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Photon-number resolving and distribution verification using a multichannel superconducting nanowire single-photon detection system Dengkuan Liu, Lixing You,* Yuhao He, Chaolin Lv, Sijing Chen, Ling Zhang, Zhen Wang, and Xiaoming Xie State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Rd., Shanghai 200050, China *Corresponding author:
[email protected] Received September 11, 2013; revised December 11, 2013; accepted January 8, 2014; posted February 19, 2014 (Doc. ID 197406); published March 17, 2014 Photon-number-resolving (PNR) detection is a prerequisite for many important quantum optics applications. By using a four-channel superconducting nanowire single-photon detection system incorporating the photon multiport network technique, PNR detection of up to four photons was realized. The amplitude of the output pulse is proportional to the detected photon number. Using two channels of the system, the Poisson distribution of photon number in the faint pulsed laser was verified. The theoretical counts of the two-photon response were analyzed as a function of the mean photon number per pulse. The measurement results matched well with the theoretical calculations according to the Poisson distribution. © 2014 Optical Society of America OCIS codes: (040.3780) Low light level; (040.5160) Photodetectors; (270.5290) Photon statistics; (310.6845) Thin film devices and applications. http://dx.doi.org/10.1364/JOSAB.31.000816
1. INTRODUCTION In various quantum optics applications, photon-numberresolving (PNR) single-photon detection is a necessary prerequisite [1]. Unfortunately, most of the currently available single-photon detectors (SPDs) are so-called “on–off” detectors, which may only detect single photons and cannot resolve the photon number in one pulse. The superconducting transition-edge sensor (TES) is an exception, which has an inherent PNR ability as well as high quantum efficiency [2,3]. However, the TES suffers from long recovery time and large timing jitter, and it requires millikelvin cryogenics. There are a few techniques to realize PNR ability using non-PNR semiconducting SPDs, which include multiport networks, time-division multiplexing (TDM), and visible light photon counters (VLPCs) [4–8]. As a new SPD technology emerging in this century, the superconducting nanowire single-photon detector (SNSPD) [9,10] has proven to be a distinguished SPD that surpasses traditional semiconducting SPDs with high detection efficiency, low dark counts, small timing jitter, and a high counting rate at nearinfrared wavelengths [11–15]. However, it is also intrinsically an “on–off” detector without PNR ability. Meanwhile, an SNSPD incorporating either parallel [16–18] or serial [19,20] superconducting nanowire arrays was proven to have PNR ability that is technically equivalent to a VLPC. However, the crosstalk between different elements [16,17], the nonuniform illumination of the whole active area [21], and the efficiency fluctuation of different elements prevent the parallel/serial detectors from reaching high multiphoton detection and PNR ability. In this paper, we describe a multiport network technique that allows a multichannel SNSPD system to realize PNR 0740-3224/14/040816-05$15.00/0
ability. The four-channel SNSPD system using a 1 × 4 fiber optic beam splitter (FOBS) can detect up to four photons by indicating the photon number with different amplitudes of the response pulses. The Poisson distribution of the photon number in a faint pulsed laser with different average powers was verified using the multichannel SNSPD system. The measurement results matched well with the calculation according to the theoretical Poisson distribution.
2. SYSTEM SETUP The SNSPDs we used were fabricated from 4-nm-thick NbN films on MgO substrates using reactive magnetron sputtering in a gas mixture of Ar and N2 (partial pressures of 90% and 10%, respectively) [22]. The meander nanowire was structured using e-beam lithography (EBL) and reactive ion etching (RIE). The nanowire had a width of 100 nm with a filling ratio of 50%, and the size of the active area was 15 μm × 15 μm [23]. The SNSPDs were cooled by a Gifford–McMahon (G-M) cryocooler. Owing to the excellent performance of the cryocooler [24], up to six SNSPDs could be integrated onto the cold stage whose working temperature could reach as low as 2.1 K. The system detection efficiency (SDE) of each channel at the wavelength of 1550 nm was measured to be 4%–10% at the dark count rate (Rdc ) of 100 Hz for the SNSPDs without using any optical cavity structures or lensed fiber. Figure 1 shows the schematic of the SNSPD system with PNR ability. It has four SNSPDs installed in one G-M cryocooler to realize a four-channel SNSPD system [25,26], and they share the same isolated voltage source. At the same time, four adjustable resistors are used to optimize the bias current for each detector. No crosstalk is observed when the four © 2014 Optical Society of America
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Fig. 1. Schematic of the four-channel SNSPD system with PNR ability. The dashed lines represent the optical paths for single-mode fibers, while the solid lines represent the paths of electric circuits. A 1 × 4 fiber optical splitter was adopted to split the multiphoton pulse into four equivalent branches. A power combiner was used to sum the amplified photon-response voltage signals from the four channels.
SNSPDs work simultaneously [21]. The four detectors used in the system have various critical currents from 18 to 30 μA due to the imperfect fabrication process. The SDEs of the detectors we chose are all around 5% at the Rdc of 100 Hz. A 1550 nm femtosecond pulsed laser diode with a pulse duration of 0.5 ps as the light source can be attenuated to an average power level of any number of photons per pulse by precise attenuators [27]. Then the attenuated pulsed laser is split by a 1 × 4 FOBS, and each output is connected to a different channel of the SNSPD system. The response signal of the SNSPD is amplified by a room-temperature low-noise amplifier (LNA650 from RF Bays, Inc.). The amplified response signals are then combined by a power combiner (ZFSC-4-3+from MiniCircuits) to integrate the compound signal for further counting or monitoring.
3. PHOTON-NUMBER RESOLVING Since the SDE is evidently less than unity, we set the average photon number to be 100 per pulse before the 1 × 4 FOBS. In this way, we recorded the real-time photon response of the SNSPD system by a real-time oscilloscope as shown in Fig. 2(a). The amplitude of the response signals can be divided into four levels, which correspond to different photon numbers. The result indicates that the four-channel SNSPD system can be used to realize the PNR ability of up to four photons. We noticed that the amplitudes of the response signals for the same photon number are not exactly the same, which is due to the different bias currents for different SNSPDs, i.e., different amplitudes of single-photon-pulse signals. Figure 2(b) shows the four representative waveforms of the response signal corresponding to 1–4 detected photons, respectively. Since the structure of the detectors is the same [28] and there is no evident difference in the delay in each of the four channels, all the response signals have the same profile except for the difference in the pulse amplitude. The amplitude is proportional to the detected photon number in the optical pulse. We measured the pulse height distribution of our system, which is shown as the inset of Fig. 2(b). The black dots in the inset show the measured distribution as a function of the pulse height recorded by the oscilloscope. The histogram can be well fitted with a multiple-peak
Fig. 2. (a) Single-shot oscilloscope trace of the SNSPD system under the illumination of the femtosecond pulsed laser diode. The average photon number per pulse before the fiber splitter was set to 100. (b) Typical voltage pulses corresponding to responses for 1–4 photons. Inset: measured (black dots) and fitted (solid pink line) pulse height distribution using the multichannel SNSPD system.
Gaussian distribution, shown as the solid pink line in the inset. The four peaks correspond to one-, two-, three-, and fourphoton response, respectively. Owing to the similar bias current of each detector, there is no overlap for different photon-number Poisson distributions, which is better than the previous result using the SNSPD array (e.g., Fig. 4(b) in Ref. [19]).
4. POISSON DISTRIBUTION VERIFICATION The above results proved the four-channel SNSPD system with PNR ability, which may have potential applications in quantum optics. One example of the typical PNR application would be to reconstruct the photon-number statistics of an unknown photon source [29,30]. Due to the lack of mature single-photon sources, the faint pulsed laser is widely used in quantum key distribution experiments as a pseudo singlephoton source by attenuating a pulsed laser to an average power level of less than a single photon per pulse. Theoretical research has proven that for both Poisson and non-Poisson laser sources, after being attenuated into a faint laser with an ultralow mean photon number, the photon-number distribution would be approximately a Poisson distribution [31]. To simplify the demonstration and avoid a low SDE for multiphotons, we used two channels of the SNSPD system incorporating a 1 × 2 FOBS to verify the Poisson distribution of the
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photon numbers of the faint pulsed laser. Figure 3(a) shows the dependence of SDE (S 1 and S 2 ) and Rdc (Rdc1 and Rdc2 ) on the relative bias currents for the two channels that we chose. S 1 and S 2 were 4.6% and 5.4%, respectively, at 0.98I c , where Rdc is several hundred hertz. The combined dark count rate of the two channels (Rdc12 ) can be defined as the sum of the error counts that have the amplitude of a two-photon-response signal; however, this is not caused by two-photon responses in two separate channels. Rdc12 can be expressed as
(a)
Rdc12 T d · Rdc1 · Rdc2 T d · f · μ · S 1 · Rdc2 S 2 · Rdc1 ; (1) where T d is the time delay of two response pulses from each channel whose combined amplitude is higher than the discrimination level (DL) set in the photon counter, f is the repetition rate of the laser, and μ is the average photon number per pulse. The first term on the right side of Eq. (1) represents the error counts caused by the superposition of the dark count pulses in two different channels; the second term represents the error counts caused by the superposition of a singlephoton pulse from one channel and the dark count pulse from the other. T d depends on the amplitudes and durations of pulses from the two channels. At 0.97I c , T d was measured to be about 27 ns when DL equaled 1.5 times the pulse amplitude of one channel. For simplicity, we considered T d to have a linear relationship with the normalized bias current. Taking the measured results of SDE and Rdc shown in Fig. 3(a) into Eq. (1), the theoretical value of Rdc12 with μ 0.1 is shown as the square dots in Fig. 3(b). The Rdc12 is three orders of magnitude smaller than the Rdc of each channel and decreases rapidly with the decrease of the bias current. When the detectors were both biased at 0.98I c , 0.96I c , and 0.94I c , the Rdc12 was 3, 0.1, and 0.002 Hz, respectively. We also measured Rdc12 as a function of the normalized bias current when μ 0.1, which is shown as the triangle dots in Fig. 3(b). The measurement results follow the calculation very well. The extremely low dark rate guarantees the validity of the Poisson distribution verification experiment. According to a Poisson distribution, the probability of a given pulse containing n photons P Poi n is P Poi n
μn · e−μ : n!
(2)
The pulsed laser is divided into two paths when passing through the 1 × 2 FOBS. Although the light power in the two paths is equal, the photons in the pulse choose the paths randomly at the FOBS. Assuming that there are k photons in one path and n − k in another, the probabilities of forming a single-photon response pulse in each channel are kS 1 and n − kS 2 , since S 1 , S 2 ≪ 1. Considering all the possible photon distributions when photons pass through the 1 × 2 FOBS, the probability of a two-photon response for an n-photon pulse P 2p n is written as P 2p n
n X C kn k0
2n
· k · S 1 · n − k · S 2 :
(3)
Equation (3) holds only when both kS 1 and n − kS 2 are smaller than 100%, which limits the input photon power to
(b)
Fig. 3. (a) SDE and Rdc of the two channels as a function of the normalized bias current. The I c s of the two detectors we chose are both 18.5 μA. The data of Rdc were collected with the fiber terminal of the SNSPD system blocked. (b) Calculated and measured Rdc12 as a function of the normalized bias current when μ 0.1.
a weak signal and avoids the saturation of the detectors. With fixed S 1 and S 2 , Eq. (3) can be expressed as P 2p n S 1 · S 2 ·
n · n − 1 : 4
(4)
The probability of forming a two-photon response only depends on SDEs of two channels and the incident photon number n before the 1 × 2 FOBS. Considering the Poisson distribution of the photon numbers, the overall two-photonresponse count per second N 2p is N 2p f ·
∞ X n2
P Poi n · P 2p n
∞ f · S1 · S2 X μn · . μ 4·e n − 2! n2
(5)
We may conclude from Eq. (5) that for a given μ, N 2p is determined by f , S 1 , and S 2 . For μ 0.1, 0.5, 1, and 2, the twophoton-response counts N 2p are measured at different bias currents and shown as the symbols in Fig. 4. The calculated values of N 2p based on Eq. (5) are shown as the solid-line curves for comparison. S 1 and S 2 at different bias currents are taken from Fig. 3(a) for the calculation, and f 20 MHz. The results indicate that, for all four different values of μ, the experimental values show good agreement with the theoretical calculation, which proves that the photon number of the faint pulsed laser obeys the Poisson distribution very well. The measurement error of the experiment depends mainly on the acquisition time of the data. In all the experiments, we
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REFERENCES AND NOTES
Fig. 4. Counts of two-photon response as a function of the normalized bias current when the average number of photons per pulse equals 2, 1, 0.5, and 0.1. The solid-line curves indicate the calculated result based on the SDEs of the two detectors, and the four different symbols indicate the measured results.
chose a suitable time to control the measurement error within an acceptable level. For the data in Figs. 3(a), 3(b), and 4, the acquisition times of each data point were 10, 50, and 10 s, respectively. Besides, in the calculation of Eq. (5), we use the sum of the first four terms in the binomial for simplicity. There are 2% relative errors in the calculated results shown as the solid-line curves in Fig. 4. In this work, we measured only the two-photon response in the Poisson verification because only two channels of the multichannel SNSPD system are adopted for the measurement. If we use more detectors, e.g., four SNSPDs, we can measure two-, three-, and four-photon response, and the results will be more convincing and powerful. However, the theoretical calculation for fitting will be more complicated. On the other hand, due to the low detection efficiency for multiphotons, the measurement error may be larger. SNSPDs with higher SDE by adopting the optical cavity structures can be used in further experiments, and better results will be achieved in the future.
5. CONCLUSION In summary, a four-channel SNSPD system based on the G-M cryocooler was integrated. The system has a PNR ability of up to four photons by incorporating a 1 × 4 FOBS. The photon number can be determined by the amplitude of the electrical response signal. The measured low dark count rate of the twophoton-response signal follows the calculated results. Using this multichannel SNSPD system with PNR ability, the Poisson distribution of the photon number in a faint pulsed laser was verified by examining the two-photon-response counts. The measurement results fit well with the calculation at four different photon levels of the pulse.
ACKNOWLEDGMENTS This work was supported in part by the National Natural Science Foundation of China (grant 91121022), the 973 Program (grant 2011CBA00202), the 863 Program (grant 2011AA010802), and the “Strategic Priority Research Program (B)” of the Chinese Academy of Sciences (grants XDB04010200 and XDB04020100).
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