## Superconducting series nanowire detector counting up to twelve photons |

Optics Express, Vol. 22, Issue 3, pp. 3475-3489 (2014)

http://dx.doi.org/10.1364/OE.22.003475

Acrobat PDF (2575 KB)

### Abstract

We demonstrate a superconducting photon-number-resolving detector capable of resolving up to twelve photons at telecommunication wavelengths. It is based on a series array of twelve superconducting NbN nanowire elements, each connected in parallel with an integrated resistor. The photon-induced voltage signals from the twelve elements are summed up into a single readout pulse with a height proportional to the detected photon number. Thirteen distinct output levels corresponding to the detection of *n* = 0-12 photons are observed experimentally. A detailed analysis of the linearity and of the excess noise shows the potential of scaling to an even larger dynamic range.

© 2014 Optical Society of America

## 1. Introduction

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^{3}Ω) is much larger than the load resistance (50 Ω), the absorption of more than one photon in the wire results in a readout pulse with nearly the same height as the one produced by the absorption of a single photon. Therefore the SSPDs give a binary response to the number of incident photons (either ‘0 photon’ or ‘≥ 1 photon’). Lowering the bias current of the SSPD will bring it to the multi-photon detection regimes [11

11. G. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. **79**(6), 705 (2001). [CrossRef]

13. D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, and A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. **10**(8), 2977–2981 (2010). [CrossRef] [PubMed]

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*n*photons) but not as a PNR detector. Integrating an SSPD with a high impedance pre-amplifier may in principle enable the SSPD to have the PNR functionality [16

16. M. Bell, A. Antipov, B. Karasik, A. Sergeev, V. Mitin, and A. Verevkin, “Photon number-resolved detection with sequentially connected nanowires,” IEEE Trans. Appl. Supercond. **17**(2), 289–292 (2007). [CrossRef]

17. J. Kitaygorsky, S. Dorenbos, E. Reiger, R. Schouten, V. Zwiller, and R. Sobolewski, “HEMT-based readout technique for dark- and photon-count studies in NbN superconducting single-photon detectors,” IEEE Trans. Appl. Supercond. **19**(3), 346–349 (2009). [CrossRef]

19. A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Goltsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics **2**(5), 302–306 (2008). [CrossRef]

19. A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Goltsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics **2**(5), 302–306 (2008). [CrossRef]

19. A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Goltsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics **2**(5), 302–306 (2008). [CrossRef]

20. F. Marsili, D. Bitauld, A. Gaggero, S. Jahanmirinejad, R. Leoni, F. Mattioli, and A. Fiore, “Physics and application of photon number resolving detectors based on superconducting parallel nanowires,” New J. Phys. **11**(4), 045022 (2009). [CrossRef]

*et al.*[21

21. S. Jahanmirinejad and A. Fiore, “Proposal for a superconducting photon number resolving detector with large dynamic range,” Opt. Express **20**(5), 5017–5028 (2012). [CrossRef] [PubMed]

*N*superconducting nanowires named

*series nanowire detector*(SND), which solves the current redistribution problem and is in principle scalable to large photon numbers. The first experimental demonstration of the SND, as a proof of principle, was reported in [22

22. S. Jahanmirinejad, G. Frucci, F. Mattioli, D. Sahin, A. Gaggero, R. Leoni, and A. Fiore, “Photon-number resolving detector based on a series array of superconducting nanowires,” Appl. Phys. Lett. **101**(7), 072602 (2012). [CrossRef]

23. D. Sahin, A. Gaggero, Z. Zhou, S. Jahanmirinejad, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Hofling, and A. Fiore, “Waveguide photon-number-resolving detectors for quantum photonic integrated circuits,” Appl. Phys. Lett. **103**(11), 111116 (2013). [CrossRef]

*n*= 0-12 photons were obtained in the measurement, representing a record dynamic range for the fast PNR detectors at telecommunication wavelengths. The device quantum efficiency and the temporal properties of the device were characterized. Photon statistics were performed on the experimental data and shows a good agreement with the theory. A detailed analysis of the 12-SND’s excess noise and linearity is presented, providing valuable information on the SND operation and on the potential for further scaling the dynamic range.

## 2. Device and experimental setup

*R*

_{p}. The working principle of each element is similar to a standard SSPD [11

11. G. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. **79**(6), 705 (2001). [CrossRef]

*I*

_{B}, slightly lower than the critical current

*I*

_{C}, using a current source. When no photon arrives, the nanowire is in the superconducting state and the

*I*

_{B}flows through the nanowire. When a photon is absorbed, the photon energy suppresses the superconductivity in the nanowire and triggers the transition to the normal state. Since the resistance of the nanowire after photon absorption is much larger than the value of

*R*

_{p}, the

*I*

_{B}is diverted to the

*R*

_{p}and builds a voltage pulse across it. The photo-induced voltages of different elements are summed up in the readout resistor

*R*

_{L}(50Ω), producing a single output voltage pulse with a height proportional to the number of firing elements, and therefore to the number of detected photons.

22. S. Jahanmirinejad, G. Frucci, F. Mattioli, D. Sahin, A. Gaggero, R. Leoni, and A. Fiore, “Photon-number resolving detector based on a series array of superconducting nanowires,” Appl. Phys. Lett. **101**(7), 072602 (2012). [CrossRef]

24. A. Gaggero, S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Notzel, R. Sanjines, and A. Fiore, “Nanowire superconducting single-photon detectors on GaAs for integrated quantum photonic applications,” Appl. Phys. Lett. **97**(15), 151108 (2010). [CrossRef]

*I*

_{B}flows through these contact pads [marked by S (signal) and G (ground) in Fig. 1(b)] into the device. Second, for each 12-SND, twenty-four smaller contact pads [Ti(5 nm)/Au(20 nm)] were made for the electrical contact of the twelve

*R*

_{p}s. Third, the NbN film was patterned by reactive ion etching using hydrogen silsesquioxane as an etch mask. The twelve active NbN nanowire sections [highlighted by different colors in Fig. 1(b)] were patterned in a 12 μm × 12 μm array with a filling factor of 40%. The nominal width of the NbN nanowires in the array is 100 nm, but the width was observed to vary from 75 nm to 105 nm in different pixels, depending on their position in the array, due to the proximity effect. In the last step, twelve

*R*

_{p}s [Ti(10 nm)/AuPd(50 nm)] were fabricated by lift-off using a PMMA stencil mask. The twelve

*R*

_{p}s locate on the sides of the nanowire array, each of them has a design value of 50 Ω and is connected to the array through the 250 nm-wide NbN nanowires.

*I*

_{C}of the device was 13.4 μA at 1.2 K. The typical relaxation-oscillation regime is not observed on the IV curve (solid red line) due to the presence of the twelve

*R*

_{p}s. When

*I*

_{B}exceeds

*I*

_{C}, the entire nanowire becomes resistive, so the measured resistance (d

*V*

_{B}/d

*I*

_{B}) equals to the parallel equivalent of the nanowire’s normal resistance and the value of 12 ×

*R*

_{p}. Since the resistance of the normal nanowire is much larger than the value of 12 ×

*R*

_{p}, the value of d

*V*

_{B}/d

*I*

_{B}can be approximated to be 12 ×

*R*

_{p}[22

22. S. Jahanmirinejad, G. Frucci, F. Mattioli, D. Sahin, A. Gaggero, R. Leoni, and A. Fiore, “Photon-number resolving detector based on a series array of superconducting nanowires,” Appl. Phys. Lett. **101**(7), 072602 (2012). [CrossRef]

23. D. Sahin, A. Gaggero, Z. Zhou, S. Jahanmirinejad, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Hofling, and A. Fiore, “Waveguide photon-number-resolving detectors for quantum photonic integrated circuits,” Appl. Phys. Lett. **103**(11), 111116 (2013). [CrossRef]

*R*

_{p}was determined to be ~542 Ω, and thus the average value of

*R*

_{p}was ~45.2 Ω, in good agreement with the design value of 50 Ω . The asymmetric shape of the IV curve in the normal region, which also showed hysteresis, was attributed to spurious reflections from the amplifier, which was connected to the device via the bias-T in the IV measurement and in the optical characterizations presented below.

*τ*

_{p}) of ~100 ps was used for the optical characterization in this work. The laser was triggered externally by a function generator with a repetition rate of 1 MHz. The 12-SND was illuminated by the laser through a polarization-maintaining single-mode lensed fiber mounted on a XYZ-piezo stage in the cryostat. The light spot was aligned to the center of the 12-SND and the lensed fiber tip was lifted up from its optimal focusing position to achieve a uniform illumination on the active area of the device. The full width at half maximum (FWHM) of the Gaussian spot was measured to be ~11.8 μm using the knife-edge method [25

25. J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Clavière, E. A. Franke, and J. M. Franke, “Technique for fast measurement of Gaussian laser beam parameters,” Appl. Opt. **10**(12), 2775–2776 (1971). [CrossRef] [PubMed]

## 3. Characterization of multi-photon response

*I*

_{B}of 13.0 μA. The sampling oscilloscope was synchronized with the laser’s trigger signal and measured the amplified output voltage signals (

*V*

_{out}) from the device. A low-pass filter with a cutoff wavelength of 80 MHz was added in the readout circuit to improve the signal-to-noise ratio (SNR) of the output signals by removing high frequency noises. A MITEQ low-noise amplifier with 51 dB amplification, a 1.1 dB noise figure, and a passband of from 0.5 to 500 MHz, was used in this measurement. The histograms of the output signals obtained in a power range of 0-64 nW are shown in Fig. 3 (All the light power values indicated in the following refer to the power exiting the lensed fiber). They were recorded within a 50 ps time window in order to make the DCR negligible. Thirteen distinct output levels corresponding to the detections of 0-12 photons were obtained, showing a large dynamic range of the 12-SND.

*n*th and the (

*n*+ 1)th output levels in Fig. 3 so that the counter only recorded the ‘≥

*n*-photon’ responses. According to [22

**101**(7), 072602 (2012). [CrossRef]

*η*is the device quantum efficiency obtained with respect to

*n*th-order of the light power. This is confirmed by our results as shown in Fig. 4. In the power range of up to 4 nW, which approximately corresponds to

26. V. Anant, A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, and K. K. Berggren, “Optical properties of superconducting nanowire single-photon detectors,” Opt. Express **16**(14), 10750–10761 (2008). [CrossRef] [PubMed]

*η*was measured by measuring the CR with the counter whose trigger level is set between the 0th and 1st output levels. As shown in Fig. 5, the value of

*η*is plotted as a function of

*I*

_{B}, reaching a maximum value of ~0.17% at

*I*

_{B}= 13.2 μA. The low efficiency of the present device is due to the low optical absorptance (in the order of few percent [24

24. A. Gaggero, S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Notzel, R. Sanjines, and A. Fiore, “Nanowire superconducting single-photon detectors on GaAs for integrated quantum photonic applications,” Appl. Phys. Lett. **97**(15), 151108 (2010). [CrossRef]

27. A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, V. Anant, K. K. Berggren, G. N. Gol’tsman, and B. M. Voronov, “Constriction-limited detection efficiency of superconducting nanowire single-photon detectors,” Appl. Phys. Lett. **90**(10), 101110 (2007). [CrossRef]

28. F. Mattioli, R. Leoni, A. Gaggero, M. G. Castellano, P. Carelli, F. Marsili, and A. Fiore, “Electrical characterization of superconducting single-photon detectors,” J. Appl. Phys. **101**(5), 054302 (2007). [CrossRef]

26. V. Anant, A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, and K. K. Berggren, “Optical properties of superconducting nanowire single-photon detectors,” Opt. Express **16**(14), 10750–10761 (2008). [CrossRef] [PubMed]

24. A. Gaggero, S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Notzel, R. Sanjines, and A. Fiore, “Nanowire superconducting single-photon detectors on GaAs for integrated quantum photonic applications,” Appl. Phys. Lett. **97**(15), 151108 (2010). [CrossRef]

29. K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, and K. K. Berggren, “Nanowire Single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express **14**(2), 527–534 (2006). [CrossRef] [PubMed]

23. D. Sahin, A. Gaggero, Z. Zhou, S. Jahanmirinejad, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Hofling, and A. Fiore, “Waveguide photon-number-resolving detectors for quantum photonic integrated circuits,” Appl. Phys. Lett. **103**(11), 111116 (2013). [CrossRef]

21. S. Jahanmirinejad and A. Fiore, “Proposal for a superconducting photon number resolving detector with large dynamic range,” Opt. Express **20**(5), 5017–5028 (2012). [CrossRef] [PubMed]

30. J. K. W. Yang, A. J. Kerman, E. A. Dauler, V. Anant, K. M. Rosfjord, and K. K. Berggren, “Modeling the electrical and thermal response of superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. **17**(2), 581–585 (2007). [CrossRef]

*τ*

_{fall}of ~11.3 ns, which enables a maximum repetition rate of ~30 MHz. The system time jitter was measured at the leading edge of the photoresponse pulse to be ~89 ps, including the jitter of the 12-SND, of the laser and of the amplifiers. We note that with the present 12-SND, a trade-off exists between the temporal performance and the SNR in the PNR operation, depending on whether the low-pass filter is used in the circuit. However, this will not intrinsically limit the performance of the SNDs. We can increase the SNR by using cryogenic pre-amplifiers and by improving the uniformity of the device, releasing the need for a low-pass filter.

## 4. Photon number statistics

*n*= 0-6 and

*n*= 3-10 photons, respectively.

*n*th output level corresponds to the probability

*P*of detecting

*n*photons. This detection probability distribution deviates from the simple Poissonian statistics of the light source due to the possibility that several photons are absorbed in the same element, which is intrinsic to all multiplexed PNR detectors with a finite number of elements. According to Fitch

*et al.*[5

5. 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**(4), 043814 (2003). [CrossRef]

*N*detection elements, the probability

*P*of detecting

*n*photons can be written as,

*η*for each power. A good agreement between the measurements and the calculations is achieved over the entire power range. The fitted values of

*η*are lower than the value reported in Fig. 5 for the

*I*

_{B}of 13.0 μA, since in this case the polarization was not aligned along the wires.

*η*first decreases and then maintains the minimum value at higher powers, as shown in the inset of Fig. 7. We attribute this observation to the non-uniformity of the elements’ efficiency of the 12-SND. With low powers (low

*η*in the low power range; when

31. E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Gol’tsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. **56**(2–3), 364–373 (2009). [CrossRef]

*I*

_{uf}) when other elements fired. As shown in Fig. 8(a), we calculated the value of

*I*

_{uf}as a function of time based on the electro-thermal model [21

21. S. Jahanmirinejad and A. Fiore, “Proposal for a superconducting photon number resolving detector with large dynamic range,” Opt. Express **20**(5), 5017–5028 (2012). [CrossRef] [PubMed]

30. J. K. W. Yang, A. J. Kerman, E. A. Dauler, V. Anant, K. M. Rosfjord, and K. K. Berggren, “Modeling the electrical and thermal response of superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. **17**(2), 581–585 (2007). [CrossRef]

*I*

_{uf}obviously decreases in the cases of detecting

*n*= 1-11 photons due to the partial redistribution of the

*I*

_{B}to the 50 Ω load [21

**20**(5), 5017–5028 (2012). [CrossRef] [PubMed]

*I*

_{uf}, where the temporal profile of the incident pulse (

*τ*

_{p}= 100 ps) is also indicated. Since the value of

*I*

_{uf}decreases in the time window where the detection events take place, the efficiency of the unfiring elements will decrease. Although this is not desirable for PNR detection, it can be avoided by using a much shorter light pulse or using a larger load resistance (e.g. a pre-amplifier with high input impedance [21

**20**(5), 5017–5028 (2012). [CrossRef] [PubMed]

*I*

_{uf}for

*R*

_{L}= 1 MΩ was performed and is presented in Fig. 8(b), keeping the other parameters unchanged. In this case, the value of

*I*

_{uf}remains constant so the efficiency of the unfiring elements will not decrease as a function of time.

## 5. Detection linearity of the 12-SND

*n*-photon output levels on the light power. The height (

*H*) of the output voltage levels, defined as the height of the fitting Gaussian peaks extracted from Fig. 3, is plotted as a function of light power in the range of 1.95-30.11 nW for

*n*= 0-11 in Fig. 9(a) (

*H*of the

*n*= 12 peak is not shown here since the

*n*= 12 peak is only observed when the power is larger than 30.11 nW, where the fitting becomes unreliable due to the noise at high powers). As shown in Fig. 9(a), for each

*n*, the value of

*H*is almost independent of the power when the power is low; as the power increases, the value of

*H*starts to slightly decrease. To visualize the small amount of the change of

*H*, we define Δ

*H*as the value of

*H*at different powers subtracted by the value of

*H*at the lowest power for the same

*n*as shown in Fig. 9(a). The value of Δ

*H*is plotted in Fig. 9(b) as a function of the power for different

*n*, showing a decrease of

*H*by up to a few percent as the power increases. Since the value of Δ

*H*is small, the increase of light power does not have a significant influence on the detection linearity.

*H*decreases as the power increases. Indeed we have also observed that the height of the photoresponse pulses from a standard SSPD decreases with the light power. A similar observation was reported in [17

17. J. Kitaygorsky, S. Dorenbos, E. Reiger, R. Schouten, V. Zwiller, and R. Sobolewski, “HEMT-based readout technique for dark- and photon-count studies in NbN superconducting single-photon detectors,” IEEE Trans. Appl. Supercond. **19**(3), 346–349 (2009). [CrossRef]

*H*on

*n*. Since the change of

*H*is relatively small as the power changes, we calculated the value of

*H*averaged for different powers (namely

*n*in Fig. 10(a). A power-law fit to

*A*and

*α*are fitting parameters), is also plotted, giving

*α*= 0.81. The difference between the value of

*n*in the inset of Fig. 10(a), showing that the value of

*n*. We calculated the value of

*V*

_{out}as a function of time for

*n*= 1-12 using the electro-thermal model [21

**20**(5), 5017–5028 (2012). [CrossRef] [PubMed]

30. J. K. W. Yang, A. J. Kerman, E. A. Dauler, V. Anant, K. M. Rosfjord, and K. K. Berggren, “Modeling the electrical and thermal response of superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. **17**(2), 581–585 (2007). [CrossRef]

*H*, i.e. the maximum value of

*V*

_{out}of these pulses, is extracted and plotted as a function of

*n*in the main panel of Fig. 10(b). By fitting the calculated value of

*H*, we obtained an

*α*of 0.98, showing a better linearity than that in the experiment.

*α*values between the experiment and the simulation to the inhomogeneities among different elements, e.g. variation in the wire’s cross section between different elements. In principle, the elements with narrower wires have higher efficiency, so with small

*n*only they will contribute to the readout voltage pulse; the wider elements will participate in detections as

*n*increases. Since the voltage pulse produced by the wider elements is lower than that of the narrower elements, the height of total voltage pulse scales nonlinearly with the

*n*. As shown in the discussions below, this variation in the voltage amplitudes of different elements has major consequences also in the noise.

## 6. Detection noise of the 12-SND

*n*. The noise

*V*

_{N}on the output levels, defined as the FWHM of the fitting Gaussian peak, is extracted from Fig. 3 for

*n*= 0-11 in the power range of 1.95-30.11 nW.

*V*

_{EN}, defined as

*n*at fixed light powers as shown in Fig. 11(b). Interestingly, for all powers, the value of

*V*

_{EN}first increases with

*n*, reaching a maximum for

*n*≈4-6, depending on the power, then decreases. This dependence indicates a surprising suppression of the excess noise, which is key to the measurement of large photon numbers.

**101**(7), 072602 (2012). [CrossRef]

*R*

_{p}may also change the pulse height, but it is not considered in the following discussion for simplicity). Based on our explanation to Fig. 10(a), we assume at low powers, only the most efficient element, which has the narrowest wire and produces the highest photoresponse pulse, participates in the detection, and at high powers, the least efficient element starts to participate. In this case, according to the inset of Fig. 10(a), the most efficient element produces a pulse height of ~12.8 mV; likewise, the element with the lowest efficiency produces a pulse height of ~7.5 mV, and the other elements produce pulse heights distributed around a mean value of ~10 mV. We further assume that variation of the output pulse height of different elements is the only noise source for Fig. 11(b), so the pulse height distribution has a width of ~2 mV according to Fig. 11(b) as

*n*= 1.

*n*-photon detection. We assume an arbitrary distribution

*N*

_{element}(

*H*

_{1}) of the number of elements producing a peak height

*H*

_{1}for the one-photon detection (

*n*= 1) [grey bars in Fig. 12(a), right axis], chosen so that the highest and the least pulse height have values of 12.8 mV and 7.5 mV, and the width is ~2 mV [using a Gaussian fit (red line)]. Based on the distribution of

*N*

_{element}(

*H*

_{1}), we are able to calculate the distribution of

*P*(

_{n}*H*) considering a uniform distribution of the elements’ efficiency, where

_{n}*P*is the probability of detecting a pulse with the height of

_{n}*n*-photon detection event (

*n*= 0-12). When

*n*= 0,

*H*

_{0}= 0 and the width of the distribution equals zero. When

*n*= 1, the distribution of

*P*

_{1}(

*H*

_{1}) [Fig. 12(a), left axis] reproduces the distribution of

*N*

_{element}(

*H*

_{1}). When

*n*>1, each

*n*-photon detection is a combination of

*n*one-photon detections corresponding to any

*n*of the twelve elements. The value of

*P*(

_{n}*H*) equals to the sum of the probabilities for all the possible combinations which produce

_{n}*H*. The calculation of

_{n}*P*(

_{n}*H*) for

_{n}*n*= 0-12 has been done based on the above rules. Four examples for

*n*= 1, 4, 6 and 11 are plotted as histograms (grey bars) in Figs. 12(a)-12(d), respectively. Each calculated

*P*(

_{n}*H*) distribution is fitted by a Gaussian peak [red lines in Figs. 12(a)-12(d)]. The FWHM of the fitting Gaussian peak, which represents the calculated

_{n}*V*

_{EN}, is plotted as a function of

*n*in Fig. 12(e). Interestingly, the shape of the

*P*(

_{n}*H*) distribution for the

_{n}*n*-photon event is identical to that of the (12-

*n*)-photon event. For instance, the one-photon event as shown in Fig. 12(a) reproduces the distribution of the eleven-photon event as shown in Fig. 12(d), despite of the shift of the

*n*= 12 as shown in Fig. 12(e). Indeed, if all the twelve elements are triggered, only a single value of

*n*= 12. The calculated

*n*-dependence of

*V*

_{EN}agrees with the experimental data. The calculation [Fig. 12(e)] gives the highest noise at

*n*= 6, while in the experiment [Fig. 11(b)] the highest noises take place in the range of

*n*= 4-6. The agreement clearly indicates that the statistical distribution of the nanowire’s normal resistance plays an important role in the observed excess noise.

## 7. PNR capability of the 12-SND

*H*/

*V*

_{N}as a measure of the 12-SND’s PNR capability. Indeed, the fidelity of discriminating an

*n*-photon detection from (

*n*-1) or (

*n*+ 1) directly depends on the ratio between the peak spacing and the peak width, i.e. the noise. For example, for equally spaced Gaussian peaks with constant width, the probability of correctly measuring an

*n*-photon peak with an optimal discrimination threshold [32] is 76.09%, 98.15% and 99.96% for Δ

*H*/

*V*

_{N}= 1, 2 and 3, respectively. The measured ratio of Δ

*H*/

*V*

_{N}[calculated based on the data of Fig. 9(a) and Fig. 11(a)] is plotted it in Fig. 13 as a function of

*n*for different powers.

*V*

_{N}, is increased as the power increases. Secondly, the PNR capability decreases as

*n*increases when

*n*is small and then tends to stop decreasing when

*n*becomes larger. This is due to the saturation of

*V*

_{EN}as discussed above, showing a potential of scaling to larger dynamic range. The ratio of Δ

*H*/

*V*

_{N}may be greatly increased by using a cryogenic high-impedance pre-amplifier to boost the Δ

*H*[21

**20**(5), 5017–5028 (2012). [CrossRef] [PubMed]

31. E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Gol’tsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. **56**(2–3), 364–373 (2009). [CrossRef]

## 8. Conclusions

**20**(5), 5017–5028 (2012). [CrossRef] [PubMed]

## Acknowledgments

## References and links

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

2. | N. Sangouard, C. Simon, J. Minář, H. Zbinden, H. de Riedmatten, and N. Gisin, “Long-distance entanglement distribution with single-photon sources,” Phys. Rev. A |

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

4. | M. Fujiwara and M. Sasaki, “Direct measurement of photon number statistics at telecom wavelengths using a charge integration photon detector,” Appl. Opt. |

5. | 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 |

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

7. | D. A. Kalashnikov, S. H. Tan, and L. A. Krivitsky, “Crosstalk calibration of multi-pixel photon counters using coherent states,” Opt. Express |

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

9. | 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. |

10. | B. E. Kardynał, Z. L. Yuan, and A. J. Shields, “An avalanche-photodiode-based photon-number-resolving detector,” Nat. Photonics |

11. | G. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. |

12. | F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics |

13. | D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, and A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. |

14. | Z. Zhou, G. Frucci, F. Mattioli, A. Gaggero, R. Leoni, S. Jahanmirinejad, T. B. Hoang, and A. Fiore, “Ultrasensitive |

15. | J. J. Renema, G. Frucci, Z. Zhou, F. Mattioli, A. Gaggero, R. Leoni, M. J. A. de Dood, A. Fiore, and M. P. van Exter, “Modified detector tomography technique applied to a superconducting multiphoton nanodetector,” Opt. Express |

16. | M. Bell, A. Antipov, B. Karasik, A. Sergeev, V. Mitin, and A. Verevkin, “Photon number-resolved detection with sequentially connected nanowires,” IEEE Trans. Appl. Supercond. |

17. | J. Kitaygorsky, S. Dorenbos, E. Reiger, R. Schouten, V. Zwiller, and R. Sobolewski, “HEMT-based readout technique for dark- and photon-count studies in NbN superconducting single-photon detectors,” IEEE Trans. Appl. Supercond. |

18. | E. A. Dauler, B. S. Robinson, A. J. Kerman, J. K. W. Yang, K. M. Rosfjord, V. Anant, B. Voronov, G. Gol’tsman, and K. K. Berggren, “Multi-element superconducting nanowire single-photon detector,” IEEE Trans Appl. Supercond. |

19. | A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Goltsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics |

20. | F. Marsili, D. Bitauld, A. Gaggero, S. Jahanmirinejad, R. Leoni, F. Mattioli, and A. Fiore, “Physics and application of photon number resolving detectors based on superconducting parallel nanowires,” New J. Phys. |

21. | S. Jahanmirinejad and A. Fiore, “Proposal for a superconducting photon number resolving detector with large dynamic range,” Opt. Express |

22. | S. Jahanmirinejad, G. Frucci, F. Mattioli, D. Sahin, A. Gaggero, R. Leoni, and A. Fiore, “Photon-number resolving detector based on a series array of superconducting nanowires,” Appl. Phys. Lett. |

23. | D. Sahin, A. Gaggero, Z. Zhou, S. Jahanmirinejad, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Hofling, and A. Fiore, “Waveguide photon-number-resolving detectors for quantum photonic integrated circuits,” Appl. Phys. Lett. |

24. | A. Gaggero, S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Notzel, R. Sanjines, and A. Fiore, “Nanowire superconducting single-photon detectors on GaAs for integrated quantum photonic applications,” Appl. Phys. Lett. |

25. | J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Clavière, E. A. Franke, and J. M. Franke, “Technique for fast measurement of Gaussian laser beam parameters,” Appl. Opt. |

26. | V. Anant, A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, and K. K. Berggren, “Optical properties of superconducting nanowire single-photon detectors,” Opt. Express |

27. | A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, V. Anant, K. K. Berggren, G. N. Gol’tsman, and B. M. Voronov, “Constriction-limited detection efficiency of superconducting nanowire single-photon detectors,” Appl. Phys. Lett. |

28. | F. Mattioli, R. Leoni, A. Gaggero, M. G. Castellano, P. Carelli, F. Marsili, and A. Fiore, “Electrical characterization of superconducting single-photon detectors,” J. Appl. Phys. |

29. | K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, and K. K. Berggren, “Nanowire Single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express |

30. | J. K. W. Yang, A. J. Kerman, E. A. Dauler, V. Anant, K. M. Rosfjord, and K. K. Berggren, “Modeling the electrical and thermal response of superconducting nanowire single-photon detectors,” IEEE Trans. Appl. Supercond. |

31. | E. A. Dauler, A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Gol’tsman, S. A. Hamilton, and K. K. Berggren, “Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors,” J. Mod. Opt. |

32. | G. P. Agrawal, |

**OCIS Codes**

(030.5260) Coherence and statistical optics : Photon counting

(040.5160) Detectors : Photodetectors

**ToC Category:**

Detectors

**History**

Original Manuscript: October 22, 2013

Revised Manuscript: December 13, 2013

Manuscript Accepted: December 30, 2013

Published: February 6, 2014

**Citation**

Zili Zhou, Saeedeh Jahanmirinejad, Francesco Mattioli, Döndü Sahin, Giulia Frucci, Alessandro Gaggero, Roberto Leoni, and Andrea Fiore, "Superconducting series nanowire detector counting up to twelve photons," Opt. Express **22**, 3475-3489 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-3475

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### References

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- G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, New York, 2002), Chap. 4.5.

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