超导纳米线单光子探测器光子响应机制研究进展

张彪; 陈奇; 管焰秋; 靳飞飞; 王昊; 张蜡宝; 涂学凑; 赵清源; 贾小氢; 康琳; 陈健; 吴培亨

doi:10.7498/aps.70.20210652

摘要

超导纳米线单光子探测器(SNSPD)已在量子信息、深空激光通信、激光雷达等众多领域发挥了重要的作用. 虽然SNSPD经过二十年的研究, 但其光子响应本征机制还有待完善. 深入理解与厘清其光子响应过程是研发高性能探测器的前提与关键. 现在较为成熟的超导纳米线单光子探测器响应理论有热点模型和涡旋模型. 但是这两种理论都存在一定的缺陷, 前者存在截止波长, 后者存在尺寸效应, 都需要进一步完善. 超导相位滑移是超导体的内禀性耗散, 有望用于解释超导纳米线单光子探测器的光子响应过程, 形成统一完备的理论. 这三种模型是对SNSPD光子检测理解的不断深入: 热点模型是一种唯象模型, 研究电子-声子等准粒子体系的相互作用; 涡旋模型由Ginzburg–Landau方程和电磁学方程出发, 研究涡旋在超导体中的运动及其带来的超导态耗散; 相位滑移模型是基于量子力学的解释, 研究热扰动和宏观量子隧穿引发的超导态耗散. 本文综述了热点模型、涡旋模型和超导相位滑移的基本概念、发展历史和研究进展, 讨论和对比了这三种理论的特点和发展前景, 为超导纳米线单光子探测器光子检测理论研究提供参考和借鉴.

关键词:

Abstract

Superconducting nanowire single photon detector (SNSPD) plays a significant role in plenty of fields such as quantum information, deep space laser communication and lidar, while the mechanism of the photon response process still lacks a recognized theory. It is prerequisite and essential for fabricating high-performance SNSPD to understand in depth and clarify the photon response mechanism of the SNSPD. As mature theories on the SNSPD response progress, hot-spot model and vortex-based model both have their disadvantages: in the former there exists the cut-off wavelength and in the later there is the size effect, so they both need further improving. The Cut-off wavelength means that the detection efficiency of the SNSPD drops to zero with the increase of light wavelength, which is indicated by the hot-spot model but not yet observed in experiment. The size effect implies that the vortex does not exist in the weak link with the width less than 4.41ξ, where ξ is the GL coherence length. Phase slip is responsible for the intrinsic dissipation of superconductors, which promises to expound the SNSPD photon response progress and to establish a complete theory. This paper reviews and discusses the fundamental conception, the development history and the research progress of the hot-spot models, i.e. the vortex-based model and the superconductor phase slips, providing a reference for studying the SNSPD photon response mechanism.

Keywords:

superconducting single photon detector /
hot-sopt model /
vortex-based model /
phase slip

作者及机构信息

南京大学电子科学与工程学院, 超导电子学研究所, 南京　210023

通信作者: 张蜡宝, lzhang@nju.edu.cn

基金项目: 国家重点研发计划(批准号: 2017YFA0304002)、国家自然科学基金(批准号: 12033002, 62071218, 61521001, 62071214, 61801206, 11227904)、广东省重点领域研究与发展计划(批准号: 2020B0303020001)、江苏省自然科学基金优秀青年基金(BK20200060)、中央高校基础研究基金、江苏省高等学校优势学科建设工程、青年人才引进计划和江苏省“青蓝工程”资助的课题

Authors and contacts

Reaserch Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China

Corresponding author: Zhang La-Bao, lzhang@nju.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2017YFA0304002), the National Natural Science Foundation of China (Grant Nos. 12033002, 62071218, 61521001, 62071214, 61801206, 11227904), the Key-Area Research and Development Program of Guangdong Province, China (Grant No. 2020B0303020001), the Excellent Youth Foundation of Jiangsu Natural Science Foundation, China (Grant No. BK20200060), the Fundamental Research Funds for the Central Universities, the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), the Recruitment Program for Young Professionals, China, the Qing Lan Project and the Jiangsu Provincial Key Laboratory of Advanced Manipulating Technique of Electromagnetic Waves, China.

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施引文献

图 1 热点模型的发展　(a)超导铅膜对激光敏感的实验^[38]. 上方是激光脉冲, 下方是超导铅膜的电阻变化曲线, 可以发现激光辐照时, 铅膜的电阻值突然增加; (b)超导微桥中不同大小的热点温度分布示意图^[39], 超导微桥采用锡膜制备; (c)超导氮化铌薄膜吸收光子时能量的平衡过程^[40]

Fig. 1. The development of hot spot model: (a) The experiment of superconducting lead film which is sensitive to laser^[38]. The curve above is the laser pulse and the curve below is the resistance curve of the superconducting lead film. The resistance of the lead film increases suddenly when laser irradiates on it; (b) temperature distribution of hot spots with different sizes in superconducting microbridge fabricated of tin film^[39]; (c) energy balance of the superconducting niobium nitride film absorbing photons^[40].

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图 2 Gol'tsman等^[9]于2001年首次制备出SNSPD, 将热点模型应用在解释其光子响应,　(a)—(d)分别表示光子入射、热点形成、热点长大、纳米线全部失超

Fig. 2. Gol'tsman et al^[9]. fabricated SNSPD for the first time in 2001, and applied the hot spot model to explain its photon response. (a)–(d) denote photon incidence, hot spot formation, hot spot growth and thoroughly shut down of the nanowire, respectively.

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图 3 涡旋模型的发展 (a), (b)涡旋周围的超导电流分布^[33], (a)单个涡旋将电流挤压到周围, 中间的超导态被抑制, (b)涡旋-反涡旋对, 可能形成于较高的偏置电流; (c), (d)基于涡旋穿越的超导薄膜耗散机制^[45], (c)单涡旋穿越, (d)光子辅助涡旋穿越模型. 两种耗散都可以使SNSPD产生可观测的电压响应; (e)上图表示没有光子时, 涡旋穿越导致暗计数形成; 下图表示光子入射导致局部热点形成, 随后引发涡旋穿越导致响应^[46]

Fig. 3. The development of the vortex-based model: (a), (b) The supercurrent distribution around the vortex^[33], (a) current diverting around the region with depressed superconductivity on the scale of the vortex-core area, (b) closely spaced vortex pair oriented properly in near-critical applied current; (c), (d) sketch of a segment of the strip in the presence of a bias current^[45], (c) a single vortex causes a hot crossing, (d) A single photon creates a hotspot and induces a subsequent hot vortex crossing. Both processes result in detectable voltage in SNSPD; (e) Top: thermally excited vortex crossing and subsequent formation of a normal-state hot belt across the strip width resulting in a dark count. Bottom: an incident photon creates a hot spot across the superconducting strip, followed by the thermally induced vortex crossing^[46].

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图 4 不同理论之间的讨论　(a)探测器层析法得到的SNSPD响应归一化曲线, 不同符号代表了不同的光子数响应模式和不同的入射波长^[48]; (b)热点模型、扩散热点模型和涨落协助模型对实验的拟合结果, 结果显示扩散热点模型具有最好的拟合效果^[48]; (c)不同模型对实验数据的拟合曲线, 结果表明扩散热点模型是最有可能的结果^[35]

Fig. 4. Discussions on various theories: (a) The universial detection curve of SNSPD utilizing the detector tomography, different symbols representing corresponding photon number and wavelength^[48]; (b) the fit of experimental data of the diffusion hotspot model, the normal-core hotspot model and the fluctuation model. It turns out that the diffusion hotspot model fits best to the data^[48]; (c) different models fitting to the experimental data and the diffusion hot spot model turns out to be the most probable one^[35].

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图 5 热激发相位滑移　(a)复变函数Ψ(x)随x的变化. 这是2种可能情况: A点附近, Ψ₁(x)在复平面上环绕一周, Ψ₀(x)没有发生环绕^[36]; (b)两种主要的相位滑移过程: TAPS(蓝色部分, 自由能翻越势垒)和QPS(红色部分, 自由能隧穿势垒); (c)自由能F与波矢k的关系. 当不存在电流时势垒是对称的, 都等于∆F₀. 当有电流在纳米线中流动时, 相位滑移势垒将变得不再对称

Fig. 5. Thermally activated phase slips: (a) The order parameter Ψ(x) which is complex is drawn as a function of position. Two possible confgurations are shown. Near A, Ψ₁(x) makes an excursion round the Argand diagram while Ψ₀(x) does not^[36]; (b) two major processes of phase slip, the TAPS (blue line, the free energy changes it’s quantuam state by jumping over the energy barrier) and the QPS (red line, the free energy changes it’s quantuam state by tunneling to another potential minimum); (c) free energy F and wave vector k. In the absence of bias current, the energy barrier between adjacent energy minima is identical and equal to ∆F₀. The barrier becomes asymmetric at a small current.

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图 6 相位滑移过程的时空变化　(a)幅值变化; (b)是相位变化. 在τ = 0时, 序参量的幅值变为0, 相位发生2π的改变

Fig. 6. Temporal-spacial evolution of the phase slip: (a) Amplitute evolution; (b) phase evolution. The absolute value of the order parameter is suppressed to zero allowing the phase to flip by 2π at τ = 0.

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图 7 CQPS和PSC　(a)超导纳米线的电流存在一个大约为300 µV的临界电压, 这预示着CQPS现象^[67]; (b)相位滑移中心在I-V曲线中的体现, 虚线所对应的电阻值是R_q的整数倍^[67]

Fig. 7. The CQPS and PSC: (a) No current is measured below the critical voltage V_c ≈ 300 µV, and this behaviour is suggestive of the presence of coherent quantum phase slip^[67]; (b) PSC in the I-V curve of the SNSPD. The resistance corresponding to the dotted line is integral multiple of quantum resistance R_q^[67].

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图 8 实验中通过P(I)分布获得Г(I)^[74]

Fig. 8. Acquiring Г(I) by measuring the distribution of P(I)^[74].

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图 9 相位滑移早期实验　(a)Lukens等^[77]在锡晶须上测量的R-T数据, 虚线是根据TAPS公式拟合的结果; (b)在临近T_c的温度测量超导线的I-V曲线, 呈现出双曲正弦关系^[77]; (c)Giordano^[61]首次观察到In超导线的R-T曲线偏离TAPS的行为, 并称之为QPS现象

Fig. 9. Early experiments on phase slip: (a) R-T measurement of the tin whisker, and the dotted line is the result of TAPS fitting^[77]; (b) current-voltage characteristics at fixed temperature. Solid line, V = sinhI/2I₁; closed circles, data points^[77]; (c) Giordano^[61] observed the R-T curve of In nanowire diviated from the TAPS theory for the first time and named this phenomenon quantum phase slip.

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图 10 近期相位滑移实验进展　(a)随着纳米线长度的增加, 相位滑移的频率同时增加, 黑色线是电流源偏置, 灰色是电压源偏置^[81]; (b)铝纳米线I_c的标准差随温度变化明显分为3个区域, 分别对应于QPS、单TAPS和多TAPS过程^[75]; (c)随着外加磁场和电流的改变, Nb纳米线的R-T曲线出现了分离的电阻值, 可能是纳米线的一部分区域产生了相位滑移中心, 而其他区域仍然保持为超导态^[82]

Fig. 10. Current experiments on phase slip: (a) The phase slip rate increases with the increase of length of the nanowire. Black line: current source mode, grey line, voltage source mode^[81]; (b) the standard deviation of the I_c of the Al nanowire is distributed into three distinct temperature zones, corresponding to QPS, single TAPS and multi-TAPS, respectively^[75]; (c) the R-T curves of the Nb nanowire are splitted into different resistance with the change of the current and magnetic field, which may be caused by the phase slip centers emerging in some area of the nanowire^[82].

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图 11 YBCO纳米线中能级量子化现象, 并提出了SNSPD光子探测的相位滑移解释^[84]

Fig. 11. Energy level quantification in the YBCO nanowire, and the phase-slip based photon detection mechanism of SNSPD is proposed^[84].

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表 1 热点模型、涡旋模型、相位滑移模型特点总结

Table 1. The summary of the hot spot model, vortex-based model and phase-slip-based model

模型名称	基本内容	适用范围	特点	不足
热点模型	纳米线吸收光子形成热点, 热点在电流作用下长大, 破坏超导电性	适用于光子波长较短、能量较强的情况	唯象模型, 基于热力学, 理论体系完备	存在截止波长, 但是在实验上并未发现
涡旋模型	光子入射形成涡旋或者VAP, 涡旋穿越纳米线, 破坏超导电性	适用于光子波长较长、能量较弱的情况	基于电磁学理论, 发展较为成熟	存在尺寸效应: 一般认为, 宽度小于4.41ξ的弱连接中不存在涡旋
相位滑移模型	光子入射使相位滑移事件大量发生, 破坏了纳米线的超导电性	从短波到长波光子均适用	基于量子力学, 能解释宽光谱、窄线条的光子响应	发展较晚, 还未形成完备的理论体系

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