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一个理想的单光子探测器(single-photon detector,SPD)可以理解为如下系统:输入信号为单个光子,输出信号为电压脉冲(或者其他电信号); 通过对电压脉冲计数达到对光子计数的目的。换言之,理想的单光子探测器能如实地告知有无入射光子,不漏计、不误报、不重计, 这种探测器也被称为桶探测器(bucket detector),如图 3a所示。但事实上,没有一个SPD是理想的或完美的:有时有光子入射,但SPD却没有输出电压脉冲; 有时没有光子入射,但SPD却输出电压脉冲; 有时有一个光子入射,但SPD却输出多个电压脉冲。
另一方面,SPD除了告知有无入射光子,还可能提供光所携带的其他信息:时间模式、空间模式、偏振模式、波长、光子数。也就是说,SPD可能具有时间分辨、空间分辨、偏振分辨、波长分辨、光子数分辨的能力。
为了表征SPD如实探测光子的能力以及获取光所携带的其他信息的能力,需要采用系列的性能指标予以衡量。
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如图 3b所示,SPD有时会“漏掉”入射光子而没有探测到。假设没有后脉冲,由入射光子所致的SPD输出电压脉冲的概率就是SDE。如果有m个入射光子产生了n个输出脉冲,那么SPD的系统探测效率为n/m。
对于SNSPD,需要考虑光耦合、光吸收、产生电压脉冲这3个顺次的物理过程,SDE是光耦合效率、光吸收效率、内量子效率的乘积:
$ \eta_{\mathrm{SDE}}=\eta_{\text {coupling }} \times \eta_{\text {absorption }} \times \eta_{\text {intrinsic }} $
(1) 式中,ηcoupling是光耦合效率,表示入射光子耦合到SNSPD光敏面的概率,是光子所在空间模式与SNSPD光敏面的交叠积分; ηabsorption是光吸收效率,表示入射到SNSPD光敏面的光子被纳米线吸收的概率; ηintrinsic是内量子效率,表示一个光子被纳米线吸收后产生电压脉冲的概率。排除光耦合效率在外不考虑,光吸收效率与内量子效率的乘积被称为DDE。从(1)式可以看到,光耦合效率、光吸收效率、内量子效率对于SDE都很重要。作为估算,假设这3个效率相等,如果要到达90%, 95%, 99%的SDE,那么这3个效率的每一个相应地要达到96.5%, 98.3%, 99.7%。
SDE一般随着偏置电流的增大而单调增大,SDE-偏置电流曲线在线性坐标系呈现S型,具有高SDE的器件往往在高偏置电流区间,SDE呈现平坦的饱和趋势。除了偏置电流,SDE与很多器件参数、测试参数、光的模式有关:薄膜材料、器件结构、光学耦合、工作温度、入射光的波长、偏振、光子通量。
为了准确测量SDE,要从测量的电压脉冲计数中排除误计数(false counts)[81],也要准确测量入射光功率从而准确计算入射光子数[2, 9]。
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对于最常用的回形纳米线结构,SNSPD的SDE偏振依赖。为了量化SDE对入射光子偏振态的敏感程度,引入偏振敏感度(polarization sensitivity, PS)。参考文献中有两种等价的定义[7, 82]:SPS=ηSDE, max/ηSDE, min以及SPS=(ηSDE, max-ηSDE, min)/(ηSDE, max+ηSDE, min),其中,ηSDE, max和ηSDE, min分别是偏振最大和偏振最小的SDE。SDE的偏振依赖既来源于光吸收效率的偏振依赖[83],也来源于内量子效率的偏振依赖[83]。通过器件结构设计,可以减小[5, 7, 57, 82, 84-89]或者增大PS[90-95],以满足不同的应用需求。
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如图 3c所示,在没有入射光子的情况下,SPD有时会自发地输出电压脉冲,这些电压脉冲所产生的错误计数被称为暗计数(dark count); 单位时间产生的暗计数被称为暗计数率(DCR)。对于应用而言,暗计数是一种噪声; SNSPD产生暗计数的主要物理机制是涡旋-反涡旋的拆对(vortex-antivortex depairing)[68]以及通过光纤耦合到SNSPD的黑体辐射[71, 96]。如图 1f所示,SNSPD的暗计数率一般随偏置电流的增大而增大。
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如图 3d所示,有时SPD探测到一个光子后,不是输出一个电压脉冲,而是输出了两个或者两个以上(N个)的电压脉冲,第2个~第N个电压脉冲被称为后脉冲(afterpulse)。由单根纳米线构成的SNSPD在正常工作时不产生后脉冲; 由多根纳米线并联构成的SNAP在一定的偏置区间会产生后脉冲[97]。
暗计数和后脉冲统称为误计数。在测量SDE时需要排除误计数; 一种排除误计数测量SDE的方法是做时间关联计数[81]。
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SPD在完成一个光子探测事件后需要经过一定的恢复时间才能有效地探测下一个光子,这个时间被称为响应恢复时间(recovery time)。定性地讲,响应恢复时间描述SPD能够“多快”地探测光子。如图 3e所示,如果两个或多个光子接连入射SPD,它们之间的时间间隔短,那么这些光子无法被有效地探测。也就是说,在入射光子通量高的情况下,SPD的SDE降低了。SNSPD的响应恢复时间定义为在完成一个光子探测事件后SDE恢复到低光子通量下SDE的90%所需要的时间。影响SNSPD响应恢复时间的因素有器件的电学时间常数τe(主要取决于器件的动能电感Lk)、电路读出方式(交流耦合读出还是直流耦合读出)、器件的热学时间常数τth。实验上测量SNSPD响应恢复时间的方法是可变时延的双光脉冲法[98-99]。也可以采用输出电压脉冲的后沿回复1/e所对应时间的3倍近似表征SNSPD的响应恢复时间,其中e为自然常数。
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当入射光子通量增大,SDE降低; 为了描述SPD能够“多快”地探测光子,也可以采用SDE降低3dB所对应的入射光子通量来表征。
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一个SPD的输入信号是光子,输出信号是电压脉冲,在输出与输入之间有时延(latency),如图 3f所示,这个时延不是固定的,而是变化的或者说是抖动的,这种现象被称为SPD的时域抖动。采用时延概率密度分布函数的半峰全宽(full width at half maxima,FWHM)作为时域抖动的具体数值。时域抖动描述SPD获取入射光子时间模式信息的能力。SNSPD的时域抖动源自于各种噪声[100-107],这一点会在后面第3.6节中详细阐述。
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实用化SNSPD系统的重要参数还有尺寸、重量与功耗(size, weight and power, SWaP)。因为要工作在液氦温区,相比于采用帕尔帖热电制冷的半导体单光子探测器[108],SNSPD在SWaP方面目前没有优势。对于需要将探测器系统置于卫星或者其他航天器上的应用,降低SNSPD的SWaP尤为重要; 制冷机轻小型化的研究近期已有报道[109-112]。
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提高SNSPD系统综合性能的主要难点是上述性能之间相互制约。对材料、器件、读出、系统进行优化,往往“牵一发而动全身”,提升了一个性能指标,却降低甚至牺牲了另一个或几个。一个主要的相互制约关系(tradeoff)是SDE与包括响应恢复时间和时域抖动在内的时域性能之间的相互制约关系; SDE与暗计数率之间也存在着明显的相互制约关系; SNSPD的性能与系统的SWaP之间也存在相互制约关系。
提高SNSPD系统的综合性能另一个难点是器件物理不是完全清晰。这就造成了对器件和系统的综合性能难以进行全面的、定量的、有预言能力的数值仿真和模拟。但是另一方面,对器件物理研究和认识的不断深入,的确促使了SNSPD器件和系统性能的提升。一个正面的例子就是近年来对时域抖动机理的研究[100-107],促进了低时域抖动SNSPD的研究[11, 113],也促进了对时域抖动和SDE的同时优化[4, 7, 114]。由此可见,仍然需要对SNSPD的器件物理开展更多更加深入的研究工作。
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研究SNSPD的器件物理,理解SNSPD如何探测单光子,是为了能够全面地、定量地、有预言能力地数值仿真模拟SNSPD单光子探测的过程,有据可依地优化超导材料、器件结构、读出电路、制冷系统,优化SNSPD的综合性能或者按照应用需求有的放矢地突出某些性能。目前,这些目标并未完全达成。
关于SNSPD单光子探测的物理图景,光耦合过程与光吸收过程是完全清楚的。一个光子被纳米线吸收后,初始的有阻区是如何形成的,却不完全清楚,尽管在理论研究方面已经有若干模型[1, 72-75],并与实验结果进行了比对[80]。这种不清晰的状态直接影响人们对内量子效率和时延、时域抖动等时域性质的理解和定量仿真。要刻画光子吸收后准粒子的弛豫过程以至于形成初始的有阻区(或者超导电性被抑制的区域),需要在一定的初值和边值条件下求解含时金兹堡-朗道(Ginzburg-Landau)方程[75, 115]。初始有阻区形成以后的热电相互作用,可以由热电模型清楚地刻画[76-78],因此可以较为准确地仿真SNSPD输出电压脉冲的波形。当纳米线较长时,为了准确仿真SNSPD的时域性能,需要把纳米线等效为传输线而不是分立的电感元件[116]。此外,暗计数的物理图景也比较清楚。在无光照的情况下,热激发可以拆散涡旋-反涡旋对[68],产生暗计数; 黑体辐射也可以通过光纤耦合到SNSPD,产生“暗计数”[71, 96]。
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超导纳米线是一个动能电感[98](或称为“动态电感”)。有别于几何电感(geometric inductance)中的储能主要是磁场能,动能电感中的储能主要是超导纳米线中载流子的动能[115]。动能电感的充放电对应于纳米线中的载流子加速或者减速的过程。SNSPD的动能电感可由Lk=lkl/(dw)表示,其中,lk为超导纳米线动能电感率,l为超导纳米线长度,d为超导纳米线厚度,w为超导纳米线宽度。
动能电感影响SNSPD的时域特性。(1)动能电感决定了SNSPD的电学时间常数τe=Lk/Z0,其中,Z0为读出端负载电阻,一般为50Ω; 而电学时间常数影响SNSPD的响应恢复时间[98]; (2)超导纳米线的动能电感远大于几何电感,导致射频信号沿纳米线的传输速度远低于真空光速,长度较长的纳米线就需要考虑它的传输线效应[101, 116]; (3)动能电感影响SNSPD的时域抖动,这是因为动能电感影响SNSPD输出脉冲前沿斜率,进而影响电学噪声[100, 103]与纳米线不均匀性[105]所致的时域抖动; 也影响输出电压信号沿着超导纳米线的传输速度,进而产生传输线效应所致的时域抖动[101, 116]。
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如图 4a所示,直条形状超导纳米线中的超导电流密度J沿宽度方向的分布基本是均匀的(纳米线边缘处除外); 当超导纳米线几何形状发生变化,尤其是出现弯曲时,J的分布不再是均匀的,出现电流拥挤效应[117],即:拐弯内侧电流密度大于拐弯外侧电流密度,如图 4b~图 4d所示。电流拥挤效应是SNSPD临界电流的一个主要限制因素,不利于SNSPD实现高内量子效率和低时域抖动。也正是因为电流拥挤效应,具有高占空比回型线结构的SNSPD临界电流和内量子效率会降低[118]。因此,从目前已有的实验结果看,在器件设计时应注意优化SNSPD几何结构以避免或减弱电流拥挤效应。
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SNSPD暗计数按照来源可以分为两类:非本征暗计数与本征暗计数。非本征暗计数是环境光、黑体辐射等耦合到SNSPD产生的计数。通过合适的光学滤波[71, 96],可以消除大部分的非本征暗计数。本征暗计数的物理机制是纳米线中的涡旋与反涡旋由于受到不同方向的洛伦兹力,以一定的概率拆对(depairing),当拆分的涡旋和反涡旋在纳米线垂直于电流的纳米线横向(即宽度方向)移动时,会产生有阻区进而产生计数[68]。通过涡旋-反涡旋对拆对理论计算出的本征暗计数与实验测试结果相吻合[68]。MURPHY等人测量了SNSPD的超导转变电流分布标准差随SNSPD工作温度变化的曲线,发现曲线存在两个拐点,结合理论分析,他们认为当SNSPD工作在低温时,本征暗计数主要来源于宏观量子隧穿效应(macroscopic quantum tunneling),而当SNSPD工作在较高温度时,本征暗计数主要来源于多个相位滑移(multiple phase-slips)[119]。
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SNSPD的内量子效率-偏置电流曲线都有相似的特性:(1)在线性坐标下,SNSPD内量子效率随偏置电流变化的曲线一般为S型曲线(高偏置下存在内量子效率饱和平台)或者指数型曲线(不存在内量子效率饱和平台),在半对数坐标下,内量子效率如图 5a所示,其中,SNSPD探测阈值电流Ith定义为曲线的拐点[120]; (2)在半对数坐标下,探测效率随波长变化的曲线如图 5b所示,SNSPD最小可探测光子能量Emin定义为曲线的拐点[72]。
RENEMA等人通过量子探测器层析术(quantum detector tomography)对SNSPD进行了表征[80, 121-122],研究发现, SNSPD的探测阈值电流与最小可探测光子能量存在线性关系,即Ith=I0-γEmin,其中I0和γ为拟合参数。根据相关文献中的研究结果[80, 121-122]可知,该关系对于不同拓扑结构的SNSPD都具有普适性。
SNSPD的内量子效率随偏置电流变化的曲线可由误差函数拟合[104],$P_{\mathrm{r}}=\frac{1}{2} \operatorname{erfc}\left(\frac{I_{\mathrm{b}}-I_{\mathrm{co}}}{\sqrt{2} \sigma}\right) $,其中Ico为内量子效率随偏置电流变化曲线的拐点,σ为拟合参量,在实际物理模型中受多个参数影响,包括纳米线宽度、纳米线分布式不均匀性、入射光子能量、法诺涨落、温度、磁场。
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有关光致有阻区的形成,目前尚无完善的模型; 现有模型大致是以下5种:有阻热点模型(normal-core hotspot model)[1]、基于扩散的热点模型(diffusion-based hotspot model)[72]、光子触发涡旋进入模型(photon-triggered vortex-entry model)[69, 73]、基于扩散的涡旋进入模型(diffusion-based vortex-entry model)[74, 123]、有阻区涡旋模型(normal-core vortex model)[75, 124-127]。这5种模型各自都能解释SNSPD的部分实验结果,也都存在与实验不符之处。
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有阻热点模型是最早提出的SNSPD探测机理模型[1]:超导纳米线吸收一个能量远大于纳米线超导能隙参量Δ的光子③,产生一个与入射光子能量相当的激发态电子; 这个激发态电子在弛豫过程中产生准粒子与声子; 准粒子扩散,纳米线局部的超导电性被抑制,在准粒子的扩散中心形成一个有阻热点; 有阻热点产生后,超导纳米线上的偏置电流会绕过有阻热点区域; 如果有阻热点区域足够大,两侧的电流密度会超过超导临界电流密度,形成横跨纳米线的有阻区。有阻热点模型初步解释了光致有阻区的形成,但该模型预测:(1)长波长的光子无法产生有阻热点[72]; (2)SNSPD的探测阈值电流Ith与入射光子能量的平方根相关[26],都与实验结果不符[26, 80]。
③ 一个近红外入射光子的能量在1eV的量级; 目前用于SNSPD的超导材料能隙参数Δ一般是几个毫电子伏特(meV)的量级。
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2005年,研究者提出基于扩散的热点模型[72]。该模型将有阻热点模型中的有阻热点替换为横跨纳米线且长度为金兹堡-朗道相干长度ζ的带; 由于光子入射,ζ带中的库珀对(Cooper pairs)数量减小。为了维持纳米线中电流连续,ζ带中的库珀对需要加速,当ζ带中库珀对的速度超过超导临界速度时,ζ带会变成有阻态,从而产生探测事件。基于扩散的热点模型与实验结果部分相符:(1)SNSPD探测阈值电流Ith与光子能量的一次方相关[80]; (2)SNSPD探测阈值电流Ith与纳米线厚度和宽度的一次方相关[128]; (3)SNSPD探测阈值电流Ith与态密度、超导能隙参数Δ、准粒子扩散系数的关系[129]; (4)低温下(T <0.5Tc)SNSPD探测阈值电流Ith与温度的关系[26]。然而,该模型的预言仍存在与实验结果不符之处:(1)SNSPD探测阈值电流Ith与实验相比偏大[26]; (2)当T>0.5Tc时,探测阈值电流Ith会有所下降,实验并未观察到这样的下降[26]; (3)无法解释SNSPD探测阈值电流Ith随光子入射横向位置的关系[130]。
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2011年前后,有研究者提出光子触发涡旋进入模型[69, 73]。在这个模型中,假设SNSPD吸收入射光子后产生一个热带,在热带区域内超导序参量被均匀地抑制,但光子能量不足以产生有阻区,因此偏置电流在纳米线宽度方向仍然基本均匀分布。超导序参量被抑制,降低了涡旋进入的等效势垒,实现涡旋进入纳米线、渡越并产生探测事件。该模型可以解释在偏置电流高于探测阈值电流Ith时,SNSPD内量子效率趋于饱和,在偏置电流低于探测阈值电流Ith时,内量子效率逐渐下降。但是,该模型预测了:(1)SNSPD探测阈值电流Ith与光子能量的非线性关系[26]; (2)SNSPD最小可探测光子能量与纳米线宽度的平方成正比,都与实验结果不符[80, 128]。
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2013年前后,有研究者提出基于扩散的涡旋进入模型[74, 123],该模型认为SNSPD探测光子过程如下:SNSPD吸收入射光子产生准粒子,准粒子的扩散使得超导电子密度降低,引起超导电流分布的变化。而超导电流分布的变化降低了涡旋进入纳米线的等效势垒,当等效势垒降为0时,涡旋进入纳米线作横向运动,产生有阻区和相应的探测事件。该模型预测的SNSPD探测阈值电流Ith与光子能量的一次方相关[80],SNSPD探测阈值电流Ith与光子入射位置的关系[130],都与实验结果相符。但该模型预测的SNSPD探测阈值电流Ith随纳米线宽度、工作温度的变化关系与实验结果不符[80, 128]。
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有阻态涡旋模型是利用含时Ginzburg-Landau方程研究超导纳米线的单光子探测过程[75, 124-127]。该模型假设SNSPD吸收入射光子并产生准粒子,形成与一个圆形或半圆形热区(取决于光子入射在纳米线上的横向位置); 之后利用含时Ginzburg-Landau方程、热扩散方程、电势泊松方程计算得到超导序参量的演化,进而得到纳米线的超导态演化过程与探测事件的产生过程[75, 124-127]。该模型可以准确预测SNSPD探测阈值电流与光子能量之间的线性相关[80]。然而,该模型预测的SNSPD探测阈值电流与光子入射位置的关系与实验结果不符[130]。
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尽管初始光致有阻区的形成过程并不完全清楚,但是一旦形成了初始有阻区,后续在电热相互作用下,有阻区沿纳米线的纵向增大、减小、消失,并同时伴随着电流的动态转移和电压脉冲输出的过程是清楚的。这一过程用热电模型描述[76-78],SNSPD的电路模型如图 6a所示。
2007年,有研究者提出了基于热扩散方程与电路方程耦合的1维热电模型[76]:
$ \begin{gathered} J^{2} \rho+\kappa \frac{\partial^{2} T}{\partial x^{2}}-\frac{\alpha}{d}\left(T-T_{\text {sub }}\right)=\frac{\partial(c T)}{\partial t} \end{gathered} $
(2) $ C_{\mathrm{bt}}\left[\frac{\mathrm{d}^{2}\left(L_{\mathrm{k}} I\right)}{\mathrm{d} t^{2}}+\frac{\mathrm{d}\left(I R_{\text {nomal }}\right)}{\mathrm{d} t}+Z_{0} \frac{\mathrm{d} I}{\mathrm{~d} t}\right]=I_{\mathrm{b}}-I $
(3) 式中,J为电流密度的幅值,ρ为纳米线的电阻率,κ为纳米线的热导率,α为纳米线和衬底之间的热导率,d为纳米线的厚度,Tsub为基底的温度,c为纳米线的体积比热容,Cbt为T型偏置器的电容,Lk为超导纳米线的动能电感,I为超导纳米线中的电流,Rnormal为纳米线有阻区的电阻,Z0为负载电阻,Ib为SNSPD的偏置电流。
当SNSPD的电学时间常数τe=Lk/(Z0+Rs)大于热学时间常数τth时,有阻区经过一定时间后会转变为超导初态(如图 6b所示); 而当SNSPD的电学时间常数τe小于热学时间常数τth时,电流回流过快,会使得有阻区被钳制在一个稳定的状态,SNSPD无法自动回复到完全超导的初态(如图 6c所示),电流无法完全回流纳米线,纳米线无法连续地探测光子(即SNSPD无法工作在自由运行模式(free-running mode)),这种现象被称为闭锁(latching)。当纳米线的动能电感过小,或者增加与纳米线串联的电阻Rs且阻值过大,电学时间常数τe都会变得过小以至于发生闭锁。由此可见,热学时间常数τth设定了SNSPD运行速度的上限。
在1维热电模型之后,有研究者提出了2维热电模型[78],也提出了完全用电路涵盖热电演化物理内涵的仿真电路模拟器(simulation program with integrated circuit emphasis, SPICE)模型[131]。热电模型成功地描述了初始有阻区的热电演化过程、电流的动态转移、时域脉冲的波形(还要考虑到射频放大器的带宽),解释了闭锁[76],也被用于研究纳米线不均匀性所致的时域抖动[105]。
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时域抖动决定了SNSPD测量光子时间的不确定度; 在与光子时间相关的应用中,具有低时域抖动的SNSPD至关重要。比如,基于光子飞行时间激光雷达的测距精度就在很大程度上取决于SNSPD的时域抖动。但是长期以来,人们对产生SNSPD时域抖动的物理因素与机制仅仅停留在电噪声、光纤色散所致的外部时域抖动[100, 103]; 对于器件本身的本征时域抖动只有推算,机制并不知晓。从2016年开始,包括天津大学、美国麻省理工学院(Massachusetts Institnte of Technology, MIT)、美国国家标准与技术研究院(National Institute of Standard and Technology, NIST)、美国喷气推进实验室(Jet Propulation Laboratory, JPL)在内的若干研究小组,对SNSPD的器件时域抖动展开研究,使得产生SNSPD器件时域抖动的物理图景逐渐清晰。
如图 7所示,目前已报道的SNSPD时域抖动机制共有6种:(1)法诺涨落引起的时域抖动[104]; (2)涡旋(反涡旋)渡越引起的时域抖动[102]; (3)涡旋隧穿量子效应引起的时域抖动[107]; (4)纳米线的不均匀性引起的时域抖动[105-106]; (5)纳米线的传输线效应引起的时域抖动[101]; (6)电学噪声引起的时域抖动[100, 103]。
法诺涨落描述了光电探测器吸收单光子或其他单粒子后,吸收的能量在探测器中带电粒子与中性粒子之间的概率性分配过程[132]。法诺涨落引起SNSPD时域抖动的机制为:吸收的光子能量在纳米线中产生的准粒子和泄露到基底产生的声子之间进行分配[104]。因此,沉积在纳米线中的能量会在一个平均值附近以一定的概率分布而涨落。沉积到纳米线上的能量不同,产生的探测时延就不同,使得SNSPD的探测时延具有一定的概率分布,从而导致时域抖动。
涡旋(反涡旋)渡越引起的时域抖动发生在纳米线局部吸收光子之后,开始热电演化阶段之前。利用基于扩散的涡旋进入和渡越模型[74, 123],2017年,天津大学的WU等人提出:由于光子吸收可以发生在纳米线横向上的不同位置,导致了每次光子吸收导致的涡旋进入纳米线和渡越的时间不同,产生不同的探测时延,从而引起时域抖动[102]。但上述研究工作忽略了纳米线吸收光子引起的涡旋-反涡旋拆分过程。2019年, VODOLAZOV等人进一步利用含时Ginzburg-Landau方程计算了纳米线横向不同位置处被光子触发引起的时域抖动[133],补充了涡旋进入和渡越引起时域抖动理论。
量子效应引起的时域抖动[107]发生在纳米线局部吸收光子之后,开始热电演化阶段之前。当SNSPD工作在低偏置电流,光子触发引起涡旋势垒降低但无法降到0以下,但由于热涨落,涡旋仍有一定概率能够越过势垒,进入纳米线,发生渡越,产生概率性的探测事件。在热涨落引起的涡旋进入和渡越过程中,探测时延呈现概率分布,从而引起时域抖动。
纳米线不均匀性引起的时域抖动是指纳米线长度和宽度方向超导能隙参数、宽度与厚度的分布不均匀所引起的时域抖动[105-106]。不均匀性的产生是由于超导薄膜沉积与纳米加工过程中引入的缺陷所致。具有一定空间模式的入射光子在纳米线的不同位置被吸收,不均匀性既会影响初始有阻区的形成过程,也会影响后续的热电演化过程,产生不同的探测时延,引起时域抖动。
传输线效应引起的时域抖动是指光子探测产生的射频输出信号沿着纳米线传输,较长的纳米线应被视为射频传输线,具有一定空间模式的入射光子在纳米线纵向的不同位置被吸收时,射频信号沿纳米线传输引起的时延不同,进而产生了时域抖动[101]。采用双端差分读出电路可以减小传输线效应引起的时域抖动[101]。
此外,电学噪声、光脉冲宽度、测试仪器本身的时域抖动[100, 103],都会引起SNSPD系统的时域抖动,这些外部因素引起的时域抖动统称为SNSPD的非本征时域抖动。
SNSPD的时延概率密度分布呈类似高斯函数的分布,取时间延迟统计直方图的峰值作为时延的具体数值,取时延概率密度分布的半峰全宽作为时域抖动的具体数值。SNSPD总体的时延概率密度分布是各个独立因素引起时延的概率密度分布的卷积。
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SNSPD需要由制冷系统提供低温工作环境。基于多晶态材料(如NbN, NbTiN)的SNSPD,超导转变温度一般比基于非晶态材料(如WSi, MoSi)的SNSPD高,工作温度在2K附近,多采用0.1W小型闭循环GM制冷机制冷。基于小型GM制冷机,中国科学院上海微系统与信息技术研究所、荷兰代尔夫特理工大学、天津大学等单位都实现了SDE高于90%的SNSPD系统[3-4, 6-7, 9]。基于非晶态材料(如WSi, MoSi)的SNSPD,工作温度一般小于1K[2, 5, 8],通常工作在亚开尔文温区的制冷机中,如吸附式[8]、稀释式[254]、绝热去磁式[2],但也有工作在2K温区的非晶态SNSPD的研究工作[156, 255]。表 1中列举了目前文献报道的SDE超过90%的SNSPD系统。
表 1 系统探测效率超过90%的SNSPD系统
制冷机类型 温度/K 材料 波长/nm SDE/% 参考文献 绝热去磁式 0.12 WSi 1550 93 2013年,MARSILI等人[2] GM式 2.1 NbN 1550 90.2 2017年,ZHANG等人[3] GM式 2.5 NbTiN 1310 >92 2017年,ESMAEIL ZADEH等人[4] GM式 2.1 NbTiN 1550 90.1 2018年,LI等人[256] GM式 2.3 NbN 1310 94 2018年,SMIRNOV等人[257] PT式 2.3 NbTiN 940 90.0 2018年,EROTOKRITOU等人[258] 吸附式 0.7 MoSi 1550 96 2019年,REDDY等人[5] GM式 2.2 NbN 1550 92 2019年,ZHANG等人[166] GM式 2.05 NbTiN 1590 91 2020年,MENG等人[7] 吸附式 0.8 NbN 1590 98 2020年,HU等人[6] 吸附式 0.72~0.78 MoSi 1550 98 2020年,REDDY等人[8] GM式 2.5~2.8 NbTiN 1290~1500 94~99.5 2021年,CHANG等人[9] 吸附式 0.84 NbN 1550 92.2 2021年,XU等人[57] PT+JT式 2.4 NbN 1550 93 2021年,HU等人[259] GM式 2.2 NbN 1550 93.7 2021年,GENG等人[260] -
用于SNSPD系统的GM制冷机一般为二级制冷结构,可以给SNSPD提供最低约2K的工作温度,并能够长时间、不间断地工作。常用于SNSPD系统的商用GM制冷机包括日本住友的RDK-101D制冷机[261]、中船重工鹏力(南京)超低温技术有限公司的KDE401SA制冷机[262]。
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GM制冷机在工作时有机械振动,在一些应用场合对光耦合不利。2014年,WANG等人为了减小机械振动,也为了获得更低的工作温度,通过在两级脉管(pulse-tube, PT)制冷机的4K冷头上集成焦耳汤姆逊(Joule-Thomson, JT)阀,配合真空泵形成闭循环JT制冷回路,实现了几乎无振动、最低工作温度为1.62K的闭循环制冷系统[263]。
在深空激光通信、激光雷达等应用场景中,需要对SNSPD系统的SWaP进行综合优化。对于GM制冷机,额定功率为千瓦量级,而为4K温区所提供的制冷功率仅为0.1W,制冷效率较低,体积和重量较大。中国科学院上海微系统与信息技术研究所与中科院理化技术研究所、中国科学院上海技术物理研究所、英国格拉斯哥大学与荷兰Single Quantum、美国NIST等单位提出了多级脉管制冷机或斯特灵(Stirling)制冷机与焦耳汤姆逊制冷机混合制冷的方案[109-112, 259, 264],用来综合优化制冷系统SWaP。表 2中总结了目前文献报道的基于小型化制冷机的SNSPD系统性能,并与基于GM制冷机的SNSPD系统进行对比。
表 2 小型制冷机的性能对比
制冷机类型 尺寸 重量/kg 功耗/W 基础温度/K SDE/% 参考文献 GM 442mm×130mm×226mma,
610mm×383mm×450mmb7.2a
75b1200~1500 2.1 95 2020年,HU等人[6] PT+JT 直径23cm/高32cm 44 321.3 2.4 93 2021年,HU等人[259] SPTc+JT 400mm×460mm×680mm 30 466 1.6d — 2021年,ZHANG等人[264] SPTc+JT — — 390 5.68e — 2019年,DANG等人[112] PT+JT 直径30cm/高50cm 55 319.8 2.8 50 2018年,YOU等人[111] PT+JT — — < 250 2.2d — 2017年,KOTSUBO等人[110] stirling+JT — 56 130W 4.2 20 2017年,GEMMELL等人[109] 注:a—制冷机[261];b—压缩机[261];c—SPT: stirling pulse tube;d—模拟负载(simulated load);e—无负载 图 33展示了中国科学院上海微系统与信息技术研究所与中国科学院理化技术研究所合作提出的PT制冷机与JT制冷机混合制冷的SNSPD系统[111, 259]。如图 33a所示,PT制冷机为二级制冷,一级、二级冷头分别为JT制冷机提供65K、15K的预制冷; JT循环中的高压气体先后经过热交换器1(Hex1)、PT制冷机一级冷头、热交换器2(Hex2)、JT制冷机二级冷头、热交换器3(Hex3)后被预冷至低于4He气体的反转温度(inversion temperature); 由于焦耳汤姆逊效应,4He气体经过JT阀后在蒸发器(evaporator)中液化并吸收热量,对SNSPD模块制冷,经过约40h的降温过程后蒸发器达到2.8K的最低温度。图 33b展示了该混合制冷系统的照片,系统重量为55kg,功耗为319.8W。在2.8K的工作温度下,SNSPD的系统探测效率为50%,时域抖动为48ps。在此基础上,HU等人在2021年对图 33b所示系统进行了小型化设计,实现如图 33c所示更加紧凑的SNSPD系统,并利用该小型化SNSPD系统实现了2.4K的工作温度与93%的SDE[259]。未来,SNSPD系统的轻小型化将拓展SNSPD的应用空间,比如,星载SNSPD系统的实现将会大幅提升深空激光通信中数据的上行速率[15, 265]。
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相比GM制冷机,亚开尔文温区的制冷机价格高、体积和重量大、便携性差,但可以达到更低的工作温度。亚卡尔文温区的制冷系统大致有3类:吸附式[8]、稀释式[254]、绝热去磁式[2]。研究者利用亚卡尔文温区的制冷机来研究SNSPD的器件物理[68, 70]和性能极限[2, 8, 254]。
SNSPD二十年:回顾与展望
Twenty-year research and development of SNSPDs: Review and prospects
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摘要: 21世纪初,GOL’TSMAN等人开启了超导纳米线单光子探测器(SNSPD)这一研究领域。历经整整20年的发展,SNSPD已经成为综合性能优异的单光子探测器,被广泛用于量子与经典的弱光探测。本文从性能指标、器件物理、薄膜材料、器件结构、加工工艺、光学耦合、信号读出、制冷系统、应用演示等9个方面,回顾了过去20年里SNSPD的重要研究进展; 在此基础上,展望和评述了未来可能的研究与发展方向。
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关键词:
- 量子光学 /
- 单光子探测 /
- 超导纳米线单光子探测器 /
- 超导纳米条单光子探测器 /
- 超导电子器件 /
- 量子信息
Abstract: At the beginning of the 21st century, GOL'TSMAN et al. started the research field of superconducting nanowire single photon detector (SNSPD). After researches and developments in the past twenty years, SNSPDs have become a type of single-photon detectors with unprecedented comprehensive performances, and have been applied in quantum and classical faint-light detection. In this paper, the important researches and developments of SNSPDs in the past twenty years were reviewed from the following nine aspects: Performance metrics, device physics, superconducting films, device structures, fabrication, optical coupling, electronic readouts, cryogenic systems, and applications. Then, the future directions for research and development were discussed. -
图 2 SNSPD探测光子的热点模型
a—超导纳米线中通入接近超导纳米线临界电流的偏置电流 b—当超导纳米线吸收光子后,局部区域变成有阻态,该区域被称为“热点” c—当热点附近超导区域内的电流密度超过超导临界电流密度时,整个纳米线横截面变为有阻态,形成初始有阻带 d—电流通过有阻带产生的焦耳热使得有阻带沿纳米线纵向扩大,纳米线阻值上升,进而使得电流转移到与纳米线并联的低阻负载,产生电压 e—纳米线吸收的能量和产生的焦耳热逐渐通过基底耗散,纳米线的有阻区逐渐消失,变回超导态图 2a,偏置电流回流超导纳米线,电压脉冲消失,SNSPD可进行下一次光子探测
图 12 SNSPD的光学结构示意图
a—背入射集成微腔结构的SNSPD示意图[60](版权方:2006 Optical Society of America;已获重印使用许可) b—正入射集成微腔结构的SNSPD示意图[182](版权方:2009 American Institute of Physics;已获重印使用许可) c—正入射集成DBR结构的SNSPD示意图[3](版权方:2017 Science China Press and Springer-Verlag Berlin Heidelberg;已获重印使用许可) d—集成光学纳米天线的SNSPD结构示意图[177](版权方:2009 IEEE;已获重印使用许可) e—集成正面耦合光学纳米天线的SNSPD光学结构示意图[185](版权方:2015 American Chemical Society;已获重印使用许可)
图 15 SNSPD芯片的自准直封装[7]
a—钥匙孔形状的SNSPD芯片光镜照片 b—自准直封装的模块装配示意图 c—自准直封装的模块照片
图 16 基于渐变折射率透镜的芯片封装[210](版权方:2010 Optical Society of America;已获重印使用许可)
a—SNSPD芯片封装的装配示意图 b—封装后的SNSPD模块照片 c—集成渐变折射率透镜的光纤套管示意图(rf: radio frequency; MU: miniature unit; GRIN: gradient-index; SM: single-mode; NA: numerical aperture)
图 17 基于双透镜的多模光纤光耦合[211](版权方:2015 Science China Press and Springer-Verlag Berlin Heidelberg;已获重印使用许可)
a—双透镜光路图 b—基于双透镜耦合的SNSPD封装照片
图 18 基于低温纳米位移台和光纤聚焦器的低温主动耦合模块[61](版权方:2009 Optical Society of America;已获重印使用许可)
图 19 自由空间光耦合装置[169](版权方:2016 Optical Society of America;已获重印使用许可)
a—自由空间光耦合实物图 b—自由空间光耦合示意图
图 25 从SNSPD输出信号中获取光子数信息的两种方案(a/b:从SNSPD输出的前沿斜率中获取光子数信息[220]; c/d: 从SNSPD输出的幅值中获取光子数信息[221])
a—实验装置示意图(版权方:2017 Optical Society of America;已获重印使用许可) b—实验结果(Atten: attenuator; Mod: modulator; FPGA: field-programmable gate array; CW: continuous wave; 版权方:2017 Optical Society of America;已获重印使用许可) c—集成阻抗匹配结构的SNSPD示意图(版权方:2020 American Chemical Society;已获重印使用许可) d—实验结果(Prob: probability; 版权方:2020 American Chemical Society;已获重印使用许可)
图 26 行列复用的SNSPD阵列读出
a—行列复用读出电路示意图[48](圆圈表示SNSPD像元,根据输出脉冲所在的行和列可以得到SNSPD触发单元的位置; 版权方:2019 Optical Society of America;已获重印使用许可) b—行列复用SNSPD阵列的局部光学显微镜照片[48](单个SNPSD像元的光敏区为30μm×30μm; 版权方:2019 Optical Society of America;已获重印使用许可) c—行列复用SNSPD阵列的整体光学显微镜照片[48](阵列面积为1.6mm×1.6mm;版权方:2019 Optical Society of America;已获重印使用许可) d—双层热耦合的行列复用SNSPD阵列的工作原理示意图[233](版权方:2020 American Chemical Society;已获重印使用许可) e—双层热耦合的行列复用SNSPD阵列的两种布局方式[233](版权方:2020 American Chemical Society;已获重印使用许可)
图 29 幅值复用的SNSPD阵列读出
a—1种幅值复用SNSPD阵列的电路示意图[232](版权方:2019 Optical Society of America;已获重印使用许可) b—2像元SNSPD阵列的输出电压脉冲[232](版权方:2019 Optical Society of America;已获重印使用许可) c—2像元SNSPD阵列的输出脉冲的余辉图[232](版权方:2019 Optical Society of America;已获重印使用许可) d—2像元SNSPD阵列输出脉冲幅值的统计直方图[232](版权方:2019 Optical Society of America;已获重印使用许可) e—幅值双端差分SNSPD阵列的等效电路图[228] f—4像元SNSPD阵列差分输出脉冲的仿真结果[228](版权方:2013 American Institute of Physics;已获重印使用许可)
图 30 SNSPD阵列的光学读出[234](版权方:2020 Springer Nature;已获重印使用许可)
图 31 基于SFQ逻辑电路的SNSPD阵列读出[238](版权方:2018 Optical Society of America;已获重印使用许可)
a—基于SFQ逻辑电路的编码电路示意图 b—整体编码模块的光镜照片
图 34 SNSPD在量子光学与经典光学中的应用
a—SNSPD在纠缠光子对表征中的应用演示[52](a1: 实验装置示意图;a2: 实验结果; PMF: polarization-maintaining fiber; SMF: single-mode fiber; RBG: reflection Bragg grating; LPF: long-pass filter; PBS: polarizing beam splitter; NPBS: nonpolarizing beam splitter; PC: polarization controller; HWP: half-wave-plate; QWP: quarter-wave-plate; FPBC: fiber polarizing beam combiner; TAC: time-to-amplitude converter; 版权方:2010 Optical Society of America;已获重印使用许可) b—SNSPD在量子密钥分发中的应用演示[266](BS: beam splitter; IM: intensity modulator; PM: phase modulator; EPC: electrically driven polarization controller; VOA: variable optical attenuator; PW: power meter; FS: fibre stretcher; DWDM: dense wavelength division multiplexer/demultiplexer; EDFA: erbium-doped fibre amplifier; CW: continuous wave; 版权方:2021 Springer Nature;已获重印使用许可) c—“九章”量子计算原型机的实验装置示意图[16](DM: dichromic mirror; PBS: polarization beam splitter; 版权方:2020 American Association for the Advancement of Science;已获重印使用许可) d—SNSPD在激光雷达成像中的应用演示[11](版权方:2020 Springer Nature;已获重印使用许可) e—SNSPD在深空激光通信中的应用演示[15](版权方:2015 Elsevier;已获重印使用许可) f—SNSPD在荧光成像中的应用演示[45](版权方:2020 Optical Society of America;已获重印使用许可) g—SNSPD在神经形态计算中的应用演示示意图[267](SC: superconducting; LED: light emitting diode; Rx: receiver; Tx: transmitter; WG: waveguide; 版权方:2017 American Physical Society;已获重印使用许可)
表 1 系统探测效率超过90%的SNSPD系统
制冷机类型 温度/K 材料 波长/nm SDE/% 参考文献 绝热去磁式 0.12 WSi 1550 93 2013年,MARSILI等人[2] GM式 2.1 NbN 1550 90.2 2017年,ZHANG等人[3] GM式 2.5 NbTiN 1310 >92 2017年,ESMAEIL ZADEH等人[4] GM式 2.1 NbTiN 1550 90.1 2018年,LI等人[256] GM式 2.3 NbN 1310 94 2018年,SMIRNOV等人[257] PT式 2.3 NbTiN 940 90.0 2018年,EROTOKRITOU等人[258] 吸附式 0.7 MoSi 1550 96 2019年,REDDY等人[5] GM式 2.2 NbN 1550 92 2019年,ZHANG等人[166] GM式 2.05 NbTiN 1590 91 2020年,MENG等人[7] 吸附式 0.8 NbN 1590 98 2020年,HU等人[6] 吸附式 0.72~0.78 MoSi 1550 98 2020年,REDDY等人[8] GM式 2.5~2.8 NbTiN 1290~1500 94~99.5 2021年,CHANG等人[9] 吸附式 0.84 NbN 1550 92.2 2021年,XU等人[57] PT+JT式 2.4 NbN 1550 93 2021年,HU等人[259] GM式 2.2 NbN 1550 93.7 2021年,GENG等人[260] 表 2 小型制冷机的性能对比
制冷机类型 尺寸 重量/kg 功耗/W 基础温度/K SDE/% 参考文献 GM 442mm×130mm×226mma,
610mm×383mm×450mmb7.2a
75b1200~1500 2.1 95 2020年,HU等人[6] PT+JT 直径23cm/高32cm 44 321.3 2.4 93 2021年,HU等人[259] SPTc+JT 400mm×460mm×680mm 30 466 1.6d — 2021年,ZHANG等人[264] SPTc+JT — — 390 5.68e — 2019年,DANG等人[112] PT+JT 直径30cm/高50cm 55 319.8 2.8 50 2018年,YOU等人[111] PT+JT — — < 250 2.2d — 2017年,KOTSUBO等人[110] stirling+JT — 56 130W 4.2 20 2017年,GEMMELL等人[109] 注:a—制冷机[261];b—压缩机[261];c—SPT: stirling pulse tube;d—模拟负载(simulated load);e—无负载 -
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