1.Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China 2.School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 12033007, 61875205, 61801458, 91836301), the Frontier Science Key Research Project of Chinese Academy of Sciences (Grant No. QYZDB-SW-SLH007), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDC07020200), the “Western Young Scholar” Project of Chinese Academy of Sciences (Grant Nos. XAB2019B17, XAB2019B15), the Key R&D Program of Guangdong province, China (Grant No. 2018B030325001), the Chinese Academy of Sciences Key Project, China (Grant No. ZDRW-KT-2019-1-0103)
Received Date:06 October 2020
Accepted Date:30 October 2020
Available Online:25 March 2021
Published Online:05 April 2021
Abstract:Semiconductor single-photon avalanche detectors (SPADs) have played an important role in practical quantum communication technology due to their advantages of small size, low cost and easy operation. Among them, InGaAs/InP SPADs have been widely used in fiber-optic quantum key distribution systems due to their response wavelength range in a near-infrared optical communication band. In order to avoid the influence of dark count and afterpulsing on single photon detection, the gated quenching technologies are widely applied to the InGaAs/InP SPADs. Typically, the duration of gate pulse is set to be as short as a few nanoseconds or even less. As the detection of the arrival of single photons depends on the coincidence between the arrival time of gate pulse and the arrival time of photon, the gate pulse duration of the InGaAs/InP SPADs inevitably affects the effective detection of the single photons. Without the influence of dispersion, the temporal width of the transmitted photons is usually on the order of picoseconds or even less, which is much shorter than the gate width of the InGaAs/InP SPAD. Therefore, the gate width normally has no influence on the temporal measurement of the detected photons. However, in quantum systems involving large dispersion, such as the long-distance fiber-optic quantum communication system, the temporal width of the transmitted photons is significantly broadened by the experienced dispersion so that it may approach to or even exceed the gate width of the single-photon detector. As a result, the effect of the gate width on the recording of the arrival time of the dispersed photons should be taken into account. In this paper, the influence of the gate width coupled to the InGaAs/InP single photon detectors on the measurement of the two-photon coincidence time width is studied both theoretically and experimentally. The theoretical analysis and experimental results are in good agreement with each other, showing that the finally measured coincidence time width of the two-photon state after dispersion is not more than half of the effective gate pulses width. The maximum observable coincidence time width based on the gated single photon detector is fundamentally limited by the gate width, which restricts its applications in quantum information processing based on the two-photon temporal correlation measurement. Keywords:coincidence detection/ single-photon detectors/ gate pulses/ temporal filtering
3.实验装置为验证上述理论分析, 本文分别利用基于超导纳米线单光子探测器(SNSPD)和门控下InGaAs/InP半导体单光子探测器对实验室已产生的频率纠缠双光子源经光纤色散展宽后的双光子符合宽度进行了测量研究. 用于产生频率纠缠光子对的实验装置如图3所示. 其中图3(a1)和图3(a2)分别表示基于I类和II类SPDC的频率纠缠源产生过程, 其中780 nm泵浦光源通过大功率1560 nm激光源结合基于PPKTP准相位匹配晶体的外腔倍频技术产生[34], 通过间接实验测量, 得到该780 nm倍频光的3 dB带宽约为0.025 nm[35]. 为实现不同频谱带宽的下转换双光子, 实验中通过对780 nm分束, 同时泵浦两类(I类和II类)相位匹配的PPKTP晶体. 其中I类相位匹配的PPKTP晶体长度为10 mm, 晶体的极化周期为24.945 μm. II类相位匹配的PPKTP晶体长度为10 mm, 晶体的极化周期为46.146 μm. 将共线传输的780 nm泵浦光从下转换双光子源中有效滤除后, 双光子源被耦合进光纤分束器.II类下转换产生的光子对被耦合到光纤偏振分束器(PBS-15-P1-FC/APC, FPBS, 插入损耗为1.2 dB), 通过调整FPBS前的半波片可实现信号光子与闲置光子的偏振方向分别与FPBS的快慢轴方向重合, 从而使得信号光子与闲置光子分别从FPBS的两个输出端输出. 对于I类下转换产生的双光子源经过中心波长在1560 nm、带宽为12 nm的滤波器(FB1560-12)后, 通过一根50/50光纤分束器(WIC-1 X2-1550-50/50, FBS, 插入损耗分别为3.19 和3.02 dB)分成两路输出, 分别作为信号光子与闲置光子进行传输. 图 3 通信波段频率反关联纠缠光源的产生及其双光子符合测量实验装置图 (a1), (a2)基于I类和II类SPDC的频率纠缠源产生过程; (b)信号光子和闲置光子分别经过光纤SMF1和SMF2的传输过程; (c1), (c2)基于超导纳米线单光子探测器(SNSPD)和InGaAs/InP单光子探测器(SPD4)的测量系统 Figure3. Experimental setup diagram of the generation of frequency anti-correlated entangled light sources in the telecommunication band and their two-photon joint distribution measurement after dispersive propagation: (a1), (a2) The generation process of entangled sources from type-I and type-II SPDC pumped by 780 nm quasi-monochromatic laser; (b) photon transmission through sperate single-mode fiber SMF1 and SMF2; (c1), (c2) coincidence measurement system based on the Superconducting nanowire single-photon detectors (SNSPD) and InGaAs/InP single-photon detectors (SPD4).
信号光子与闲置光子分别经过相同长度的单模光纤SMF1和SMF2后, 双光子关联时间宽度被光纤色散展宽. 当色散展宽影响远大于单光子探测器的时间抖动时, 双光子关联时间宽度随SMF长度呈线性增长. 光子信号在经过传输、色散展宽后到达最终的测量系统(图3(c1)和图3(c2)). 首先将SMF传输后的信号光子与闲置光子分别接到测量系统(图3(c1))的2台SNSPD上(上海赋同科技, SNSPD-1& SNSPD-2), 两单光子探测器输出的电脉冲信号分别作为开始和结束信号接到一个时间相关计数器(PicoHarp300, TCSPC), 用来实现对信号光子与闲置光子间的符合测量. 由于SNSPD工作于自由运转模式, 符合测量结果不受门控技术影响, 将反映双光子的时间关联分布. 随后将由SNSPD组成的测量系统(图3(c1))替换为由2台InGaAs/InP半导体单光子探测器(上海朗研光电SPD4, SPD4-1& SPD4-2)组成的测量系统(图3(c2)). 该单光子探测器运行在门控条件下, 外部触发信号由波形发生器(Tektronix AFG3252)提供, 该信号为脉冲波信号, 频率为75 MHz. 两个单光子探测器的门控脉冲宽度均约为1 ns, 当探测效率为25%时, 对应暗计数率约为3.3 k cps. 4.实验结果与分析为了验证单光子探测器的门控脉冲对于测量的符合时间宽度的限制作用, 分别采用自由运转模式下的SNSPD和门控模式下的SPD4, 对实验室II类SPDC产生的频率反关联纠缠双光子源经光纤色散展宽后的双光子符合分布进行了测量研究. 实验结果如图4所示, 其中图4(a)—图4(d)表示每臂分别经过约为1, 3, 5和10 km的SMF色散展宽后, 测量得到的双光子符合分布结果. 其中红色实线表示由两台SPD4测得的符合结果, 与之对应, 黑色实线表示由两台SNSPD测得的符合结果. 由图4(a)和图4(b)可以看到, 在每臂SMF约为1和3 km时, SPD4与SNSPD测量得到的符合分布图样相差不大; 但在每臂SMF约为5 km时(图4(c)), SPD4与SNSPD测量得到的双光子符合时间FWHM分别为320.02与467.40 ps; 每臂SMF约为10 km时(图4(d)), SPD4与SNSPD测量得到的双光子符合时间FWHM分别为428.78与877.76 ps. 由于APD单光子探测器的后脉冲特性[36], 在每臂SMF约为10 km时符合曲线中存在肩膀形的结构; 通过比较可以看出, SPD4由于门控脉冲宽度的限制, 当双光子二阶时间关联分布宽度较大时测量到的符合分布宽度明显小于实际二阶关联宽度. 图 4 基于II类SPDC过程的纠缠光子对, 每臂经过不同长度SMF色散展宽之后, 进行符合测量的结果 (a) 1 km; (b) 3 km; (c) 5 km; (d) 10 km Figure4. The coincidence measurement results of the entangled photon pair from type-II SPDC process when the photon is dispersed by SMF with different lengths: (a) 1 km; (b) 3 km; (c) 5 km; (d) 10 km.
图5所示为分别采用SNSPD和SPD4测量到的双光子符合时间宽度(3 dB)随着两臂SMF的变化结果. 图5(a)和图5(b)分别对应I类下转换和II类下转换产生的双光子源经过不同长度SMF后的结果, 其中绿色点表示利用SNSPD测得的双光子符合时间FWHM, 反映了双光子时间关联FWHM随SMF长度增加而导致的色散展宽. 不加光纤时, 测得双光子的符合时间FWHM为56.02 ps, 对应SNSPD的时间抖动. 紫色实线表示理论拟合双光子关联时间FWHM随着SMF长度增加的变化曲线, 其中计入了SNSPD时间抖动的影响. 根据理论拟合, 得到I类下转换和II类下转换产生的双光子源的3 dB频谱宽度分别为7.17 和2.46 nm. 其中II类下转换产生的双光子源的3 dB频谱宽度拟合结果与之前实验结果[34]符合. 图 5 使用不同类型反关联频率纠缠光源下, 符合测量FWHM随SMF长度变化的测量和理论结果 (a) I类SPDC; (b) II类SPDC Figure5. The measurement and theoretical FWHM results of the temporal coincidence measurement for different types of anti-correlated frequency entangled light with different SMF length: (a) Type I SPDC; (b) Type II SPDC.
采用SPD4半导体单光子探测器测量到的双光子符合时间宽度(3 dB)随SMF长度的变化结果如图5(a)和图5(b)中的蓝色点所示. 不加光纤时, 符合时间FWHM约为155 ps, 对应SPD4的时间抖动. 黑色虚线为计入SPD4时间抖动,在不考虑门控脉冲作用的影响下对应的双光子关联时间FWHM随着SMF色散展宽的理论曲线. 通过比较可以看到, 当双光子二阶时间关联分布FWHM大于250 ps时, 测量到的符合分布宽度开始明显小于实际二阶关联宽度; 最终符合测量结果不再随着双光子时间关联分布FWHM的增大而增大, 而是达到饱和值, 本实验中该饱和值约为500 ps. 当考虑门控脉冲的作用时, 取门控脉冲的有效时间宽度为1 ns(与SPD4半导体单光子探测器的门控参数一致), 理论拟合曲线由红色实线所示. 实验测量结果与理论结果符合良好, 揭示了半导体单光子探测器的门控脉冲宽度是导致最大可测量的符合时间宽度受限的主要因素. 为进一步验证门控脉冲对单光子探测器用于符合测量的影响, 本文将其中一台SPD4替换为id Quantique公司的半导体探测器(ID210), 在相同门控触发和探测效率条件下, 通过调节该探测器的参数, 使得ID210具有与SPD4相同的暗计数, 此时可认为ID210的有效门脉冲宽度与SPD4相同[18]. 基于该ID210和另一台SPD4, 本文测量了I类下转换产生的双光子源经FB1560-12后, 每臂分别经过相同长度SMF后的符合时间宽度. 该实验结果如图6中红色方形点所示, 蓝色圆点为前面基于两台SPD4单光子探测器的测量结果. 从图6中可以看出, 不加光纤时测量到的双光子符合宽度主要由单光子探测器的固有时间抖动决定, 采用具有更大时间抖动的ID210将增大测量到的符合时间宽度. 然而, 随着光纤色散影响增大, 基于上述两种单光子探测器组合测量到的符合时间FWHM基本一致. 在此基础上, 通过改变ID210的门控宽度设置, 进一步研究了不同门控宽度对于测量符合时间宽度的限制作用. 鉴于ID210的说明书中指出: 用户设置的门控宽度和有效门控宽度之间存在差异[37], 本文对于该ID210的不同门控宽度(Gate width)对于符合测量的影响仅做了定性分析. 实验结果如图7所示, 其中图7(a)和图7(b)分别表示每臂经过约为1与3 km的SMF色散展宽后, 测量得到的双光子符合分布结果. 其中IDQ探测器Gate width为3.5, 4.0和4.5 ns时测得的符合结果分别由黑色虚线、红色虚线以及蓝色虚线表示. 可以看到, 随着门控宽度的增加, 测量得到的双光子符合时间FWHM也在逐渐变宽; 同时, 随着门控宽度的增加, 后脉冲效应随之更为明显, 暗计数也显著增加[37]. 上述实验测量结果均验证了半导体单光子探测器最大可测量的双光子符合宽度受限于探测器的有效门控时间宽度. 图 6 基于I类SPDC的纠缠光子对符合测量时间FWHM随SMF的长度变化的结果 Figure6. The measurement FWHM results of the temporal coincidence measurement for type-I SPDC process when the photon is dispersed with different SMF length.
图 7 基于I类SPDC过程的纠缠光子对每臂经过不同长度SMF色散展宽之后, 采用ID210与SPD4进行符合测量的结果 (a) 约1 km; (b) 约3 km Figure7. After each photon is dispersed by the SMF with different lengths, the coincidence measurement of the photon pairs from the type-I SPDC process is made by using ID210 and SPD4: (a) About 1 km; (b) about 3 km.