Derivation of sensitivity of a Geiger mode APDs detector from a given efficiency for QKD experiments 9 0 0 2 Kiyotaka Hammura and David Williams n Hitachi Cambridge Laboratory,Cavendish Laboratory, J J Thomson Avenue, a Cambridge CB3 0HE, United Kingdom J 5 E-mail: [email protected] ] h Abstract. The detection sensitivity (DS) of the commercial single-photon-receiver p basedonInGaAsgate-modeavalanchephotodiodeisestimated. Instalmentofadigital- - t blanking-system(DBS)toreducedarkcurrentmakesthedifferencebetweenDS,which n a is an efficiency of the detector during its open-gate/active state, and the total/overall u detection efficiency (DE). By numerical simulations, it is found that the average q number of light-pulses, blanked by DBS, following a registered pulse is 0.333. DS [ is estimated at 0.216, which can be used for estimating DE for an arbitrary photon 1 arriving rate and a gating frequency of the receiver. v 5 2 5 Keywords: Quantum Cryptography, Detection sensitivity and efficiency 0 . 1 0 9 0 : v i X r a Derivationofsensitivityof a GeigermodeAPDs detectorfrom agivenefficiencyforQKDexperiments2 1. Introduction The emergence of a commercial single-photon-receiver (SPR) would help reduce development time to integrate quantum key distribution (QKD) system. Since QKD[1] was firstly experimentally demonstrated[2], tremendous efforts have continued towards QKD’s further performance improvements[3]. Many efforts have been dedicated to the development of two essential devices which constitutes QKD, i.e., single-photon- emitters[4, 5, 6] and SPRs[7, 11, 12, 13, 8, 14, 15, 16, 17, 9, 10]. For current QKD systems under development, almost all of the performances depend on those of SPRs. This is because the single-photon-emitters, the other essential device, have normally been implemented by attenuated commercial lasers. The performances of them have been completely characterised already, meaning that there is no room to improve. The commercial SPR of Princeton Lightwave[18], for example, is a highly integrated one. This SPR features not only highdetection efficiencies, DEs, at telecom wavelengths and low dark count probabilities but also a digital-blanking system (DBS) to dramatically reduce the effect of afterpulsing on dark count. Itshouldbenoted,however, thatthegivenDE doesnotclarifyaboutsomeintrinsic figure-of-merit of the SPR concerning its sensitivity to incident single-photons. We should have a figure-of-merit of how sensitive the SPR in its open-gate state is (which will be designated as a detection sensitivity, DS, hereafter) while the given DE is simply a ratio of the number of registration to that of all incident light-pulses. The verbal definitions of these two figures follow: How many light-pulses are registered DE ≡ , (1) How many light-pulses hit the detector How many light-pulses are registered DS ≡ . (2) How many light-pulses hit the detector in open-gate status Thanks to the DBS, a designated number of bias pulses for gating the detector are neglected once a registration occurs. In this paper, DS of the commercial SPR[18] is estimated. DS is helpful to estimate the photon registration number for various operation conditions while DE is helpful only for a set of conditions to give the DE. DS should be defined as a ratio of the number of registrations to that of light-pules which hit the detector in open-gate status (Eq.(2)). Such number of light-pulses is to be estimated by subtracting the number of light-pulses blanked by DBS, N , from all B incident ones. The N will be numerically estimated as below. B 2. Method DS can be derived using one experimental data and the number of light-pulses blanked by DBS. Eq.(2) is expressed as, N G DS = (3) N +N A G N G = , (4) (N +N +N )−N A G B B Derivationofsensitivityof a GeigermodeAPDs detectorfrom agivenefficiencyforQKDexperiments3 where N and N designate the numbers per second of how many light-pulses are G A registered, how many light-pulses hit the detector in gate-open status but are not registered due to detector’s poor sensitiveness as a whole, respectively. The relations among N ,N , and N are illustrated in FIG 1. We use an experimental data given by G A B photon pulse 250 KHz time photon arriving 0.1 photon/pulse time SPD triggering 500 KHz time detector status blanking=6 blanking=6 blanking=6 (active timing) time detected ? time event classification G B G B A G Figure 1. N , N , and N in the text refer to the numbers per second of incidents A B G denoted by A, B, and G. the manufacturer[19] for N in the numerator in Eq.(4). G N is calculated under the following experimental conditions: the light-pulse B arriving rate, N = 250 × 103 s−1, the mean number of photons per pulse, µ = 0.1, T the triggering rate of the detector, N = 500×103 s−1, the number of gatings blanked TR by DBS, B = 6. The simulation is conducted according to the following 3 steps. All L figures below are those for one second. (i) Distribute 25000 (= NT · µ × 1 s ≡ N0) incident single-photons randomly over 250000 (= N ×1 s) time-bins. The specific procedure is to take a random number T between 1 to 250000, for each of 25000 figures. Then, arrange the 25000 figures in ascending order of their associated random numbers. The random numbers mean the occupied time-bins. (ii) Estimate how many light-pulses in average, designated as N , are found sitting B,AVG intheconsecutive 3blanked bins following thetime-binwhich isactually registered. To do this, choose randomly an occupied time-bin and count up the number of photon-pulses in the blanked bins, resulting in N . Repeat this procedure B,AVG until N reaches some asymptotic number. The reason why the number of B,AVG blanked bins is not 6 (= B ) but 3 comes from the fact that the triggering rate, L N , is twice faster than the light-pulse arriving rate, N . Blanking 6 time-bins TR T only means blanking 3 pulses. (iii) N is given by multiplying an experimental data value of N by N . B G B,AVG Derivationofsensitivityof a GeigermodeAPDs detectorfrom agivenefficiencyforQKDexperiments4 Table 1. Results of the numerical simulation of N and the resultant DE for several p specific combinations of the photon arrival rate and the detector triggering rate. The mean photon number and the DBS number are fixed at 0.1 and 6, respectively. (NT,NTR) N0 Nbin Ndist Np DE (100 MHz,5 MHz) 500×103s−1 5×106s−1 500×103s−1 296×103s−1 0.128 (2.5,5) 250×103 5×106 250×103 183×103 0.158 (1.25,5) 125×103 5×106 125×103 106×103 0.183 (0.625,5) 62.5×103 5×106 62.5×103 59×103 0.204 (100,2.5) 250×103 2.5×106 250×103 153×103 0.132 (1.25,2.5) 125×103 2.5×106 125×103 93×103 0.161 (0.625,2.5) 62.5×103 2.5×106 62.5×103 52×103 0.180 3. Result Numerical simulations of N results in 0.333 s−1. With Eq.(4), DS is estimated at B,AVG 0.216 as follows: N G DS = (5) (N +N +N )−N ×N A B G G B,AVG 5033 = = 0.216 , (6) 25000−5033×0.333 where NG = 5033 s−1[19] and NA +NB +NG ≡ N0. DE for an arbitrary combination of the light-pulse arriving rate, the triggering rate, the mean photon number per pulse, and DBS number, (N ,N ,µ,B), can be T TR estimated using the constant value of DS. The numerator in the definition of DE in Eq.(1) is decomposed as N ×DS DE ≡ p . (7) N 0 , where N designates the quantity of how many photons could be registered at the p maximum. For N0, N ×µ (N ≥ N ) N0 = TR T TR (8) (NT ×µ (NT ≤ NTR) ForN , numerical simulations forµ = 0.1and B = 6 will bedone asfollows: Distribute p L incident light-pulses, Ndist (=N0), randomly over the time-bins, Nbin (=NTR), resulting in identifying occupied bins. Then, count up how many occupied bins can be chosen at the maximum so that if you choose an occupied bin it is not allowed to count up any occupied bins sitting in 6 time-bins following the chosen occupied bin to meet B = 6. L Simulated results of N and DE for several sets of (N ,N ) are summarised in p T TR Table 1 and Figure 2. For a fixed triggering rate of the detector, Np do not decrease so rapidly as N0, leading to the increase in DE. Derivationofsensitivityof a GeigermodeAPDs detectorfrom agivenefficiencyforQKDexperiments5 0.22 NT = 0.625 MHz 0.20 E 0.18 NT = 0.625 MHz NT = 1.25 MHz D y, c n Efficie 0.16 NT = 1.25 MHz NT = 2.5 MHz n o cti 0.14 e Det NT = 100 MHz NT = 100 MHz 0.12 0.10 2 3 4 5 Triggering rate of the detector, N (MHz) TR Figure 2. Plots of Detection Efficiency, DE, for several combinations of light-pulse arrivingrate,N ,andtriggeringrateofthedetector,N ,underµ=0.1andB =6. T TR L DE increases with increasing N as long as N ≤N , reflecting decreasing in the TR T TR probability of a distributed photon being found sitting in the blanked time-bins with increasingtotaltime-bins. DE increaseswithdecreasingN foreitherN ,reflecting T TR decreasing in the probability of a distributed photon being blanked due to the sparse distribution. 4. Discussions By estimating the effect of blanking on the number of photon detection registration, DS of the detector is derived under the condition that dark count events are all neglected. We established a method to derive DS, which is more suitable figure-of-merit to characterise device parameters of SPADs. The estimation shows that 0.333 light-pulse is in fact blanked by DBS in average. This correction might look negligible in experiments. The importance of the figure, however, does not lie in its magnitude but in that it enables us to derive the significant performance characteristic intrinsic to the specific detector. The intrinsic DS value enables us to estimate detection efficiencies, DE, under arbitrary combinations of operation parameters, i.e., N ,N ,µ,B . For a fixed N , T TG L T DE increases with increasing N . This is because the probability of a distributed TR light-pulse being sitting in the 6 time-bins (=blanked bins) following a registered pulse decreases with increasing triggering rate as the triggering rate means the number of time-bins. For a fixed N , DE increases with decreasing N . This is because the TG T probability of a distributed light-pulse being sitting in the blanked bins decreases faster than the decrease in the total number of distributed light-pulses. The discrepancy in decreasing speed of the two quantities depends on the number of DBS setting. In the development of optical communications systems using single photon detectors, it is crucial to know in prior how many photons will be registered under Derivationofsensitivityof a GeigermodeAPDs detectorfrom agivenefficiencyforQKDexperiments6 the perfect operation condition. DS enables us to do this. For example, applying DS = 0.216 to our experimental configurations: N = 5×106 s−1 and N = 100×106 TR T −1 −1 s , the total photon count for a single photon stream is estimated at 64800 s (=N × DS). This figure is helpful in the respect of system optimization because it p gives the maximum number of photon registration achievable in the configurations. Throughout all the calculations in this paper including the derivation of DS and the estimation of DE, the dark count event is neglected for simplicity. The legitimacy of this approximation is able to be checked in experiments using a single photon emitter implemented by an attenuated laser. Even if the general characteristic of DE associated with the specific detector under various operation conditions would be successfully verified experimentally, a potential futureresearch isto evaluateDS andDE moreprecisely withmoreelaboratesimulation model including dark count events. References [1] C. H. Bennett, and G. Brassard, Quantum cryptography: public key distribution and coin tossing, Proceedings of the International Conference on Computer Systems and Signal Processing, Institute of Electrical and Electronics Engineers, New York, 175 (1984). [2] Charles H. Bennett, Francois Bessette, Gilles Brassard, Louis Salvali, and John Smolin, Experimental Quantum Cryptography, Journal of Cryptography 5, 3 (1992). [3] N.Gisin,G.Ribordy,W.Titel,andH.Zbinden,Quantum Cryptrography, Rev.Mod.Phys.74,145 (2002). [4] XiulaiXu,D.A.Williams,andJ.R.A.Cleaver,Electrically pumpedsingle-photon sources inlateral p-i-n junctions, Appl. Phys. Lett. 85, 3238 (2004). [5] XiulaiXu,IanToft,RichardT.Phillips,JonathanMar,KiyotakaHammura,andDavidA.Williams, “Plug and play” single-photon sources, Appl. Phys. Lett. 90, 061103 (2007). [6] Xiulai Xu, Frederic Brossard, Kiyotaka Hammura, David A. Williams, B. Alloing, L. H. Li, and Andrea Fiore, “Plug and Play” single photons at 1.3 µm approaching gigahertz operation, Appl. Phys. Lett. 93, 021124 (2008). [7] D. Bethune, W. Risk, and G. Pabst, A high-performance integrated single-photon detector for telecom wavelengths, J. Mod. Opt. 15, 1359 (2004). [8] D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden,Quantum key distribution over 67 km with a plug&play system, New J. Phys, 4, 41.1 (2002). [9] A.Yoshizawa,R.Kaji,andH.Tuschida,After-pulse-discarding in single-photon detection to reduce bit errors in quantum key distribution, Opt. Express, 11, 13 (2003). [10] Y. Kang, H. X. Lu, and Y. -H. Lo, D. S. Bethune, and W. P. Risk, Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection, Appl. Phys. Lett. 83, 2955 (2003). [11] A. Lacaita, F. Zappa, S. Cova, and P. Lovati, Single-photon detection beyond 1µm: performance of commercially available InGaAs/InP detectors, Appl. Opt. 35, 2986 (1996). [12] F. Zappa, A. Lacaita, and C. Cova, Nanosecond single-photon timing with InGaAs/InP photodiodes, Opt. Lett. 19, 846 (1994). [13] S. Cova, M Ghioni, A. Lacaita. C. Samori, and F. Zappa, Avalanche photodiodes and quenching circuits for single-photon detection, Appl. Opt. 35, 1956 (1996). [14] H. Henri, P. Deschamps, B. Dion, A. D. MacGregor, D. MacSween, R. J. Mclntyre, C. Trottier, and P. P. Webb, Photon counting techniques with silicon avalanche photodiodes, Appl. Opt. 32, 3894 (1993). Derivationofsensitivityof a GeigermodeAPDs detectorfrom agivenefficiencyforQKDexperiments7 [15] V. Golovin, and V. Saveliev, Novel type of avalanche photodetector with Geiger mode operation, Nucl. Instr. and Meth. A 518, 560 (2004). [16] S. Vasile, P. Gothoskar, R. Farrell, and D. Sdrulla, Photon Detection with High Gain Avalanche Photodiode Arrays, IEEE Trans. Nucl. Sci. 45, 720 (1998). [17] J. Kim, S. Takeuchi, and Y. Yamamoto, Multiphoton detection using visible light photon counter, Appl. Phys. Lett. 74, 902 (1999). [18] Princeton Lightwave Inc., Single Photon Benchtop Receiver PLI-AGD-SC-Rx. Performance specifications of this model is downloadable at www.photoncount.org/Portals/0/SPAD Ben.pdf. [19] Figures 5033 is given through private communications with the manufacture of the detector (Princeton Lightwave Inc.).