## Counting near-infrared single-photons with 95% efficiency

Optics Express, Vol. 16, Issue 5, pp. 3032-3040 (2008)

http://dx.doi.org/10.1364/OE.16.003032

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### Abstract

Single-photon detectors operating at visible and near-infrared wavelengths with high detection efficiency and low noise are a requirement for many quantum-information applications. Superconducting transition-edge sensors (TESs) are capable of detecting visible and near-infrared light at the single-photon level and are capable of discriminating between one-and two-photon absorption events; however these capabilities place stringent design requirements on the TES heat capacity, thermometry, and optical detection efficiency. We describe the fabrication and evaluation of a fiber-coupled, photon-number-resolving TES detector optimized for absorption at 1550 and 1310 nm wavelengths. The measured system detection efficiency at 1556 nm is 95 %±2 %, which to our knowledge is the highest system detection efficiency reported for a near-infrared single-photon detector.Work of US government: not subject to US copyright

© 2008 Optical Society of America

## 1. Introduction

*T*

_{c}) in the ~100 mK range and the relative weak coupling between its electron and phonon systems at these temperatures [8

8. 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]

## 2. Device fabrication

9. A. J. Miller, S. 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]

10. D. Rosenberg, A. E. Lita, A. J. Miller, and S. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys Rev. A **71**, 061803 (2005). [CrossRef]

^{2}and are approximately 20 nm thick with

*T*=178±5 mK. These sensors have superconducting transition temperature higher than those for the previous generation, which enables thermal recovery times to be less than 1 µs while maintaining excellent number discrimination between multiphoton events.

_{c}*in situ*, which was found to enhance and stabilize the tungsten

*T*

_{c}against thermal-stress-induced suppression. These stresses arise from the differences in coefficients of thermal expansion of the various dielectric and metallic layers used in the design [11

11. A. E. Lita, D. Rosenberg, S. Nam, A. J. Miller, D. Balzar, L. M. Kaatz, and R. E. Schwall, “Tuning of tungsten thin film superconducting transition temperature for fabrication of photon number resolving detectors,” IEEE Trans. Appl. Supercond. **15**, 3528–3531 (2005). [CrossRef]

## 3. Device packaging/alignment

12. R. Ohba, I. Uehira, and S. Kakuma, “Interferometric determination of a static optical path difference using a frequency swept laser diode,” Meas. Sci. Technol. **1**, 500–504 (1990). [CrossRef]

*d*≅λ

^{2}/2Δλ, where λ is the average wavelength over the scan and Δλ is the fringe spacing. Using this method and knowing how much d shrinks due to thermal contraction of detector package, we can position the fiber to within 10 µm of the device surface when at cryogenic temperatures.

## 4. Device performance

### 4.1 Measurement setup

*T*~178 mK). The stability of the voltage bias is due to negative electro-thermal feedback (ETF) [13

_{c}13. K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” Appl. Phys. Lett. **66**, 1998–2000 (1995). [CrossRef]

*ΔI*) by the bias voltage (

*V*

_{bias}) :

*E*=

*V*

_{bias}∫Δ

*I*(

*t*)

*dt*.

*I*) shunted through a small resistor (

_{bias}*R*~20 mΩ) at 4 K, in parallel with the TES. The detector current is amplified by a low-noise cryogenic preamp consisting of a 100-element series array of dc-superconducting quantum interference device (SQUID) amplifiers [14

_{s}14. M. E. Huber, A. M. Corey, K. L. Lumpkins, F. N. Nafe, J. O. Rantschler, G. C. Hilton, J. M. Martinis, and A. H. Steinbach, “DC SQUID series arrays with intracoil damping to reduce resonance distortions,” Applied Superconductivity **5**, 425 (1998). [CrossRef]

### 4.2 I-V Characteristics

### 4.3 Device energy resolution

8. 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]

*C*=γ

*T*with γ=1.3 mJ/(mole-K

^{2}) and is then multiplied by 2.43, the factor from the Bardeen-Cooper-Schrieffer (BCS) theory, corresponding to the increase in heat capacity of a superconductor just below

*T*

_{c}. We obtain

*C*=0.74 fJ/K for our detector volume of 25 µm×25 µm×20 nm. From Fig. 4(b) we extract the quiescent power as

*P*

_{0}=1600 fW. For substrate temperatures well below

*T*

_{c}we can estimate the thermal conductances using the formula

*g*=

*dP*/

*dT*~

*nP*

_{0}/

*T*

_{c}, where

*n*is the power law dependence of the thermal conductance between the electron system and the substrate (

*n*=5 for electron-phonon limited conductance [8

8. 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]

*g*=56 pW/K for our system. Consequently, the intrinsic time constant τ

_{0}=

*C*/

*g*, is 13 µs. The actual time constants we measure are smaller due to ETF and relate to the intrinsic time constants through τ

_{ETF}=τ

_{0}/(1+

*α*/

*n*), where

*α*=

*d*ln

*R*/

*d*ln

*T*|

_{V=constant}and describes the sharpness of the superconducting transition [13

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

*α*~60. The theoretical energy resolution limit is given by

*α, C, n*=5, and measured

*T*

_{c}’s, we can calculate the best achievable energy resolution. Finally, taking into account that only ~0.4 fraction of the initial photoelectron energy is captured by the tungsten electron system [8

**73**, 735–737 (1998). [CrossRef]

*σ*). For our pulsed laser, we expect the probability of producing an

_{E}*n*-photon state as given by the Poisson distribution

*P*(

*n*)=(

*µ*/

^{n}*n*!)

*e*

^{-µ}, where

*µ*=<

*n*> is the mean number of photons per pulse. For our measurement, we expect the data to show this Poisson distribution, but with the mean number of absorbed photons per pulse reduced by multiplying by the system efficiency. A multi-peak fit to the data gives a value of

*µ*=2.449±0.002 (statistical error) for the average photon number and

*σ*=0.29 eV as the measured energy resolution (as the full width half maximum (FWHM) of histograms of pulse heights). The difference between the expected energy resolution and the measured resolution is due to noise from our electronics and possibly excess noise in the sensors [15

_{E}15. J. N. Ullom, W. B. Doriese, G. C. Hilton, J. A. Beall, S. Deiker, W. D. Duncan, L. Ferreira, K. D. Irwin, C. D. Reintsema, and L. R. Vale, “Characterization and reduction of unexplained noise in superconducting transition-edge sensors, “Appl. Phys. Lett. **84**, 4206–4208 (2004). [CrossRef]

10. D. Rosenberg, A. E. Lita, A. J. Miller, and S. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys Rev. A **71**, 061803 (2005). [CrossRef]

### 4.4 System detection efficiency at 1556 nm

10. D. Rosenberg, A. E. Lita, A. J. Miller, and S. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys Rev. A **71**, 061803 (2005). [CrossRef]

16. A. J. Miller, A. E. Lita, D. Rosenberg, S. Gruber, and S. Nam, “Superconducting photon number resolving detectors: performance and promise,” Proceedings of the 8th International Conference on Quantum Communication, Measurement and Computing, J. O. Hirota, H. Shapiro, and M. Sasaki, Eds., NICT Press, 445–450, (2007). [PubMed]

*not*detect a photon to estimate the fraction of time

*f*(

*n*=0) we observed no photons. Assuming a Poisson distribution to the photon number,

*f*(

*n*=0) will be equal to

*P*(

*n*=0)=

*e*

^{-µ}, and therefore, the average number of photons detected per pulse is given by -

*ln f*(

*n*=

*0*).

## 5. Conclusion

## Acknowledgments

## References and links

1. | A. L. Migdal, D. Branning, and S. Castelletto, “Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source,” Phys. Rev. A |

2. | D. Bouwmeester, “Quantum physics - high noon for photons,” Nature |

3. | E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature |

4. | P. A. Hiskett, D. Rosenberg, C. G. Peterson, R. J. Hughes, S. Nam, A. E. Lita, A. J. Miller, and J. E. Nordholt, “Long distance quantum key distribution in optical fibre,” New J. Phys. |

5. | A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67, 661–663 (1991), C.H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992). [CrossRef] [PubMed] |

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

7. | D. Rosenberg, S. Nam, A. J. Miller, A. Salminen, E. Grossman, R. E. Schwall, and J. M. Martinis, “Near-unity absorption of near-infrared light in tungsten films,” Nucl. Instrum. Methods Phys. Res. A |

8. | 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. |

9. | A. J. Miller, S. Nam, J. M. Martinis, and A. V. Sergienko, “Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination,” Appl. Phys. Lett. , |

10. | D. Rosenberg, A. E. Lita, A. J. Miller, and S. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys Rev. A |

11. | A. E. Lita, D. Rosenberg, S. Nam, A. J. Miller, D. Balzar, L. M. Kaatz, and R. E. Schwall, “Tuning of tungsten thin film superconducting transition temperature for fabrication of photon number resolving detectors,” IEEE Trans. Appl. Supercond. |

12. | R. Ohba, I. Uehira, and S. Kakuma, “Interferometric determination of a static optical path difference using a frequency swept laser diode,” Meas. Sci. Technol. |

13. | K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” Appl. Phys. Lett. |

14. | M. E. Huber, A. M. Corey, K. L. Lumpkins, F. N. Nafe, J. O. Rantschler, G. C. Hilton, J. M. Martinis, and A. H. Steinbach, “DC SQUID series arrays with intracoil damping to reduce resonance distortions,” Applied Superconductivity |

15. | J. N. Ullom, W. B. Doriese, G. C. Hilton, J. A. Beall, S. Deiker, W. D. Duncan, L. Ferreira, K. D. Irwin, C. D. Reintsema, and L. R. Vale, “Characterization and reduction of unexplained noise in superconducting transition-edge sensors, “Appl. Phys. Lett. |

16. | A. J. Miller, A. E. Lita, D. Rosenberg, S. Gruber, and S. Nam, “Superconducting photon number resolving detectors: performance and promise,” Proceedings of the 8th International Conference on Quantum Communication, Measurement and Computing, J. O. Hirota, H. Shapiro, and M. Sasaki, Eds., NICT Press, 445–450, (2007). [PubMed] |

**OCIS Codes**

(220.0220) Optical design and fabrication : Optical design and fabrication

(270.5570) Quantum optics : Quantum detectors

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: January 2, 2008

Revised Manuscript: February 14, 2008

Manuscript Accepted: February 16, 2008

Published: February 20, 2008

**Citation**

Adriana E. Lita, Aaron J. Miller, and Sae Woo Nam, "Counting near-infrared single-photons with 95% efficiency," Opt. Express **16**, 3032-3040 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-5-3032

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### References

- A. L. Migdal, D. Branning, and S. Castelletto, "Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source," Phys. Rev. A 66, 053805 (2002). [CrossRef]
- D. Bouwmeester, "Quantum physics - high noon for photons," Nature 429, 139-141 (2004). [CrossRef] [PubMed]
- E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001). [CrossRef] [PubMed]
- P. A. Hiskett D. Rosenberg, C. G. Peterson, R. J. Hughes, S. Nam, A. E. Lita, A. J. Miller and J. E. Nordholt, "Long distance quantum key distribution in optical fibre," New J. Phys. 8, 193 (2006). [CrossRef]
- A. K. Ekert, "Quantum cryptography based on Bell’s theorem, " Phys. Rev. Lett. 67, 661-663 (1991), C.H. Bennett, G. Brassard, and N. D. Mermin, "Quantum cryptography without Bell’s theorem," Phys. Rev. Lett. 68, 557-559 (1992). [CrossRef] [PubMed]
- 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]
- D. Rosenberg, S. Nam, A. J. Miller, A. Salminen, E. Grossman, R. E. Schwall, and J. M. Martinis, "Near-unity absorption of near-infrared light in tungsten films," Nucl. Instrum. Methods Phys. Res. A 520, 537-540, (2004). [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]
- A. J. Miller, S. 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]
- D. Rosenberg, A. E. Lita, A. J. Miller and S. Nam, "Noise-free high-efficiency photon-number-resolving detectors," Phys Rev. A 71, 061803 (2005). [CrossRef]
- A. E. Lita, D. Rosenberg, S. Nam, A. J. Miller, D. Balzar, L. M. Kaatz, and R. E. Schwall, "Tuning of tungsten thin film superconducting transition temperature for fabrication of photon number resolving detectors," IEEE Trans. Appl. Supercond. 15, 3528-3531 (2005). [CrossRef]
- R. Ohba, I. Uehira and S. Kakuma, "Interferometric determination of a static optical path difference using a frequency swept laser diode," Meas. Sci. Technol. 1, 500-504 (1990). [CrossRef]
- K. D. Irwin, "An application of electrothermal feedback for high resolution cryogenic particle detection," Appl. Phys. Lett. 66, 1998-2000 (1995). [CrossRef]
- M. E. Huber, A. M. Corey, K. L. Lumpkins, F. N. Nafe, J. O. Rantschler, G. C. Hilton, J. M. Martinis, and A. H. Steinbach, "DC SQUID series arrays with intracoil damping to reduce resonance distortions," Appl. Supercond. 5, 425 (1998) [CrossRef]
- J. N. Ullom, W. B. Doriese, G. C. Hilton, J. A. Beall, S. Deiker, W. D. Duncan, L. Ferreira, K. D. Irwin, C. D. Reintsema, and L. R. Vale, "Characterization and reduction of unexplained noise in superconducting transition-edge sensors, "Appl. Phys. Lett. 84, 4206-4208 (2004). [CrossRef]
- A. J. Miller, A. E. Lita, D. Rosenberg, S. Gruber, and S. Nam, "Superconducting photon number resolving detectors: performance and promise," Proceedings of the 8th International Conference on Quantum Communication, Measurement and Computing, J. O. Hirota, H. Shapiro and M. Sasaki, Eds., NICT Press, 445-450, (2007). [PubMed]

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