 23249-23257 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-23249

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- Incidentally, if one wants to provide a precise estimate of the naked TES based detector quantum efficiency η it is necessary a careful estimation of the optical transmittance τ, accounting for the coupling efficiency in the optical fiber and the optical losses in the non-linear crystal. According to the results of Ref.s [S.V. Polyakov, A.L. Migdall, Opt. Express 15, 1390 (2007); J. Y. Cheung et al., Appl. Opt. (submitted)], one could provide an estimate of this parameter with a less than 1% uncertainty.

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