## Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime |

Optics Express, Vol. 20, Issue 21, pp. 23798-23810 (2012)

http://dx.doi.org/10.1364/OE.20.023798

Acrobat PDF (1614 KB)

### 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 · 10^{6} 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

## 1. Introduction

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. Photonics **1**, 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. A **82**, 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 of **13**, 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. Express **17**, 6275–6282 (2009). [CrossRef] [PubMed]

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,” Nature **429**, 158–161 (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. Express **18**, 8107–8114 (2010). [CrossRef] [PubMed]

12. A. Garg and N.D. Mermin, “Detector inefficiencies in the Einstein-Podolsky-Rosen experiment,” Phys. Rev. D **35**, 3831–3835 (1987). [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,” Metrologia **47**, 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. Express **19**, 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. Express **16**, 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. Express **19**, 870–875 (2011). [CrossRef] [PubMed]

^{6}photons per pulse (or 10

^{9}photons/s in our case). This latter characteristic may be particularly advantageous as a radiometric tool for bridging the gap from single-photon sensitivity to picowatt-levels that analog detectors can detect.

22. R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics **3**, 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. A **610**, 131–134 (2009). [CrossRef]

22. R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics **3**, 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]

22. R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics **3**, 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]

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. Express **16**, 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. B **75**, 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 conference2012http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2012-QTu3E.1

## 2. Calibration of Single-Photon Detectors

*N*̄) in some measurement time and comparing it to the output of the photon-counting detector when illuminated by that attenuated source [30

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. Express **19**, 9102–9110 (2011). [CrossRef] [PubMed]

*σ*

_{Coh}), in this case a coherent laser beam, which obeys Poisson statistics and scales as

*i.e.*Fock states, as Fock states are not subject to shot or other noises. A measurement of a detector made with Fock state illumination would have only the shot noise uncertainty associated with the detection efficiency of the device (and, of course, any other uncertainties associated with the detector itself). The spread of the photon number distribution for an

*N*

_{F}-Fock state is limited only by the detection inefficiency and is given by the variation of the binomial distribution: where

*η*is the overall detection efficiency and

*N*

_{F}is the number of photons present in the Fock state. (Related examples of employing nonclassical states produced via parametric downconversion for sub-shot noise measurement of transmittance have been implemented [31

31. P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A **44**, 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]

## 3. Modeling transition edge sensor response

*C*

_{e}(

*T*

_{e}) and

*C*

_{p}(

*T*

_{p}) are the temperature-dependent heat capacities of the electron and phonon systems.

*T*

_{e},

*T*

_{p}, and

*T*

_{b}are the electron, phonon and thermal bath temperatures, respectively and

*δ*(

*t*) is the Dirac delta function.

*κ*

_{e−p}and

*κ*

_{p−b}are the thermal coupling parameters for the electron-phonon and phonon-bath thermal links.

*P*

_{J}is the joule heating power due to the TES voltage bias:

*V*

_{b}is the bias voltage and

*R*(

*T*) is the temperature-dependent TES resistance [34

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

*δ*(

*t*)

*P*is the absorbed optical power incident at the TES at initial time

_{γ}*t*= 0, and

*η*is the fraction of the optical energy remaining in the electron system after the optical pulse is absorbed and 1 −

_{γ}*η*is the fraction of the optical energy lost to the phonon system. We assume the light’s absorption and the subsequent energy loss to the phonon system happens instantaneously. Therefore, the initial electron temperature,

_{γ}*T*

_{e}(0), can be calculated by the amount of photon energy absorbed by the sensor

*E*

_{p}=

*ηN*̄

*h*̄

*ω*=

*N*̄

_{a}

*h*̄

*ω*= ∫

*δ*(

*t*

_{0})

*P*and the portion of that energy absorbed and retained by the electron system: where

_{γ}dt*N*̄

*is the absorbed mean photon number per pulse, 𝒞*

_{a}_{e}·

*T*is the volumetric electronic heat capacity,

*V*is the sensor volume and

*T*

_{c}is the sensor’s critical temperature. Similarly we can calculate the initial heat-up of the phonon system: where 𝒞

_{p}·

*T*

^{3}is the volumetric phonon heat capacity. Note that because of the large range of temperatures involved, we have to take into account the temperature dependencies of the heat capacities.

## 4. Experimental setup

*μ*m ×25

*μ*m×20 nm tungsten film with a superconducting transition temperature of 140 mK. The TES was embedded in a stack of dielectrics and had an overall detection efficiency of 89 ± 1.5 % at 1550 nm [30

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. Express **19**, 9102–9110 (2011). [CrossRef] [PubMed]

*μ*m thick silicon substrate. We mounted the TES inside a commercial adiabatic demagnetization refrigerator (ADR) and used a commercial telecom fiber to couple the light pulses from the attenuated laser at room temperature to the detector inside the ADR. The cold stage of the ADR was held at a regulated temperature of 90 ± 1 mK. Voltage biasing of the TES ensured that the sensor was biased in the transition region at

*T*

_{c}≈ 140 mK before the arrival of each light pulse. We delivered bright light pulses using a pulsed coherent laser source at a wavelength of 1550 nm at a repetition rate of 1 kHz. Determination of the laser pulse energy (in terms of the mean photon number per pulse,

*N*̄) was achieved by comparison to a calibrated detector as described in Ref. [30

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. Express **19**, 9102–9110 (2011). [CrossRef] [PubMed]

## 5. Results

*N*̄. We found that fitting the data to our simple model works well for

*N*̄ > 60. The crosses in Fig. 1(b) show the mean of the TRTs obtained from the fits as a function of

*N*̄. A strong dependence of the TRT with

*N*̄ is observed up to

*N*̄ ≈ 1000 photons. The subsequent flatter region is due to the strong initial heating of the electron system when absorbing brighter laser pulses. By examining Eq. (2), and noting that initially the electron temperature is much greater than the phonon temperature, one finds that the

*N*̄ is smaller than for low laser pulse energies. This can also be found by numerically integrating Eq. (2), shown by the solid line in Fig. 1(b). The simulation fits our data well and yields the following parameters:

*κ*

_{e−p}= 9.3 nWK

^{−5};

*κ*

_{p−b}= 150 nWK

^{−4}; 𝒞

_{e}= 123 Jm

^{−3}K

^{−2}; 𝒞

_{p}= 4.0 Jm

^{−3}K

^{−4};

*η*= 0.61. The upturn of the TRT dependence at very high input mean photon numbers (

_{γ}*N*̄ > 10

^{5}) is due to heating of the TES substrate (heat bath). Due to the relatively short delay between successive laser pulses (1 ms), the substrate experiences cumulative heating. This heating also ultimately limits the maximum number of photons that can be detected at a given laser repetition rate. This limit is reached when the substrate temperature is close to or in excess of the TES’s transition temperature of 140 mK. The dashed line shows the predicted sensor response when no cumulative substrate heating is present. It remains flat beyond 10000 photons.

*N*̄. These are the uncertainties of the measurement of the energy proxy ℰ

_{P}, which in this case is the TRT as just described, or the matched filter result as described below. Included in the figure are the overall uncertainties, the uncertainties due to the detection process and the uncertainties due to the shot noise of the input photon state. We calculated standard deviations in units of photon number (

*σ*̄) via: where ℰ̄

_{N}_{P}and

*σ*

_{ℰP}are the mean and the standard deviation of the measured outcomes for each

*N*̄, respectively. In the appendix we show that we can estimate an upper bound for the uncertainty of the detection process by subtracting the input state shot noise from the variance of the measured outcomes:

*N*̄ < 1000. For

*N*̄ > 1000, the detection process uncertainty becomes larger than the shot noise due to the source and increases dramatically for

*N*̄ > 10000. The reason for this upturn is the small change of TRT with respect to the absorbed number of photons. This value is about 5000 times smaller than in the region for

*N*̄ < 1000. The theoretical variation of the TRT based on the confidence of the fit (black crosses) was obtained from a 1

*σ*confidence interval on all fitting parameters and by standard error propagation. This variation is caused by the noise in the electrical read-out and gives a lower bound on the detection process uncertainty, because this is an uncertainty of a single fit to a single TES response. Thus, it does not contain any shot-to-shot variation,

*e.g.*electron-phonon interaction statistics or variation of our laser source.

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. A **444**, 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. A **520**, 555–558 (2004). [CrossRef]

*i.e.*the ideal curve shape without noise. The inner product of the template with each individual response curve yields a proxy for the energy that has been absorbed by the sensor with high signal-to-noise ratio. However, we note that this method is not optimal in the normal conductance regime. Optimal performance using this method can be achieved in the limit of white noise and when the overall pulse shape does not change with photon number input [35

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. A **444**, 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. A **520**, 555–558 (2004). [CrossRef]

*N*̄ is shown in Fig. 2(a) (red stars), along with the upper bound estimate of the detection process uncertainty after subtracting the input state shot noise (red squares).

*N*̄. Figure 2(b) shows typical TES response curves for

*N*̄ = 4. The photon-number-resolving capability in the low photon number regime is demonstrated here. Figure 2(c) shows the output response for

*N*̄ = 17. In this regime the TES is at the upper edge of its transition region and starts to enter the normal conductance regime. Partial photon-number resolution can still be observed. An extensive analysis of an algorithm aimed at improved extraction of photon number information from a large set of TES responses to coherent pulses with some mean photon number is reported in Ref. [37

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. B **29**, 2066–2073 (2012). [CrossRef]

*N*̄ = 47. Figure 2(e) shows the TES responses after illumination with

*N*̄ = 1035. At this point the TES photon number determination is limited by detection noise, rather than being limited by the shot noise of the source.

## 6. Calibration with photon number states

*N*= 1, 20, and 80 (red bars), and for comparison coherent states with

_{F}*N̄*= 1, 20, and 80 (black bars). Clearly, the variation in the photon-number measurement is higher for the coherent state inputs with their spread of photon numbers, than for Fock state inputs, where the variation is only due to the nonunity detection efficiency (see Eq. (1)). Figure 3(b) shows an actual measurement of a heralded single-photon Fock state from a down-conversion source [38

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. Express **19**, 24434–24447 (2011). [CrossRef] [PubMed]

*i.e.*equal to the mean photon number of the heralded state.

## 7. Conclusion

^{6}absorbed photons in a single pulse, and at the operational repetition rate of 1 kHz the TES records 5.6 · 10

^{9}photons per second, corresponding to an absorbed average power of 760 pW. Our results show that the intrinsic energy resolution and single-photon sensitivity of the TES provides a route towards mating bright light level (picowatts) photo detection with single-photon counting. In principle, the TES allows for nanowatt light level detection starting in the single photon regime. The detection process uncertainty was found to be below the input state shot noise up to

*N*̄ = 1000 for single shot measurements. Better determination of the overall variation in the measurement outcome can be achieved by use of photon number (Fock) states, offering strong impetus for their development.

## Appendix

*i.e.*linear detector response, we can write exactly: which is the quadrature sum of the input state shot noise (

*σ*

_{d}.

*p*is the probability that the photon number is

_{k}*k*with a mean of

*μ*. We can model the non-linear TES response by: ℰ(

*k*) ∝ [

*k*− Δ(

*k*)], where Δ(

*k*) is the difference between the deviation from a linear detector response. ℰ(

*k*) is the proxy for the energy measurement. Δ(

*k*) is a function of

*k*. Also ℰ(

*k*) > 0 and ℰ(

*k*) →

*k*for

*k*→ 0 and ℰ(

*k*) →

*C*, for

*k*→ ∞, where

*C*is constant. ℰ(

*k*) is a continuous, monotonically increasing function. Let the measurement outcomes for each photon number

*k*be spread by a Gaussian distribution with standard deviation

*σ*: where

_{x}*x*is a continuous representation of photon number. The total distribution when convolved with the input state shot-noise then becomes: The variance of this distribution can be calculated via: whereℰ̄ is the expected value of the TES response x. Using

*x*we find: which is the variance in energy distribution. The expected value of the TES response

*x*is calculated via: To calculate the variance in photon number we apply: Combining Eq. (13) and Eq. (11) yields: As ℰ(

*k*) is a monotonically increasing function, we need only to consider the two limits,

*μ*→ 0 (ℰ(

*k*) →

*k*) and

*μ*→ ∞ (ℰ(

*k*) →

*C*). For

*μ*→ 0, using

*k*−

*ε*) →

*k*is the first order approximation of ℰ(

*k*) for

*μ*→ 0, and

*ε*

^{2}> 0. Equation (15) shows that in the limit of

*μ*→ 0, the

*ε*

^{2}) than the shot noise caused by the input state and the TES Gaussian spread

*μ*→ ∞, Eq. (15) reads: as the denominator goes to zero.

## Acknowledgments

## References and links

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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. Photonics |

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. A |

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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. |

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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. Express |

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. Express |

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. Express |

22. | R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics |

23. | M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum. |

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. A |

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. |

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

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. |

28. | A. G. Kozorezov, J. K. Wigmore, D. Martin, P. Verhoeve, and A. Peacock, “Electron energy down-conversion in thin superconducting films,” Phys. Rev. B |

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 conference2012http://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. Express |

31. | P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A |

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. , |

33. | K. D. Irwin and G. C. Hilton, “Transition-edge sensors,” Cryogenic Particle Detection, Top. Appl. Phys. |

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

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. A |

36. | D. Fixsen, S. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Meth. A |

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. B |

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. Express |

**OCIS Codes**

(040.3780) Detectors : Low light level

(040.5570) Detectors : Quantum detectors

(120.5630) Instrumentation, measurement, and metrology : Radiometry

**ToC Category:**

Detectors

**History**

Original Manuscript: July 16, 2012

Revised Manuscript: September 11, 2012

Manuscript Accepted: September 18, 2012

Published: October 2, 2012

**Citation**

Thomas Gerrits, Brice Calkins, Nathan Tomlin, Adriana E. Lita, Alan Migdall, Richard Mirin, and Sae Woo Nam, "Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime," Opt. Express **20**, 23798-23810 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-23798

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