Progress on Chip-Based Spontaneous Four-Wave Mixing Quantum Light Sources
基于芯片的自发四波混频量子光源进展
Authors Info & Affiliations
王浩洋,曾强 HTTPS://ORCID.ORG/0000-0001-7994-0633,马海强和袁志良 作者信息和附属机构
王浩洋,曾强 HTTPS://ORCID.ORG/0000-0001-7994-0633,马海强和袁志良 作者信息和附属机构
Advanced Devices & Instrumentation
高级设备与仪器
高级设备与仪器
9 Jan 2024 2024 年 1 月 9 日
Vol 5 第 5 卷
Article ID: 0032 文章编号:0032
Abstract 摘要
Quantum light generated through spontaneous four-wave mixing (SFWM) process in nonlinear materials, such as entangled photon pairs and single photons, is an important resource for various emerging quantum applications. Integrated quantum photonics has enabled the generation, manipulation, and detection of quantum states of light with steadily increasing scale and complexity levels. Importantly, the exploration of on-chip integration has accumulated substantial progresses in recent years toward the realization of low-cost, large-scale quantum photonic circuits. Here, we review the underlying mechanism and discuss state-of-the-art SFWM on-chip quantum light sources fabricated with various structures and materials on chip. Furthermore, we enumerate the most appealing applications of on-chip SFWM such as heralding single-photon source, entangled photon source, and system-level integration.
量子光通过在非线性材料中的自发四波混频(SFWM)过程产生,如缠结光子对和单光子,是各种新兴量子应用的重要资源。集成量子光子学已经实现了光的量子态的产生、操控和检测,并且规模和复杂性不断提高。重要的是,在芯片集成方面的探索在近年来取得了大量进展,为实现低成本、大规模量子光子电路铺平了道路。在此,我们回顾了 SFWM 的基本机制,并讨论了采用各种结构和材料在芯片上制造的最新 SFWM 量子光源。此外,我们列举了芯片上 SFWM 最吸引人的应用,如预报单光子源、缠结光子源和系统级集成。
量子光通过在非线性材料中的自发四波混频(SFWM)过程产生,如缠结光子对和单光子,是各种新兴量子应用的重要资源。集成量子光子学已经实现了光的量子态的产生、操控和检测,并且规模和复杂性不断提高。重要的是,在芯片集成方面的探索在近年来取得了大量进展,为实现低成本、大规模量子光子电路铺平了道路。在此,我们回顾了 SFWM 的基本机制,并讨论了采用各种结构和材料在芯片上制造的最新 SFWM 量子光源。此外,我们列举了芯片上 SFWM 最吸引人的应用,如预报单光子源、缠结光子源和系统级集成。
Introduction 简介
Individual quanta of light as quantum information carriers has exceptional advantages such as low noise, long coherence time, and compatibility with existing communication infrastructures, which have strongly propelled quantum technologies from feasibility studies to practical applications [1]. Its appealing applications, including quantum computation [2,3], imaging [4], quantum metrology [5], and communication [6,7], have profound impacts on the way we calculate, transmit, and store information. For example, ideal single-photon sources can be used to implement unconditionally secure quantum communication [8], and multiparty entangled photon sources can be used to achieve quantum computation [9,10]. Quantum light is often approximated by attenuating a laser beam down to single-photon level, which is termed weak coherent light. Although weak coherent light plays an important role in quantum information processing such as quantum key distribution (QKD) [11,12], it suffers from the multiphoton components, which may lead to information leakage [13,14]. Indeed, developing an ideal quantum light source remains a challenging issue in practical applications.
作为量子信息载体的单个光子具有低噪声、长相干时间和与现有通信基础设施兼容等优异优势,这些优势大大推动了量子技术从可行性研究走向实际应用[1]。其吸引人的应用,包括量子计算[2, 3]、成像[4]、量子测量[5]和通信[6, 7],对我们计算、传输和存储信息的方式产生了深远影响。例如,理想的单光子源可用于实现无条件安全的量子通信[8], 而多方缠绕光子源可用于实现量子计算[9, 10]。量子光通常通过将激光束衰减到单光子水平而近似得到,这称为弱相干光。尽管弱相干光在量子密钥分发等量子信息处理中起重要作用[11, 12], 但它受多光子分量的影响,可能导致信息泄露[13, 14]。事实上,开发理想的量子光源仍然是实际应用中的一个挑战性问题。
作为量子信息载体的单个光子具有低噪声、长相干时间和与现有通信基础设施兼容等优异优势,这些优势大大推动了量子技术从可行性研究走向实际应用[1]。其吸引人的应用,包括量子计算[2, 3]、成像[4]、量子测量[5]和通信[6, 7],对我们计算、传输和存储信息的方式产生了深远影响。例如,理想的单光子源可用于实现无条件安全的量子通信[8], 而多方缠绕光子源可用于实现量子计算[9, 10]。量子光通常通过将激光束衰减到单光子水平而近似得到,这称为弱相干光。尽管弱相干光在量子密钥分发等量子信息处理中起重要作用[11, 12], 但它受多光子分量的影响,可能导致信息泄露[13, 14]。事实上,开发理想的量子光源仍然是实际应用中的一个挑战性问题。
True single photons can be generated through nonlinear processes in materials, including deterministic sources based on semiconductor quantum dots [15] and probabilistic sources via spontaneous parametric down conversion (SPDC) [16] or spontaneous four-wave mixing (SFWM) [17]. Quantum dot sources are advantageous for source purity and brightness, but face severe challenges in practical applications due to their limited spectral tunability, lossy device-to-fiber coupling, and requirement of cryogenic cooling. In contrast, SPDC and SFWM sources are attractive because of their room temperature operation, high quality of generated photon sources, and relatively low preparation and maintenance costs, while the probabilistic nature can be mitigated through spatial and temporal multiplexing techniques [18–20].
真正的单光子可以通过材料中的非线性过程生成,包括基于半导体量子点的确定性源[ 15 ]以及通过自发参量下频转换(SPDC)[ 16 ]或自发四波混频(SFWM)[ 17 ]的概率性源。量子点源在源纯度和亮度方面具有优势,但由于其有限的频谱可调性、设备到光纤耦合损耗以及需要低温冷却而面临严峻挑战。相比之下,SPDC 和 SFWM 源具有室温运行、生成光子源质量高以及相对较低的准备和维护成本的吸引力,同时概率性特征可通过空间和时间复用技术得到缓解[ 18–20 ]。
真正的单光子可以通过材料中的非线性过程生成,包括基于半导体量子点的确定性源[ 15 ]以及通过自发参量下频转换(SPDC)[ 16 ]或自发四波混频(SFWM)[ 17 ]的概率性源。量子点源在源纯度和亮度方面具有优势,但由于其有限的频谱可调性、设备到光纤耦合损耗以及需要低温冷却而面临严峻挑战。相比之下,SPDC 和 SFWM 源具有室温运行、生成光子源质量高以及相对较低的准备和维护成本的吸引力,同时概率性特征可通过空间和时间复用技术得到缓解[ 18–20 ]。
In a nonlinear optical crystal, a two-photon state can be produced through SPDC process in a nonlinear optical crystal, in which the annihilation of a pump photon produces a pair of photons with lower frequency [16], as illustrated in Fig. 1A. This process conserves both energy and momentum, i.e., ωp = ωs + ωi and κp = κs + κi, where ω and κ denote the angular frequency and momentum of the corresponding pump (p), signal (s), and idler (i) photons. Conservation of momentum is also known as phase matching [21]. In order to improve the conversion efficiency, one often chooses to design a quasi-phase matching (QPM) structure, such as periodic polarization or Bragg reflection [22–26], that can substantially increase the interaction length between the photons and the nonlinear material. Quantum light sources based on SPDC have developed rapidly and achieved promising results, such as high photon pair generation rate (PGR) [24] and high signal-to-noise ratio [27].
在一个非线性光学晶体中,可以通过 SPDC 过程在非线性光学晶体中产生双光子态,在此过程中,一个泵浦光子的湮灭产生一对较低频率的光子[16],如图 1A 所示。这个过程同时保持能量和动量守恒,即ωp = ωs + ω和κp = κs + κ,其中ω和κ分别表示对应的泵浦(p)、信号(s)和闲置(i)光子的角频率和动量。动量守恒也被称为相位匹配[21]。为了提高转换效率,人们通常选择设计一个准相位匹配(QPM)结构,如周期极化或布拉格反射[22-26],这可以大大增加光子和非线性材料之间的相互作用长度。基于 SPDC 的量子光源已经快速发展并取得了很好的结果,如高光子对产生率(PGR)[24]和高信噪比[27]。
在一个非线性光学晶体中,可以通过 SPDC 过程在非线性光学晶体中产生双光子态,在此过程中,一个泵浦光子的湮灭产生一对较低频率的光子[16],如图 1A 所示。这个过程同时保持能量和动量守恒,即ωp = ωs + ω和κp = κs + κ,其中ω和κ分别表示对应的泵浦(p)、信号(s)和闲置(i)光子的角频率和动量。动量守恒也被称为相位匹配[21]。为了提高转换效率,人们通常选择设计一个准相位匹配(QPM)结构,如周期极化或布拉格反射[22-26],这可以大大增加光子和非线性材料之间的相互作用长度。基于 SPDC 的量子光源已经快速发展并取得了很好的结果,如高光子对产生率(PGR)[24]和高信噪比[27]。
SFWM is another promising method for obtaining quantum light sources [17,28]. It is a third-order nonlinear process that annihilates two pump photons of respective frequencies of ω1 and ω2 for the creation of two new photons of ω3 and ω4 frequencies with energy conservation ω1 + ω2 = ω3 + ω4, as illustrated in Fig. 1A. Compared to SPDC sources, photons generated through SFWM have similar frequencies to the pump light and it is thus easier to fulfill the phase matching requirement [29]. In particular, fiber-based SFWM sources [30,31] benefit from naturally long interaction length over small mode area, thus having high nonlinear conversion efficiency. Additionally, it avoids coupling loss when integrating into fiber-based communication systems. However, noise generated by spontaneous Raman scattering (SpRS) in the optical fiber is detrimental on the quality of the generated photon pairs. While the SpRS noise can be suppressed through cryogenic cooling [28,32], the solution will substantially increase the implementation cost.
受激四波混频(SFWM)是另一种有前景的量子光源获取方法[17,28]。它是一种三阶非线性过程,消除了分别为ω1 和ω2 的两个泵浦光子,生成了频率为ω3 和ω4 的两个新光子,满足能量守恒ω1 + ω2 = ω3 + ω4,如图 1A 所示。与 SPDC 源相比,通过 SFWM 产生的光子与泵浦光的频率相似,因此更容易满足相位匹配要求[29]。特别是基于光纤的 SFWM 源[30,31]受益于自然较长的相互作用长度和较小的模式面积,具有较高的非线性转换效率。此外,它在集成到基于光纤的通信系统时可避免耦合损耗。然而,光纤中由自发拉曼散射(SpRS)产生的噪声对生成光子对的质量有害影响。虽然 SpRS 噪声可通过低温冷却得到抑制[28,32],但这种解决方案将大大增加实施成本。
受激四波混频(SFWM)是另一种有前景的量子光源获取方法[17,28]。它是一种三阶非线性过程,消除了分别为ω1 和ω2 的两个泵浦光子,生成了频率为ω3 和ω4 的两个新光子,满足能量守恒ω1 + ω2 = ω3 + ω4,如图 1A 所示。与 SPDC 源相比,通过 SFWM 产生的光子与泵浦光的频率相似,因此更容易满足相位匹配要求[29]。特别是基于光纤的 SFWM 源[30,31]受益于自然较长的相互作用长度和较小的模式面积,具有较高的非线性转换效率。此外,它在集成到基于光纤的通信系统时可避免耦合损耗。然而,光纤中由自发拉曼散射(SpRS)产生的噪声对生成光子对的质量有害影响。虽然 SpRS 噪声可通过低温冷却得到抑制[28,32],但这种解决方案将大大增加实施成本。
For the purpose of miniaturization, generating photon pairs on chip has attracted much attention [33–36]. On-chip SFWM sources are most commonly based on silicon waveguides due to the sharp refractive index contrast between silicon core and air cladding, which leads to tight optical confinement and thus strong nonlinearity. With the help of strong χ(3) coefficient in silicon material, it is possible to achieve efficient four-wave mixing over a waveguide of just a centimeter in length [37]. Moreover, silicon-based waveguide has a narrow SpRS spectrum [38], which can be readily rejected through modest optical filtering.
出于小型化的目的,芯片上的光子对生成已引起了广泛关注[33-36]。基于硅波导的芯片上 SFWM 源是最常见的,这是由于硅芯和空气包层之间的折射率反差很大,导致了强光束缩聚,从而产生了强烈的非线性效应。借助硅材料中强大的χ(3)系数,在仅有几厘米长的波导中就能实现有效的四波混频[37]。此外,硅基波导具有很窄的斯托克斯拉曼散射谱[38],通过适度的光学滤波即可轻易地滤除。
出于小型化的目的,芯片上的光子对生成已引起了广泛关注[33-36]。基于硅波导的芯片上 SFWM 源是最常见的,这是由于硅芯和空气包层之间的折射率反差很大,导致了强光束缩聚,从而产生了强烈的非线性效应。借助硅材料中强大的χ(3)系数,在仅有几厘米长的波导中就能实现有效的四波混频[37]。此外,硅基波导具有很窄的斯托克斯拉曼散射谱[38],通过适度的光学滤波即可轻易地滤除。
With the rapid development of on-chip integration technology, photon pair sources with different materials and structures have emerged like a blowout [39]. To track these progresses, we review the recent development on the generation of photon pairs via on-chip SFWM process and their related applications. The structure of this review is organized as follows: In the “Characterization of Four-Wave Mixing Process” section, we describe the principle of on-chip SFWM process. The performance characterization of photon pair sources generated by SFWM under different structures and materials is presented in the “On-Chip SFWM” section. In the “Quantum Light Source and More Applications” section, we introduce photon pairs generated through SFWM as quantum light sources and their applications in more areas. In the “Conclusion and Outlook” section, we briefly review the relevant applications and discuss the challenges and prospects for future development.
随着片上集成技术的快速发展,不同材料和结构的光子对源如雨后春笋般涌现。为跟踪这些进展,我们回顾了最近在片上四波混频过程中生成光子对及其相关应用的发展情况。本综述的结构安排如下:在"四波混频过程的表征"部分,我们描述了片上四波混频过程的原理。在"片上四波混频"部分,介绍了在不同结构和材料下,四波混频生成的光子对源的性能表征。在"量子光源及更多应用"部分,我们介绍了通过四波混频生成的光子对作为量子光源,及其在更多领域的应用。在"结论与展望"部分,我们简要回顾了相关应用,并讨论了未来发展的挑战和前景。
随着片上集成技术的快速发展,不同材料和结构的光子对源如雨后春笋般涌现。为跟踪这些进展,我们回顾了最近在片上四波混频过程中生成光子对及其相关应用的发展情况。本综述的结构安排如下:在"四波混频过程的表征"部分,我们描述了片上四波混频过程的原理。在"片上四波混频"部分,介绍了在不同结构和材料下,四波混频生成的光子对源的性能表征。在"量子光源及更多应用"部分,我们介绍了通过四波混频生成的光子对作为量子光源,及其在更多领域的应用。在"结论与展望"部分,我们简要回顾了相关应用,并讨论了未来发展的挑战和前景。
Characterization of Four-Wave Mixing Process
四波混频过程的表征
SFWM arises from the material third-order nonlinearity (χ(3)) [17]. In this process, two pump photons transform into two daughter photons with different frequencies through interaction with the nonlinear medium. One daughter photon is called signal, and the other is called idler.
源文本: SFWM 源于材料三阶非线性 (χ(3)) [17]。在此过程中,两个泵浦光子通过与非线性介质的相互作用转换为频率不同的两个子光子。一个子光子称为信号,另一个称为闲子。
源文本: SFWM 源于材料三阶非线性 (χ(3)) [17]。在此过程中,两个泵浦光子通过与非线性介质的相互作用转换为频率不同的两个子光子。一个子光子称为信号,另一个称为闲子。
In light of the principles of quantum mechanics, that is, states that describe that the reality can be constructed through finding the Hamiltonian of its interaction and calculating the evolution of its state function, we can derive the two-photon state function in an SFWM process. Considering the coupled wave equation in the classical SFWM theory [21], the Hamiltonian of the interaction can be expressed as [17]
根据量子力学原理,也就是通过确定其相互作用的哈密顿量并计算其状态函数的演化来构建现实的观点,我们可以推导出 SFWM 过程中的双光子状态函数。考虑经典 SFWM 理论[21]中的耦合波方程,相互作用的哈密顿量可表示为[17]
根据量子力学原理,也就是通过确定其相互作用的哈密顿量并计算其状态函数的演化来构建现实的观点,我们可以推导出 SFWM 过程中的双光子状态函数。考虑经典 SFWM 理论[21]中的耦合波方程,相互作用的哈密顿量可表示为[17]
(1)
where β is a constant that is related to experimental details and ϵ0 is the vacuum permittivity. χ(3) is the third-order nonlinear optical susceptibility of the material, and term ∫V dV represents the interaction volume that can be decomposed into Aeff∫z dz, with Aeff being the effective mode field area. is the positive frequency electric field operator, corresponding to the annihilation operator. H.c represents the Hermitian conjugation.
其中β为与实验细节相关的常数,ε0 为真空介电常数。χ(3)为该材料的三阶非线性光学易化率,积分∫V dV 表示相互作用体积,可分解为 Aeff∫z dz,Aeff 为有效模场面积。 为正频率电场算符,对应湮灭算符。H.c 代表厄米共轭。
其中β为与实验细节相关的常数,ε0 为真空介电常数。χ(3)为该材料的三阶非线性光学易化率,积分∫V dV 表示相互作用体积,可分解为 Aeff∫z dz,Aeff 为有效模场面积。
Due to the small scattering probability, the Hamiltonian of the interaction can be treated as a perturbation. Therefore, through first-order perturbation theory, the two-photon state can be expressed as
由于散射概率很小,相互作用的哈密顿量可以被视为扰动。因此,通过一阶扰动理论,双光子态可以表示为
由于散射概率很小,相互作用的哈密顿量可以被视为扰动。因此,通过一阶扰动理论,双光子态可以表示为
(2)
For simplicity, we assume that the pump light is a linearly polarized Gaussian pulse, and that signal and idler photons are co-polarized and co-propagating with the pump. The electric field operator of the pump light can then be expressed as
为了简单起见,我们假设泵浦光是线性偏振的高斯脉冲,信号和闲置光子与泵浦光共轭偏振并共向传播。泵浦光的电场算符可以表示为
为了简单起见,我们假设泵浦光是线性偏振的高斯脉冲,信号和闲置光子与泵浦光共轭偏振并共向传播。泵浦光的电场算符可以表示为
(3)
where e−iγPpz is the self-phase modulation term, σp is the filter bandwidth, is the peak power of the Gaussian pump pulse, and νp = ωp − Ωp. The electric field operators of signal and idler photons can be expressed as [40]
其中 e−iγPpz 是自相位调制项,σp 是滤波带宽, 是高斯泵浦脉冲的峰值功率,以及νp=ωp−Ωp。信号和闲置光子的电场算符可以表示为[ 40]
其中 e−iγPpz 是自相位调制项,σp 是滤波带宽,
(4)
where is the creation operator of signal and idler photons with frequency ωs,i and VQ is the quantization volume. ks,i(ωs, i) = n(ωs,i)ωs,i/c is the wave vector of signal and idler photons. Substituting Eqs. 3, 4, and 1 into Eq. 2, we get the evolution function of the two-photon state
其中 是信号和闲置光子的创建算子,频率为ωs,i,VQ 是量子化体积。 ks,i(ωs, i) = n(ωs,i)ωs,i/c 是信号和闲置光子的波矢。将方程 3、4 和 1 代入方程 2,我们得到双光子态的演化函数。
其中
(5)
where 哪里
is the gain factor and F(ωs, ωi) = α(ωs, ωi)ϕ(ωs, ωi) is the amplitude function of the two-photon joint spectrum, in which α(ωs, ωi) is the pump light spectrum envelope function and ϕ(ωs, ωi) is the phase matching function. Specifically, we have
是增益因子,而 F(ωs, ω) = α(ωs, ω)ϕ(ωs, ω)是两光子联合谱的幅度函数,其中 α(ωs, ω)是泵浦光谱包络函数,ϕ(ωs, ω)是相位匹配函数。具体而言,我们有
是增益因子,而 F(ωs, ω) = α(ωs, ω)ϕ(ωs, ω)是两光子联合谱的幅度函数,其中 α(ωs, ω)是泵浦光谱包络函数,ϕ(ωs, ω)是相位匹配函数。具体而言,我们有
(6)
Here, 这里,
is the phase mismatch factor that is dependent on both dispersion and nonlinearity of the material. Term represents group velocity dispersion (GVP) around the zero dispersion wavelength λ0, and Dslope represents the slope of dispersion parameter D near the zero dispersion wavelength. 2γPp is the term of self-phase modulation of the pump light, where is the nonlinear coefficient of the material. Δ = Ωs − Ωi is the difference between center frequency of signal and idler photon. L is the effective propagation distance.
是依赖于材料色散和非线性的相位失配因子。术语 表示零色散波长λ0 附近的群速度色散(GVD),Dslope 表示色散参数 D 在零色散波长附近的斜率。2γPp 是泵浦光的自相位调制项,其中 是材料的非线性系数。Δ = Ωs − Ω是信号和双频光子中心频率之差。L 是有效传播距离。
是依赖于材料色散和非线性的相位失配因子。术语
We note that Eq. 6 is a result of energy and momentum conservation. For phase matching, when the pump wavelength is near λ0, the GVP term becomes approximately 0, suggesting that phase matching can be met at a low pump power. In the case that the pump wavelength is in anomalous dispersion region, namely, λp > λ0, k′′(Ωp) is negative and phase matching can then be achieved by increasing the value of self-phase modulation term [21]. In addition, large frequency detuning between the generated photon and pump light makes it necessary to set a special QPM structure to meet the requirements of phase matching.
我们注意到式 6 是能量和动量守恒的结果。对于相位匹配,当泵浦波长接近λ0 时,GVP 项大约为 0,这意味着相位匹配可以在较低的泵浦功率下实现。如果泵浦波长在反常色散区,即λp > λ0,k′′(Ωp)为负,则可通过增大自相位调制项的值来实现相位匹配[ 21]。此外,生成光子和泵浦光之间的较大频率偏移使得需要设置特殊的 QPM 结构以满足相位匹配的要求。
我们注意到式 6 是能量和动量守恒的结果。对于相位匹配,当泵浦波长接近λ0 时,GVP 项大约为 0,这意味着相位匹配可以在较低的泵浦功率下实现。如果泵浦波长在反常色散区,即λp > λ0,k′′(Ωp)为负,则可通过增大自相位调制项的值来实现相位匹配[ 21]。此外,生成光子和泵浦光之间的较大频率偏移使得需要设置特殊的 QPM 结构以满足相位匹配的要求。
With the above two-photon state function, we can draw some important parameters to evaluate the performance of a given SFWM photon source: spectral purity, single counting rate ( ), coincidence counting rate (Cc), and coincidence to accidental ratio (CAR). In particular, single counting rate and coincidence counting rate directly represent the efficiency of photon pair generation, while CAR reflects the signal-to-noise ratio of produced two-photon state. Below, we give the detailed analysis and expressions of these key parameters.
根据上述双光子态函数,我们可以得出一些重要参数来评估给定的 SFWM 光子源的性能:光谱纯度、单计数率( )、同时计数率(Cc)和同时计数与偶然计数的比值(CAR)。其中,单计数率和同时计数率直接代表了光子对产生的效率,而 CAR 反映了产生的双光子态的信噪比。下面,我们对这些关键参数进行详细的分析和表达。
根据上述双光子态函数,我们可以得出一些重要参数来评估给定的 SFWM 光子源的性能:光谱纯度、单计数率(
Spectral purity 谱系纯度
For applications such as boson sampling [41] and quantum computing [2,3], it is necessary to generate spectrally pure single photons, which is crucial to achieve high visibility in multiphoton interference experiments.
对于玻色采样[41]和量子计算[2,3]等应用来说,生成光谱纯度高的单光子是必要的,这对于在多光子干涉实验中实现高可见度至关重要。
对于玻色采样[41]和量子计算[2,3]等应用来说,生成光谱纯度高的单光子是必要的,这对于在多光子干涉实验中实现高可见度至关重要。
The two photon states generated by SFWM can be represented by Schmidt decomposition of signal photons and idler photon systems
基于 SFWM 产生的两个光子态可通过信号光子和对目光子系统的 Schmidt 分解来表示
基于 SFWM 产生的两个光子态可通过信号光子和对目光子系统的 Schmidt 分解来表示
(7)
Thus, the purity of daughter photons is defined by the reciprocal of the Schmidt number K [42]
因此,女儿光子的纯度由 Schmidt 数 K 的倒数定义[42]
因此,女儿光子的纯度由 Schmidt 数 K 的倒数定义[42]
(8)
where , and is the density matrix of two photon states.
其中 ,而 是两光子态的密度矩阵。
其中
Therefore, in order to obtain completely pure photons, it can only be achieved in a single Schmidt mode, in which the two-photon state can be written as the product of the signal photon state and the idle frequency photon state
因此,为了获得完全纯净的光子,只能在单个施密特模式下实现,在该模式中,两光子态可以写为信号光子态和空闲频率光子态的乘积 and amplitude function of the two-photon joint spectrum can be written as . Hence, the pure two-photon state can be achieved by making factorable.
双光子联合谱的振幅函数可以写为 。因此,通过使 可分解,可以实现纯双光子态。
因此,为了获得完全纯净的光子,只能在单个施密特模式下实现,在该模式中,两光子态可以写为信号光子态和空闲频率光子态的乘积
(9)
双光子联合谱的振幅函数可以写为
Several approaches can be adopted to improve the purity of two-photon states, including engineering an optimal cross-section of the waveguide and selecting appropriate pump wavelength and bandwidth [43]. It is also possible to use a resonant cavity structure for this purpose [44]. Due to the cavity enhancement, the SFWM signal and idler photons are naturally and independently distributed under a pulsed, broadband resonant pump [45]. With further optimization in the cavity coupling structure, spectral purity close to unit has been reported [46].
提高双光子态纯度的几种方法包括设计最优波导横截面以及选择合适的泵浦波长和带宽[43]。使用共振腔结构也可以实现这一目的[44]。由于共振腔增强效应,在脉冲宽带共振泵浦下,参数下转转换信号和关联光子自然地独立分布[45]。通过进一步优化腔耦合结构,已经报道获得接近单一的频谱纯度[46]。
提高双光子态纯度的几种方法包括设计最优波导横截面以及选择合适的泵浦波长和带宽[43]。使用共振腔结构也可以实现这一目的[44]。由于共振腔增强效应,在脉冲宽带共振泵浦下,参数下转转换信号和关联光子自然地独立分布[45]。通过进一步优化腔耦合结构,已经报道获得接近单一的频谱纯度[46]。
Single counting rate 单次计数率
In the absence of losses and noise photons, the count rate of signal (idler) photons is identical to the PGR as SFWM photons are generated in pairs. Taking signal photons as example (the case for idler photons is similar), the single counting rate can be expressed as [17]
在没有损耗和噪声光子的情况下,信号(闲置)光子的计数率与 SFWM 光子成对产生时的 PGR 相同。以信号光子为例(闲置光子的情况类似),单计数率可表示为[17]
在没有损耗和噪声光子的情况下,信号(闲置)光子的计数率与 SFWM 光子成对产生时的 PGR 相同。以信号光子为例(闲置光子的情况类似),单计数率可表示为[17]
(10)
where A1 is a constant and Isc is a double integral value (detailed process can be found in [17]). σ0 is the filtering bandwidth of the signal photon, and σp is the bandwidth of the pump pulse. As indicated in Eq. 10, the single counting rate depends quadratically on the peak power of the pump. This dependence is useful to determine the severeness of the noise photons in the system, such as SpRS, which scales linearly with the bump power. In addition, the single counting rate is proportional to the ratio of filtering bandwidth to pump bandwidth. On the one hand, this is because as the filtering bandwidth increases, more signal photons are collected. On the other hand, as the pump bandwidth increases, the pulse width decreases, which reduces the interaction time for pump photons.
式中,A1 为常数,Isc 为双重积分值(详细过程见[17])。σ0 为信号光子的滤波带宽,σp 为泵浦脉冲的带宽。如式 10 所示,单计数率随泵浦峰值功率呈二次方依赖关系。这种依赖性有利于确定系统中噪声光子(如 SpRS)的严重程度,该噪声光子与泵浦功率呈线性关系。此外,单计数率与滤波带宽和泵浦带宽的比例成正比。一方面,这是因为滤波带宽增加时,可收集更多信号光子。另一方面,泵浦带宽增加时,脉冲宽度减小,从而减少了泵浦光子的相互作用时间。
式中,A1 为常数,Isc 为双重积分值(详细过程见[17])。σ0 为信号光子的滤波带宽,σp 为泵浦脉冲的带宽。如式 10 所示,单计数率随泵浦峰值功率呈二次方依赖关系。这种依赖性有利于确定系统中噪声光子(如 SpRS)的严重程度,该噪声光子与泵浦功率呈线性关系。此外,单计数率与滤波带宽和泵浦带宽的比例成正比。一方面,这是因为滤波带宽增加时,可收集更多信号光子。另一方面,泵浦带宽增加时,脉冲宽度减小,从而减少了泵浦光子的相互作用时间。
Coincidence counting rate
偶然计数率
A coincidence refers to an event that the signal and idler photon are simultaneously detected. The coincidence rate of an SFWM source can be expressed as [17]
巧合指的是信号光子和闲置光子同时检测到的事件。SFWM 源的巧合率可以表示为 [ 17]
巧合指的是信号光子和闲置光子同时检测到的事件。SFWM 源的巧合率可以表示为 [ 17]
(11)
It can be seen from Eqs. 10 and 11 that both single counting rate and coincidence counting rate exhibit a quadratic dependence on the pump power, which comes from the fact that SFWM requires annihilation of two pump photons. Figure 1C illustrates qualitatively the dependence of the single and coincidence counting rates on the pump power. This is an important difference from an SPDC photon pair source, whose single and coincidence counting rates are linearly dependent on its pump power, as shown in Fig. 1B. This difference can be understood from their respective photon pair generation processes. An SPDC process corresponds to annihilation of a parent photon and creation of a pair of daughter photons.
从等式 10 和 11 可以看出,单计数率和偶然计数率都呈现出对泵浦功率的二次依赖性,这是由于 SFWM 需要消耗两个泵浦光子。图 1C 定性地说明了单计数率和偶然计数率对泵浦功率的依赖关系。这与 SPDC 光子对源有重要区别,后者的单计数率和偶然计数率线性依赖于其泵浦功率,如图 1B 所示。这种差异可从它们各自的光子对生成过程理解。SPDC 过程对应于一个母光子的湮灭和一对女儿光子的产生。
从等式 10 和 11 可以看出,单计数率和偶然计数率都呈现出对泵浦功率的二次依赖性,这是由于 SFWM 需要消耗两个泵浦光子。图 1C 定性地说明了单计数率和偶然计数率对泵浦功率的依赖关系。这与 SPDC 光子对源有重要区别,后者的单计数率和偶然计数率线性依赖于其泵浦功率,如图 1B 所示。这种差异可从它们各自的光子对生成过程理解。SPDC 过程对应于一个母光子的湮灭和一对女儿光子的产生。
The major difference between single counting rate and coincidence counting rate is the ratio between σ0 and σp. Here, we consider two limit cases [17]. When σ0 ≪ σp, it is equivalent to that the pump has a large frequency bandwidth, and the pump light at each frequency may produce photon pairs. Because of the narrow bandwidth of the filter, only the photon pairs produced by the pump light at a specific frequency can be detected, and the coincidence counting rate is linearly correlated to . On the contrary, when σ0 ≫ σp, the photon pairs generated by the pump light component of any frequency can be detected, so it is linearly correlated to .
单次计数率和 coincidence 计数率之间的主要区别在于σ0 和σp 之间的比率。这里,我们考虑两个极限情况[17]。当σ0≪σp 时,相当于泵浦具有较大的频带宽度,每个频率的泵浦光都可以产生光子对。由于滤波器的带宽较窄,只能检测到特定频率泵浦光产生的光子对,coincidence 计数率与
单次计数率和 coincidence 计数率之间的主要区别在于σ0 和σp 之间的比率。这里,我们考虑两个极限情况[17]。当σ0≪σp 时,相当于泵浦具有较大的频带宽度,每个频率的泵浦光都可以产生光子对。由于滤波器的带宽较窄,只能检测到特定频率泵浦光产生的光子对,coincidence 计数率与
Without noise photons, the coincidence counting rate in the experiment can be simplified as [47]
在没有噪声光子的情况下,实验中的巧合计数率可以简化为[47]
在没有噪声光子的情况下,实验中的巧合计数率可以简化为[47]
(12)
where μ is the number of photon pairs generated per pulse, which is proportional to (γPpL)2 according to Eq. 11. ηs and ηi are the collection efficiencies of signal photon and idler photon, respectively, and R is the repetition rate of pump pulse. From coincidence counting rate, we can obtain the on-chip PGR using
其中μ为每个脉冲产生的光子对数量,根据公式 11 与(γPpL)2 成正比。ηs 和η分别为信号光子和闲置光子的收集效率,R 为泵浦脉冲的重复率。从巧合计数率,我们可以使用
其中μ为每个脉冲产生的光子对数量,根据公式 11 与(γPpL)2 成正比。ηs 和η分别为信号光子和闲置光子的收集效率,R 为泵浦脉冲的重复率。从巧合计数率,我们可以使用
(13)
which represents the rate of photon pairs generated at unit power on chip. PGR allows a direct comparison of different sources’ abilities to generate photon pairs at an identical pump power.
这表示单位功率下芯片上产生的光子对的速率。PGR 允许对不同源产生光子对的能力在相同泵浦功率下进行直接比较。
这表示单位功率下芯片上产生的光子对的速率。PGR 允许对不同源产生光子对的能力在相同泵浦功率下进行直接比较。
Coincidence to accidental ratio
偶然事件与意外事件的比率
In addition to single and coincidence counting rates, CAR is another important figure of merit to parametric conversion source. In the absence of background noise, for photon pair sources generated by spontaneous parametric processes, CAR = 1/μ [48], as shown in Fig. 1D. In order to avoid multiphoton pairs, the pump power is often set such that μ < 0.1. In the presence of channel loss and the detector dark count noise in the experiment, CAR can be expressed as
除了单独和撞击计数率之外,CAR 也是参数转换源的另一个重要性能指标。如图 1D 所示,在没有背景噪声的情况下,对于由自发参数过程产生的光子对源,CAR = 1/μ [ 48]。为了避免多光子对,通常会将泵浦功率设置为 μ < 0.1。在存在信道损耗和探测器暗计数噪声的实验中,CAR 可以表示为
除了单独和撞击计数率之外,CAR 也是参数转换源的另一个重要性能指标。如图 1D 所示,在没有背景噪声的情况下,对于由自发参数过程产生的光子对源,CAR = 1/μ [ 48]。为了避免多光子对,通常会将泵浦功率设置为 μ < 0.1。在存在信道损耗和探测器暗计数噪声的实验中,CAR 可以表示为
(14)
where ds, i is the dark count rate of detectors and τ is the full width at half maximum (FWHM) of coincidence count peak. Owing to optical losses and the detector dark counts, experimentally measured CAR values are typically lower than their theoretical expectations [49].
其中 ds, i 是探测器的暗计数率,τ是偶然计数峰的全宽半高值(FWHM)。由于光学损耗和探测器暗计数,实验测量的 CAR 值通常低于其理论预期值[49]。
其中 ds, i 是探测器的暗计数率,τ是偶然计数峰的全宽半高值(FWHM)。由于光学损耗和探测器暗计数,实验测量的 CAR 值通常低于其理论预期值[49]。
When considering only the channel loss, according to Eq. 12, CAR can be expressed as
当仅考虑信道损失时,根据公式 12,CAR 可以表示为
当仅考虑信道损失时,根据公式 12,CAR 可以表示为
(15)
According to Eq. 15, in the case of obtaining the same level of coincidence counting, CAR increases with the pulse repetition rate, which is ultimately determined by the timing resolution of the single-photon detectors (SPDs) [47]. Therefore, to evaluate the performance of an SFWM photon pair source under pulsed excitation, both the pump power and the repetition frequency must be taken into consideration.
根据等式 15,在获得相同水平的巧合计数的情况下,CAR 随脉冲重复率的增加而增加,这最终由单光子探测器(SPD)的时间分辨率决定[47]。因此,为了评估脉冲激励下 SFWM 光子对源的性能,必须同时考虑泵浦功率和重复频率。
根据等式 15,在获得相同水平的巧合计数的情况下,CAR 随脉冲重复率的增加而增加,这最终由单光子探测器(SPD)的时间分辨率决定[47]。因此,为了评估脉冲激励下 SFWM 光子对源的性能,必须同时考虑泵浦功率和重复频率。
On-Chip SFWM 片上 SFWM
In this section, we review the recent development of photon pair sources generated by on-chip SFWM of different structures and materials. On-chip photon pair sources through SPDC have been reported to achieve excellent performance [24,26,50], but they often require QPM techniques, such as Bragg reflection and periodic polarization poling design of crystals, to meet the phase matching requirement. This brings difficulty in large-scale manufacuring of low-cost SPDC chips [24,26]. In contrast, it is much easier to achieve phase matching for SFWM. Hence, it is advantageous and of particular importance to develop on-chip photon pair sources based on SFWM for the technical feasibility and compatibility with large-scale production.
在本节中,我们回顾了通过不同结构和材料的芯片内四波混频产生的光子对源的最新发展。已经报告了通过芯片内自发参量下转换实现出色性能的光子对源[24、26、50],但通常需要利用相位匹配技术,如布拉格反射和晶体的周期性极化偏转设计,才能满足相位匹配要求。这给低成本自发参量下转换芯片的大规模制造带来了困难[24、26]。相比之下,实现四波混频的相位匹配要容易得多。因此,基于四波混频开发芯片内光子对源对于技术可行性和与大规模生产的兼容性很有优势和重要性。
在本节中,我们回顾了通过不同结构和材料的芯片内四波混频产生的光子对源的最新发展。已经报告了通过芯片内自发参量下转换实现出色性能的光子对源[24、26、50],但通常需要利用相位匹配技术,如布拉格反射和晶体的周期性极化偏转设计,才能满足相位匹配要求。这给低成本自发参量下转换芯片的大规模制造带来了困难[24、26]。相比之下,实现四波混频的相位匹配要容易得多。因此,基于四波混频开发芯片内光子对源对于技术可行性和与大规模生产的兼容性很有优势和重要性。
Various materials and device structures have been exploited to develop on-chip SFWM sources, as summarized in Table 1. A more intuitive summary of the state-of-the-art sources is presented in Fig. 2 in view of CAR versus coincidence. In the next section, we will focus on the relevant properties of different materials and analyze their pros and cons for on-chip SFWM sources.
各种材料和器件结构已被开发用于芯片上 SFWM 源,如表 1 所述。图 2 以 CAR 与偶发性的视角呈现了最新的 SFWM 源概况。在下一部分中,我们将着重分析不同材料的相关特性,并探讨它们在芯片上 SFWM 源方面的优缺点。
各种材料和器件结构已被开发用于芯片上 SFWM 源,如表 1 所述。图 2 以 CAR 与偶发性的视角呈现了最新的 SFWM 源概况。在下一部分中,我们将着重分析不同材料的相关特性,并探讨它们在芯片上 SFWM 源方面的优缺点。
Material 材料 | Structure 结构 | Excitation type (CW/pulse) 激励类型 (连续波/脉冲) | Repetition 重复 | PGR (pairs/s/mW2) 配对率(对/秒/毫瓦) | CAR | Detected pairs (pump power) 检测到的配对(泵功率) |
---|---|---|---|---|---|---|
Si 是 | Waveguide [83] 波导[83] | CW | - | 0.076 MHz 0.076 兆赫 | 673 | 22 kHz (10 mW) 22 kHz (10 毫瓦) |
Spiral waveguide [84] 螺旋波导 [84] | Pulse 脉搏 | 500 MHz 500 兆赫 | 403 MHz 403 兆赫兹 | 8 | 300 kHz (0.14 mW) 300 千赫 (0.14 毫瓦) | |
Microring [93] 微环形[ 93] | CW | - | 149 MHz 149 兆赫 | 12,105 | 5 kHz (0.06 mW) 5 千赫兹 (0.06 毫瓦) | |
Microdisk [152] 微型磁盘[152] | CW | - | 133.6 MHz 133.6 兆赫 | 1,386 | 11 Hz (0.08 mW) | |
PhC waveguide [104] PhC 波导[104] | Pulse 脉搏 | 50 MHz | 76.7 MHz 76.7 兆赫 | 329 | 48 Hz (0.18 mW) 48 赫兹 (0.18 毫瓦) | |
Hydex 海德克斯 | Microring [153] 微环 [ 153] | CW | - | 0.682 kHz 0.682 千赫 | 11 | 48.4 Hz (21 mW) 48.4 赫兹 (21 毫瓦) |
Si3N4 硅 3 氮 | Waveguide [49] 波导[49] | Pulse 脉搏 | 50 Mhz 50 兆赫 | 18 kHz 18 千赫 | 16 | 1.6 kHz (3.2 mW) 1.6 千赫兹 (3.2 毫瓦) |
Microring [61] 环形微腔 [ 61] | CW | - | 2.9 MHz 2.9 兆赫 | 3,780 | 18.4 kHz (0.5 mW) 18.4 千赫兹(0.5 毫瓦) | |
USRN | Waveguide [66] 波导[66] | Pulse 脉搏 | 20 MHz | 15.9 MHz 15.9 兆赫 | 7 | 1.8 Hz (0.17 mW) 1.8 赫兹(0.17 毫瓦) |
InP | Microring [67] 微环 [ 67] | CW | - | 145 MHz 145 兆赫 | 277 | 112.1 Hz (0.022 mW) 112.1 赫兹(0.022 毫瓦) |
GaInP 砷化镓铟磷 | PhC waveguide [68] 声子通道[68] | Pulse 脉搏 | 50 MHz | 34 kHz 34 千赫 | 63 | 4.5 Hz (0.35 mW) 4.5 赫兹 (0.35 毫瓦) |
AlGaAs 砷化镓(AlGaAs) | Waveguide [69] 波导[ 69] | CW | - | 96 kHz 96 千赫 | 21 | 11.8 kHz (0.35 mW) 11.8 千赫兹(0.35 毫瓦) |
Microring [70] 微环 [ 70] | CW | - | 20 GHz | 4,389 | 2.0Hz (0.027 mW) |
表 1.不同材料和不同结构下源性能的总结(在本表中,功率是芯片上泵的平均功率)
Semiconductor material platform
半导体材料平台
Unlike SPDC relying upon second-order nonlinear effect, SFWM is a third-order nonlinear process that can occur in crystals also with center symmetry. As a result, a broader set of materials is suitable for generating photon pairs through SFWM. Currently, notable platforms include silicon on insulator (SOI), silicon nitride (Si 3N4), Hydex, AlGaAs, and several other III-V semiconductor materials [33,34]. Table 2 lists the relevant characteristics of commonly used materials.
与依赖于二阶非线性效应的 SPDC 不同,SFWM 是一种三阶非线性过程,也可以在具有中心对称性的晶体中发生。因此,通过 SFWM 产生光子对的材料范围更广。目前,值得注意的平台包括硅基绝缘体(SOI)、硅氮化物(Si 3N4)、Hydex、AlGaAs 以及其他几种 III-V 半导体材料[33,34]。表 2 列出了常用材料的相关特性。
与依赖于二阶非线性效应的 SPDC 不同,SFWM 是一种三阶非线性过程,也可以在具有中心对称性的晶体中发生。因此,通过 SFWM 产生光子对的材料范围更广。目前,值得注意的平台包括硅基绝缘体(SOI)、硅氮化物(Si 3N4)、Hydex、AlGaAs 以及其他几种 III-V 半导体材料[33,34]。表 2 列出了常用材料的相关特性。
Material 材料 | χ(3) (cm2/W) | Transmission loss (dB/cm) 传输损耗(dB/cm) | Refractive index 折射率 | Bandgap (nm) 带隙(纳米) | Thermo-optic coefficient (K−1) 热光系数 (K−1) |
---|---|---|---|---|---|
Si 是 | 6.5 × 10−14 | 1.5 | ∼3.4 | 1,100 | 1.8 × 10−4 |
Si3N4 硅 3 氮 | 2.5 × 10−15 | 0.2 | ∼2.0 | 238 | 1.7 × 10−5 |
USRN | 2.8 × 10−13 | 6 | ∼3.5 ~3.5 | 590 | - |
InP | 1.1 × 10−13 | - | ∼3.2 | 922 | 2.01 × 10−5 |
Hydex 海德克斯 | 1.15 × 10−15 | 0.06 | ∼1.7 | - | - |
AlGaAs 砷化镓(AlGaAs) | 2.6 × 10−13 | 3 | ∼3.4 | 570–873 | 2.3 × 10−4 |
LiNbO3 氧化铌锂 | 5.3 × 10−15 | 0.6 | ∼2.1 | 310 | - |
表 2. 不同半导体材料平台特性概要(值在 1.55 μm 和室温下)
Among the above listed materials, SOI platform is complementary metal oxide semiconductor (CMOS) compatible and has already had a vast library of developed optical components including filters [51–53], phase modulators [54,55], and beam splitters [56]. Naturally, it has become the most explored platform for SFWM photon pair generation. However, the generation rate is limited by both its relatively high waveguide propagation loss (about several dB/cm) [57] and, more detrimentally, nonlinear losses arising from two-photon absorption (TPA) and/or free carrier absorption (FCA) [58] that cause saturation at a modest pump power [37,59].
在上述材料中,SOI 平台与互补金属氧化物半导体(CMOS)兼容,并已经拥有了包括滤波器[51-53]、相位调制器[54,55]和光束分割器[56]在内的大量已开发的光学元件库。自然,它已成为 SFWM 光子对生成的最广泛研究的平台。然而,其生成速率受到相对较高的波导传播损耗(约几 dB/cm)[57]以及更为严重的由两光子吸收(TPA)和/或自由载流子吸收(FCA)引起的非线性损耗[58]的限制,这些损耗会在较低的泵浦功率下导致饱和[37,59]。
在上述材料中,SOI 平台与互补金属氧化物半导体(CMOS)兼容,并已经拥有了包括滤波器[51-53]、相位调制器[54,55]和光束分割器[56]在内的大量已开发的光学元件库。自然,它已成为 SFWM 光子对生成的最广泛研究的平台。然而,其生成速率受到相对较高的波导传播损耗(约几 dB/cm)[57]以及更为严重的由两光子吸收(TPA)和/或自由载流子吸收(FCA)引起的非线性损耗[58]的限制,这些损耗会在较低的泵浦功率下导致饱和[37,59]。
To suppress TPA and FCA effects, incorporation of organic materials into silicon waveguides was proposed, with a theoretical simulation showing that a silicon-organic hybrid waveguide allows a much higher saturation pump power than SOI [60]. However, this scheme is yet to be experimentally demonstrated.
为抑制 TPA 和 FCA 效应,将有机材料掺入硅波导被提出,理论模拟显示硅-有机杂化波导允许比 SOI 更高的饱和泵浦功率[ 60 ]。但是,这种方案尚未得到实验验证。
为抑制 TPA 和 FCA 效应,将有机材料掺入硅波导被提出,理论模拟显示硅-有机杂化波导允许比 SOI 更高的饱和泵浦功率[ 60 ]。但是,这种方案尚未得到实验验证。
Silicon nitride is another CMOS-compatible material with low transmission loss. Its relatively high thermal stability makes it highly competitive for constructing microring devices with wavelength stability [61,62]. In addition, its large bandgap (238 nm) eliminates the effect of TPA at telecom wavelengths [62]. However, its relatively low third-order nonlinearity limits the brightness as an SFWM light source. Due to the spectral overlap between SpRS and SFWM in silicon nitride platform [63], a relatively high level of uncorrelated photons will mix into the generated photon pairs, resulting in an approximately one order of magnitude reduction in the measured CAR from the corresponding theoretical value [49]. Combining the characteristic of high nonlinearity and high bandgap, ultra-silicon-rich nitride (USRN) is newly proposed, which has a large third-order nonlinear coefficient [64,65], and can overcome nonlinear loss. However, its fabrication process is yet to be fully developed to reduce its presently considerable waveguide propagation losses [66].
氮化硅是另一种 CMOS 兼容材料,具有低传输损耗。其相对较高的热稳定性使其在构建具有波长稳定性的微环装置方面具有很强的竞争力[61,62]。此外,其较大的带隙(238 nm)消除了在电信波长下 TPA 的影响[62]。然而,其相对较低的三阶非线性限制了其作为 SFWM 光源的亮度。由于硅酰氮平台上 SpRS 和 SFWM 的光谱重叠[63],大量不相关的光子会混入产生的光子对中,导致测量的 CAR 比相应的理论值降低约一个数量级[49]。结合高非线性和高带隙的特性,新近提出的超硅富氮化物(USRN)具有较大的三阶非线性系数[64,65],可克服非线性损耗。然而,其制造工艺尚未完全成熟,以减少目前相当大的导波传播损耗[66]。
氮化硅是另一种 CMOS 兼容材料,具有低传输损耗。其相对较高的热稳定性使其在构建具有波长稳定性的微环装置方面具有很强的竞争力[61,62]。此外,其较大的带隙(238 nm)消除了在电信波长下 TPA 的影响[62]。然而,其相对较低的三阶非线性限制了其作为 SFWM 光源的亮度。由于硅酰氮平台上 SpRS 和 SFWM 的光谱重叠[63],大量不相关的光子会混入产生的光子对中,导致测量的 CAR 比相应的理论值降低约一个数量级[49]。结合高非线性和高带隙的特性,新近提出的超硅富氮化物(USRN)具有较大的三阶非线性系数[64,65],可克服非线性损耗。然而,其制造工艺尚未完全成熟,以减少目前相当大的导波传播损耗[66]。
Quantum light sources based on CMOS-incompatible semiconductor materials have also been demonstrated, including InP [67], GaInP [68], and AlGaAs [69,70]. Among them, AlGaAs material has attracted the greatest attention due to its high third-order nonlinearity as well as its ability to mitigate the TPA impact by adjusting the Al concentration and thus the alloy bandgap [71]. Promisingly, an AlGaAs microring has been reported to achieve a high PGR of 20 GHz/mW2, which is more than two orders of magnitude higher than the same structure of silicon. However, a system-level demonstration for quantum information processing remains elusive on this platform due to its CMOS incompatibility and lack of well-developed optical components.
基于 CMOS 不兼容半导体材料的量子光源也已得到了证明,包括 InP[67]、GaInP[68]和 AlGaAs[69,70]。其中,AlGaAs 材料由于其高三阶非线性以及通过调整铝浓度和合金带隙来缓解 TPA 影响的能力[71],受到了最大的关注。值得注意的是,一个 AlGaAs 微环谐振器已报告实现了 20 GHz/mW2 的高 PGR,这比同样结构的硅高两个数量级。然而,由于其与 CMOS 不兼容以及缺乏成熟的光学元件,在量子信息处理系统级演示方面仍然缺乏。
基于 CMOS 不兼容半导体材料的量子光源也已得到了证明,包括 InP[67]、GaInP[68]和 AlGaAs[69,70]。其中,AlGaAs 材料由于其高三阶非线性以及通过调整铝浓度和合金带隙来缓解 TPA 影响的能力[71],受到了最大的关注。值得注意的是,一个 AlGaAs 微环谐振器已报告实现了 20 GHz/mW2 的高 PGR,这比同样结构的硅高两个数量级。然而,由于其与 CMOS 不兼容以及缺乏成熟的光学元件,在量子信息处理系统级演示方面仍然缺乏。
Lithium niobate (LiNbO3) is a widely used material platform for integrated quantum photonics because of its high second-order nonlinearity and large electro-optic effect [72]. However, its modest third-order nonlinearity makes it unattractive to generate photon pairs through SFWM. So far, most applications uses its SPDC processes to generate photon pairs [24,50]. To combine advantages of different material platforms, heterogeneous integration has been proposed as a way forward [73–76]. It not only reduces costs but also achieves better performance compared to components based on individual materials [77,78].
氮化锂(LiNbO3)是一种广泛应用于集成量子光子学的材料平台,因其具有高二阶非线性和大电光效应[72]。然而,其适度的三阶非线性使其无法通过四波混频来发生光子对[24,50]。到目前为止,大多数应用都使用其 SPDC 过程来产生光子对[24,50]。为了结合不同材料平台的优势,异构集成被提出为一条前进的道路[73-76]。它不仅降低了成本,而且与基于单一材料的组件相比,还能获得更好的性能[77,78]。
氮化锂(LiNbO3)是一种广泛应用于集成量子光子学的材料平台,因其具有高二阶非线性和大电光效应[72]。然而,其适度的三阶非线性使其无法通过四波混频来发生光子对[24,50]。到目前为止,大多数应用都使用其 SPDC 过程来产生光子对[24,50]。为了结合不同材料平台的优势,异构集成被提出为一条前进的道路[73-76]。它不仅降低了成本,而且与基于单一材料的组件相比,还能获得更好的性能[77,78]。
Waveguide structures 波导结构
On above material platforms, a variety of waveguide structures have been explored for photon pair generation. In this subsection, we review three most important structures: plain waveguide, microring, and photonic crystal (PhC) waveguide. Among them, microring and PhC structures possess desirable characteristics, e.g., narrow spectral bandwidth, that are not possible with plain waveguides [79].
在上述材料平台上,已探索了各种波导结构用于光子对生成。在这一小节中,我们回顾了三种最重要的结构:普通波导、微环和光子晶体(PhC)波导。其中,微环和 PhC 结构具有窄频带等理想特性,这是普通波导所无法实现的[ 79 ]。
在上述材料平台上,已探索了各种波导结构用于光子对生成。在这一小节中,我们回顾了三种最重要的结构:普通波导、微环和光子晶体(PhC)波导。其中,微环和 PhC 结构具有窄频带等理想特性,这是普通波导所无法实现的[ 79 ]。
Plain waveguide 平面波导
Since waveguide-based SFWM theory first introduced in 2006 [37], a variety of materials and structures have been explored. As the simplest structure on-chip, a plain, straight SOI waveguide of 9.11 mm in length was pioneered in 2006 for photon pair generation under 50-MHz pulsed excitation [80]. Pulsed excitation allows for higher energy density and hence higher coincidence counting rates [81,82], and this partially compensated for the large chip-fiber coupling loss and poor detection efficiency of the detectors available at the time. With rapid advances of preparation processes and photonic integration technologies, the pair generation rate in SOI waveguides has now reached 0.076 MHz/mW2, with a CAR of up to 673 [83] even under continuous-wave excitation. The spiral design of waveguide structures allows a long interaction distance without expanding the device footprint and has therefore been extensively studied [84–86].
自从 2006 年[37]首次引入基于波导的 SFWM 理论以来,已经探索了各种各样的材料和结构。作为最简单的片上结构,2006 年曾开创性地使用长度为 9.11 mm 的直线 SOI 波导生成光子对,在 50 MHz 的脉冲激励下进行[80]。脉冲激励可以产生更高的能量密度,从而获得更高的偶然计数率[81,82],这在一定程度上弥补了当时可用探测器的大芯片-光纤耦合损耗和较低的检测效率。随着制备工艺和光集成技术的快速进步,在连续波激励下,SOI 波导中的对偶生成率已经达到 0.076 MHz/mW2,CAR 高达 673[83]。螺旋波导结构可以实现长的相互作用距离而不扩大设备占用面积,因此得到了广泛的研究[84-86]。
自从 2006 年[37]首次引入基于波导的 SFWM 理论以来,已经探索了各种各样的材料和结构。作为最简单的片上结构,2006 年曾开创性地使用长度为 9.11 mm 的直线 SOI 波导生成光子对,在 50 MHz 的脉冲激励下进行[80]。脉冲激励可以产生更高的能量密度,从而获得更高的偶然计数率[81,82],这在一定程度上弥补了当时可用探测器的大芯片-光纤耦合损耗和较低的检测效率。随着制备工艺和光集成技术的快速进步,在连续波激励下,SOI 波导中的对偶生成率已经达到 0.076 MHz/mW2,CAR 高达 673[83]。螺旋波导结构可以实现长的相互作用距离而不扩大设备占用面积,因此得到了广泛的研究[84-86]。
Despite high third-order nonlinear coefficients and mature fabrication process, the brightness of photon pairs by SOI devices remains limited because of the saturation of their effective pump power due to the nonlinear loss, such as TPA/FCA effects [37]. To overcome these limitations, other material platforms were aggressively explored. Silicon nitride allows a much lower waveguide propagation loss than silicon [62,87] and unaffected by TPA and FCA, thus allowing for higher excitation power. In addition, with higher χ(3) nonlinear coefficient, SFWM effect in AlGaAs waveguides under a continuous-wave pump was reported to promise a higher PGR than SOI [44,88].
尽管具有高三阶非线性系数和成熟的制造工艺,但由于非线性损耗(如 TPA/FCA 效应)导致有效泵浦功率饱和,硅光子集成设备的光子对亮度仍然受到限制。为了克服这些限制,其他材料平台被积极探索。与硅相比,硅氮化物具有更低的波导传播损耗[ 62, 87]且不受 TPA 和 FCA 的影响,因此可以使用更高的激发功率。此外,由于具有更高的 χ(3) 非线性系数,在连续波泵浦下,AlGaAs 波导中的 SFWM 效应被报告能够提供比硅光子集成设备更高的光子产生速率[ 44, 88]。
尽管具有高三阶非线性系数和成熟的制造工艺,但由于非线性损耗(如 TPA/FCA 效应)导致有效泵浦功率饱和,硅光子集成设备的光子对亮度仍然受到限制。为了克服这些限制,其他材料平台被积极探索。与硅相比,硅氮化物具有更低的波导传播损耗[ 62, 87]且不受 TPA 和 FCA 的影响,因此可以使用更高的激发功率。此外,由于具有更高的 χ(3) 非线性系数,在连续波泵浦下,AlGaAs 波导中的 SFWM 效应被报告能够提供比硅光子集成设备更高的光子产生速率[ 44, 88]。
Microring resonator 微环谐振器
While plain waveguides can generate photon pairs at high rates and with high CAR, microring resonator has become an important option for integrated photon pair sources because of its resonance enhancement effect and compact device footprint. In addition, due to the wavelength selection property, resonance microring devices offer significantly improved spectral purity compared to plain waveguides.
虽然普通波导可以产生高速率和高 CAR 的光子对,但微环谐振器由于其共振增强效应和紧凑的器件尺寸,已成为集成光子对源的重要选择。此外,由于具有波长选择特性,共振微环器件相比普通波导具有明显改善的谱纯度。
虽然普通波导可以产生高速率和高 CAR 的光子对,但微环谐振器由于其共振增强效应和紧凑的器件尺寸,已成为集成光子对源的重要选择。此外,由于具有波长选择特性,共振微环器件相比普通波导具有明显改善的谱纯度。
Feasibility of generating correlated photon through SFWM effect in microrings has been proposed [44] and experimentally verified [89]. For microring resonant structures, the PGR via SFWM can be expressed as [44,88]
在微环中通过 SFWM 效应产生相关光子的可行性已被提出[44]并得到实验验证[89]。对于微环共振结构,通过 SFWM 的 PGR 可以表达为[44,88]
在微环中通过 SFWM 效应产生相关光子的可行性已被提出[44]并得到实验验证[89]。对于微环共振结构,通过 SFWM 的 PGR 可以表达为[44,88]
(16)
where γ is the nonlinear coefficient of the material, ωp is the angular frequency of the pump light, R is the radius of the microring, and vg is the group velocity. represents the enhancement factor of the microring for the light field on-resonance under critical coupling condition, which is a function of the cavity quality factor Q of the microring. Therefore, for microring structures, the joint spectral intensity of the generated photon pairs is different from that of nonresonant structures, which is a broad spectrum of continuous distribution. Due to the resonance enhancement by the microring, the brightness of the photons of on-resonance wavelength is much greater than that of off-resonance wavelength, resulting in a discrete spectral distribution.
其中γ是材料的非线性系数,ωp 是泵浦光的角频率,R 是微环的半径,vg 是群速度。 代表微环在临界耦合条件下对光场的增强因子,这是微环腔质量因子 Q 的函数。因此,对于微环结构,生成光子对的联合光谱强度与非共振结构不同,呈现连续分布的宽频谱。由于微环的共振增强,共振波长处光子的亮度远大于非共振波长,导致离散的光谱分布。
其中γ是材料的非线性系数,ωp 是泵浦光的角频率,R 是微环的半径,vg 是群速度。
SOI is the most popular platform for manufacturing microring structures [88,90–92]. Cavity enhancement makes it possible to achieve efficient photon pair generation at an extremely low pump power. This has helped the demonstration of a record CAR of 12,000 achieved in SOI platform [93]. However, cavity also amplifies the impact of TPA and FCA effects in silicon [58], leading to saturation of photon pair generation even at a more modest pump power. A partial solution to this problem is to neutralize the pump-induced free carriers by reverse-biasing the microring in a p-i-n structure [94]. Following the theoretical model by Onodera et al. [95], a more radical approach is to use an array of silicon microrings to achieve super-SFWM, similarly to superradiance, which was experimentally verifed recently [96].
硅片上绝缘体(SOI)是制造微环结构最流行的平台[88、90-92]。腔增强使得在极低泵浦功率下实现高效光子对产生成为可能。这有助于在 SOI 平台上实现了 12,000 的创纪录 CAR 值[93]。然而,腔也放大了硅中两光子吸收和自由载流子吸收的影响[58],导致即使在较低泵浦功率下也会出现光子对产生的饱和。部分解决这一问题的方法是通过在 p-i-n 结构中给微环反向偏压来中和泵浦诱导的自由载流子[94]。根据 Onodera 等人的理论模型[95],更激进的做法是使用硅微环的阵列实现超级四波混频,类似于超辐射,这在最近的实验验证中得到证实[96]。
硅片上绝缘体(SOI)是制造微环结构最流行的平台[88、90-92]。腔增强使得在极低泵浦功率下实现高效光子对产生成为可能。这有助于在 SOI 平台上实现了 12,000 的创纪录 CAR 值[93]。然而,腔也放大了硅中两光子吸收和自由载流子吸收的影响[58],导致即使在较低泵浦功率下也会出现光子对产生的饱和。部分解决这一问题的方法是通过在 p-i-n 结构中给微环反向偏压来中和泵浦诱导的自由载流子[94]。根据 Onodera 等人的理论模型[95],更激进的做法是使用硅微环的阵列实现超级四波混频,类似于超辐射,这在最近的实验验证中得到证实[96]。
The relatively high linear loss (∼1.5 dB/cm) [84] of silicon waveguides makes it necessary to develop low-loss material platforms. Silicon nitride is an excellent choice. In addition to low loss, its lower thermo-optical effect makes it more stable compared to silicon-based platforms and allows precise thermal tuning of cavity resonance wavelengths [61,62].
硅波导的相对较高的线性损耗(约 1.5 dB/cm)[84]使得有必要开发低损耗材料平台。氮化硅是一个出色的选择。除了低损耗外,其较低的热光效应使其比基于硅的平台更稳定,并允许精确的热调谐腔体共振波长[61,62]。
硅波导的相对较高的线性损耗(约 1.5 dB/cm)[84]使得有必要开发低损耗材料平台。氮化硅是一个出色的选择。除了低损耗外,其较低的热光效应使其比基于硅的平台更稳定,并允许精确的热调谐腔体共振波长[61,62]。
III-V semiconductor materials with higher third-order nonlinear efficiency than SOI have also received considerable attention recently. Microring resonators made of AlGaAs have been reported to achieve higher PGRs than other materials [70].
近期,与 SOI 材料相比具有更高三阶非线性效率的 III-V 半导体材料也引起了广泛关注。基于 AlGaAs 材料的微环共振器被证明可以实现高于其他材料的 PGR[70]。
近期,与 SOI 材料相比具有更高三阶非线性效率的 III-V 半导体材料也引起了广泛关注。基于 AlGaAs 材料的微环共振器被证明可以实现高于其他材料的 PGR[70]。
A trade-off exists between the heralding efficiency and the generation rate for microring SFWM sources [97], due to the coupling loss from the ring to the channel waveguide. A higher PGR comes at the cost of a lower heralding efficiency. Under commonly used critical coupling conditions, resonators suffer from 3-dB loss on generated photons and the heralding efficiency is halved when used for single-photon generation [98]. Fortunately, using a dual Mach–Zehnder structure equipped with thermal tuning, the generated signal and idler photons can fully couple out of the micoring from the drop end under critical coupling conditions of bump light, thus avoiding the impact of 3-dB loss [46,99]. Moreover, the exiting times of the generated photons can differ dramatically due to the resonance, which can severely deteriorate the simultaneity of the photon pairs. This simultaneity is measured by the full width at the half maximum (FWHM) of the coincidence count peak in the time correlation detection [62] and is proportional to the cavity quality factor Q. A higher Q value corresponds to a wider correlation histogram peak and the poorer simultaneity. We note that in applications that are sensitive to simultaneity such as QKD, which decode information through the arrival times [100], microring SFWM sources may become incompetitive.
微环 SFWM 源的报警效率和产生率之间存在权衡[ 97],这是由于环到通道波导耦合损耗造成的。更高的 PGR 是以更低的报警效率为代价的。在常用的临界耦合条件下,谐振器在生成的光子上损失 3dB,且用于单光子产生时报警效率降低一半[ 98]。幸运的是,使用配备热调谐的双 Mach-Zehnder 结构,在弹波的临界耦合条件下,生成的信号和闲置光子可以完全从微环的 drop 端耦合出来,从而避免了 3dB 损失的影响[ 46,99]。此外,由于共振,生成的光子退出时间可能大不相同,这可能严重恶化光子对的同步性。这种同步性通过时间相关检测中的峰值全宽半高度(FWHM)来度量[ 62],与腔质量因子 Q 成正比。更高的 Q 值对应于更宽的相关直方图峰值,也就意味着同步性更差。我们注意到,对同步性很敏感的应用,如通过到达时间解码信息的 QKD[ 100],微环 SFWM 源可能缺乏竞争力。
微环 SFWM 源的报警效率和产生率之间存在权衡[ 97],这是由于环到通道波导耦合损耗造成的。更高的 PGR 是以更低的报警效率为代价的。在常用的临界耦合条件下,谐振器在生成的光子上损失 3dB,且用于单光子产生时报警效率降低一半[ 98]。幸运的是,使用配备热调谐的双 Mach-Zehnder 结构,在弹波的临界耦合条件下,生成的信号和闲置光子可以完全从微环的 drop 端耦合出来,从而避免了 3dB 损失的影响[ 46,99]。此外,由于共振,生成的光子退出时间可能大不相同,这可能严重恶化光子对的同步性。这种同步性通过时间相关检测中的峰值全宽半高度(FWHM)来度量[ 62],与腔质量因子 Q 成正比。更高的 Q 值对应于更宽的相关直方图峰值,也就意味着同步性更差。我们注意到,对同步性很敏感的应用,如通过到达时间解码信息的 QKD[ 100],微环 SFWM 源可能缺乏竞争力。
Strong spatial confinement of the microring, together with resonance effect, causes an operational drawback. Due to resonance, a very strong optical field can be accumulated in the ring cavity even with a modest input power. Hence, a small change in the input power can result in drastic change in the device temperature and thus cause resonance shift [101]. Therefore, an active temperature feedback mechanism is required to lock the resonant wavelength in order to counteract pump power variation.
微环的强空间限制和共振效应会导致操作缺陷。由于共振,即使输入功率适中,也可在环腔内积累非常强的光场。因此,输入功率的微小变化就可能导致设备温度显著变化,从而造成共振波长漂移[101]。因此需要有一个主动温度反馈机制来锁定共振波长,以抵消泵浦功率的变化。
微环的强空间限制和共振效应会导致操作缺陷。由于共振,即使输入功率适中,也可在环腔内积累非常强的光场。因此,输入功率的微小变化就可能导致设备温度显著变化,从而造成共振波长漂移[101]。因此需要有一个主动温度反馈机制来锁定共振波长,以抵消泵浦功率的变化。
PhC waveguides 光子晶体波导
Slow light effect in PhC structures can be exploited to enhance SFWM efficiency [59,102]. An appropriately designed PhC structure can effectively reduce the group velocity of light propagating inside. In such waveguide, the wavefront of an optical pulse is slowed down by the slow light factor and is then caught up by the latter part of the pulse. As a result, the temporal spectrum is compressed, thereby increasing the energy density of the pulsed light [103]. Compared to ordinary straight waveguides, PhC features miniaturizing devices, low excitation power, and high nonlinear coefficients.
光子晶体结构中的慢光效应可用于提高四波混频效率[59,102]。适当设计的光子晶体结构可有效降低光在其中传播的群速度。在这种波导中,光脉冲的波前由于慢光因子而减慢,然后被后续的脉冲部分赶上。因此,时间光谱被压缩,从而增加了脉冲光的能量密度[103]。与普通直波导相比,光子晶体具有微型化器件、低激励功率和高非线性系数的特点。
光子晶体结构中的慢光效应可用于提高四波混频效率[59,102]。适当设计的光子晶体结构可有效降低光在其中传播的群速度。在这种波导中,光脉冲的波前由于慢光因子而减慢,然后被后续的脉冲部分赶上。因此,时间光谱被压缩,从而增加了脉冲光的能量密度[103]。与普通直波导相比,光子晶体具有微型化器件、低激励功率和高非线性系数的特点。
Slow light enhancement has been demonstrated to offer a higher pair generation rate and benefit from a smaller footprint (in the scale of um) than plain waveguides, but such SOI device suffers from poor coincidence rates because TPA and FCA effects limit the maximally achievable pump power [59,104,105]. Because of its large bandgap, GaInP material can be used to alleviate the pump power saturation by TPA and FCA [68], and thus has a prospect to become an important material platform once its waveguide transmission loss is minimized. To date, fewer demonstrations have been reported using PhC structures to generate photon pairs as compared with plain waveguides. However, its unique advantages of slow light enhancement and compactness make it a strong candidate structure for development of quantum light sources.
慢光增强已被证明可提供更高的光子对产生率,并且受益于比普通波导更小的占地面积(微米级别),但是这种 SOI 器件由于 TPA 和 FCA 效应限制了最大泵浦功率而遭受低同步率的困扰[59,104,105]。由于其较大的带隙,GaInP 材料可用于缓解 TPA 和 FCA 导致的泵浦功率饱和[68],因此一旦其波导传输损耗最小化,就有望成为一个重要的材料平台。到目前为止,与普通波导相比,使用光子晶体结构产生光子对的演示报告较少。然而,其独特的慢光增强和紧凑性优势使其成为开发量子光源的强有力候选结构。
慢光增强已被证明可提供更高的光子对产生率,并且受益于比普通波导更小的占地面积(微米级别),但是这种 SOI 器件由于 TPA 和 FCA 效应限制了最大泵浦功率而遭受低同步率的困扰[59,104,105]。由于其较大的带隙,GaInP 材料可用于缓解 TPA 和 FCA 导致的泵浦功率饱和[68],因此一旦其波导传输损耗最小化,就有望成为一个重要的材料平台。到目前为止,与普通波导相比,使用光子晶体结构产生光子对的演示报告较少。然而,其独特的慢光增强和紧凑性优势使其成为开发量子光源的强有力候选结构。
Quantum Light Source and More Applications
量子光源及其更多应用
While there are numerous applications for on-chip SFWM photon pair sources in quantum computing [109] and quantum communication [100], we focus on heralding single-photon sources and as entangled photon sources in the following two subsections. In the third subsection, we introduce its use in system-level quantum information processing.
虽然芯片上 SFWM 光子对源在量子计算[109]和量子通信[100]领域有许多应用,但我们在以下两个小节重点关注预告单光子源和纠缠光子源。在第三个小节中,我们介绍了它在系统级量子信息处理中的应用。
虽然芯片上 SFWM 光子对源在量子计算[109]和量子通信[100]领域有许多应用,但我们在以下两个小节重点关注预告单光子源和纠缠光子源。在第三个小节中,我们介绍了它在系统级量子信息处理中的应用。
Heralded single-photon source
引导单光子源
As photons are generated in pairs, SPDC or SFWM sources can always be used to produce single photons through heralding, i.e., the detection of one photon indicates the presence of the other [18] (see Fig. 4A). The probability of obtaining heralding event by detecting this other photon is referred to as heralding efficiency, which can be expressed as [106]
由于光子是成对产生的,SPDC 或 SFWM 源始终可用于通过先报的方式产生单光子,即检测到一个光子表示另一个光子的存在[18](见图 4A)。通过检测这个另一个光子获得先报事件的概率称为先报效率,可以表示为[106]
由于光子是成对产生的,SPDC 或 SFWM 源始终可用于通过先报的方式产生单光子,即检测到一个光子表示另一个光子的存在[18](见图 4A)。通过检测这个另一个光子获得先报事件的概率称为先报效率,可以表示为[106]
(17)
where Cc is the coincidence counting rate and are respective single counting rates of the idler and signal photons, as defined previously in the “Characterization of Four-Wave Mixing Process” section.
其中 Cc 是巧合计数率, 为先前在"四波混频过程的表征"部分定义的信号光子和闲置光子的相应单计数率。
其中 Cc 是巧合计数率,
Ideally, heralding efficiency equals to the collection efficiency of signal (idler) photons. In practice, actual measured heralding efficiency is lower than the corresponding collection efficiency, because of the presence of noise counts arising from residual pump light, spontaneous Raman photons and detector dark counts, as well as spectral filtering loss [107]. As shown in Fig. 3, a portion of photon pairs have just one photon within the spectral filter windows and will not contribute to the coincidence. This filtering loss can be mitigated through engineering a source to generate narrowband photons [43], for example, microrings.
理想情况下,引导效率等于信号(闲置)光子的收集效率。实际上,实测的引导效率低于相应的收集效率,这是因为存在噪声计数,包括残余泵浦光、自发拉曼光子和探测器暗计数,以及频谱滤波损耗[107]。如图 3 所示,一部分光子对只有在频谱滤波窗内出现一个光子,不会贡献到同时性计数。这种滤波损耗可以通过设计一个产生窄带光子的光源来缓解[43],例如微环谐振器。
理想情况下,引导效率等于信号(闲置)光子的收集效率。实际上,实测的引导效率低于相应的收集效率,这是因为存在噪声计数,包括残余泵浦光、自发拉曼光子和探测器暗计数,以及频谱滤波损耗[107]。如图 3 所示,一部分光子对只有在频谱滤波窗内出现一个光子,不会贡献到同时性计数。这种滤波损耗可以通过设计一个产生窄带光子的光源来缓解[43],例如微环谐振器。
In additional to heralding efficiency, photon number purity 1 − g(2)(0) is another important parameter to evaluate the quality of a heralded single-photon source. This quantity can be experimentally measured using a setup shown in Fig. 4B. If there is just one photon in the heralded mode, only one of the two detectors behind the beam splitter will register a photon. Therefore, one can use the time-correlated single-photon counting (TCSPC) module to analyze the coincidence counts between detectors to measure the purity of a single photon, which can be expressed as [108]
除了预示效率,光子数纯度 1-g(2)(0)是评估启动单光子源质量的另一个重要参数。可以使用图 4B 所示的设置实验测量这一数量。如果启动模式中只有一个光子,则光束分光器后的两个探测器中只有一个会检测到光子。因此,可以使用时间相关单光子计数(TCSPC)模块分析探测器之间的同时计数,以测量单光子的纯度,表达为[108]
除了预示效率,光子数纯度 1-g(2)(0)是评估启动单光子源质量的另一个重要参数。可以使用图 4B 所示的设置实验测量这一数量。如果启动模式中只有一个光子,则光束分光器后的两个探测器中只有一个会检测到光子。因此,可以使用时间相关单光子计数(TCSPC)模块分析探测器之间的同时计数,以测量单光子的纯度,表达为[108]
(18)
where C1 is the counting rate in SPD 1, C12(3) is the twofold coincidence counting rate between SPD 1 and SPD 2 (SPD 3), and C123 is the threefold coincidence counting rate across all detectors. τ is the relative time delay between SPD 2 and SPD 3. When the measured g(2)(0) < 0.5, the source can be regarded as nonclassical.
其中 C1 是 SPD 1 的计数率,C12(3)是 SPD 1 和 SPD 2(SPD 3)之间的双重巧合计数率,C123 是所有探测器之间的三重巧合计数率。τ是 SPD 2 和 SPD 3 之间的相对时间延迟。当测量的 g(2)(0) < 0.5 时,该源可视为非经典。
其中 C1 是 SPD 1 的计数率,C12(3)是 SPD 1 和 SPD 2(SPD 3)之间的双重巧合计数率,C123 是所有探测器之间的三重巧合计数率。τ是 SPD 2 和 SPD 3 之间的相对时间延迟。当测量的 g(2)(0) < 0.5 时,该源可视为非经典。
As a single-photon source, it is desirable to keep both a low g(2)(0) and a high brightness. However, the g(2)(0) value increases with the source brightness for a heralded single-photon source. Because of the random nature of SFWM processes, simultaneous generation of two photon pairs is equally probable as two pairs generated at separate times. One approach to this problem is to employ either spatial [18] or temporal multiplexing [19,20] to combine weak single-photon sources into a brighter one without deterioration in the single-photon purity. Figure 5A shows a spatial multiplexing scheme based on PhC waveguides. Here, the pump light is split into N ways through a 1 × N beam splitter and excites N× identical SFWM devices, each of which generates photon pairs problematically. To ensure the purity of the multiplexed source, that is, to produce heralded single photons with the same wavelength, the filtering settings of all SFWM components must be set identical. Finally, photons in the heralded mode are actively routed into a single path through a low-loss optical switch. Temporal multiplexing is an alternative method to resolve the conflict between brightness and photon number purity. As shown in Fig. 5B, it increases the source brightness by actively routing heralded single photons of different temporal modes into a single time bin using optical switches and a fiber-based photon storage line.
作为一个单光子源,保持既低的 g(2)(0)又高的亮度是理想的。然而,对于一个预告单光子源,g(2)(0)值随着源亮度的增加而增加。由于 SFWM 过程的随机性,同时产生两对光子与分别产生两对光子同样可能。解决这个问题的一种方法是采用空间[18]或时间多路复用[19,20]来将弱的单光子源组合成一个更亮的单光子源,而不会降低单光子纯度。图 5A 显示了一种基于 PhC 导波管的空间多路复用方案。在这里,泵浦光通过 1×N 光分路器被分成 N 路,并激励 N 个相同的 SFWM 器件,每个器件都会产生成对的光子。为了确保多路复用源的纯度,即产生具有相同波长的预告单光子,所有 SFWM 组件的滤波设置必须相同。最后,预告模式中的光子通过低损耗光学开关被主动引导到单一通路。时间多路复用是解决亮度和光子数纯度冲突的另一种方法。如图 5B 所示,它通过使用光学开关和基于光纤的光子存储线将不同时间模式的预告单光子主动引导到单一时间窗,从而提高了源亮度。
作为一个单光子源,保持既低的 g(2)(0)又高的亮度是理想的。然而,对于一个预告单光子源,g(2)(0)值随着源亮度的增加而增加。由于 SFWM 过程的随机性,同时产生两对光子与分别产生两对光子同样可能。解决这个问题的一种方法是采用空间[18]或时间多路复用[19,20]来将弱的单光子源组合成一个更亮的单光子源,而不会降低单光子纯度。图 5A 显示了一种基于 PhC 导波管的空间多路复用方案。在这里,泵浦光通过 1×N 光分路器被分成 N 路,并激励 N 个相同的 SFWM 器件,每个器件都会产生成对的光子。为了确保多路复用源的纯度,即产生具有相同波长的预告单光子,所有 SFWM 组件的滤波设置必须相同。最后,预告模式中的光子通过低损耗光学开关被主动引导到单一通路。时间多路复用是解决亮度和光子数纯度冲突的另一种方法。如图 5B 所示,它通过使用光学开关和基于光纤的光子存储线将不同时间模式的预告单光子主动引导到单一时间窗,从而提高了源亮度。
Entangled photon pair source
纠缠光子对源
Entangled photon pairs are an important resource in the field of quantum information and find a wide range of applications for quantum communication, quantum computing, quantum measurement, and quantum imaging [110]. Their generation via on-chip SFWM process has advantages in scalability, compactness, and reconfigurability [111]. So far, various degrees of freedom entanglements have been demonstrated, including polarization [112], time bin [113,114], frequency bin [79,115], and transverse mode [116].
纠缠光子对是量子信息领域的一项重要资源,在量子通信、量子计算、量子测量和量子成像等方面有广泛应用[110]。通过片上四波混频(SFWM)过程生成纠缠光子对具有可扩展性、紧凑性和可重构性等优势[111]。目前已经演示了包括偏振[112]、时间窒碍[113,114]、频率窒碍[79,115]和横向模式[116]在内的各种自由度的纠缠。
纠缠光子对是量子信息领域的一项重要资源,在量子通信、量子计算、量子测量和量子成像等方面有广泛应用[110]。通过片上四波混频(SFWM)过程生成纠缠光子对具有可扩展性、紧凑性和可重构性等优势[111]。目前已经演示了包括偏振[112]、时间窒碍[113,114]、频率窒碍[79,115]和横向模式[116]在内的各种自由度的纠缠。
Polarization is the most commonly exploited degree of freedom in photonic entanglement systems. While an individual SFWM source cannot directly generate polarization entanglement like type I or II SPDC processes [117,118], it is possible to entangle photon pairs generated by a pair of identical chips sharing the same pump through on-chip polarization manipulation and subsequent coherent combining [112]. As shown in Fig. 6, when injecting a 45∘ linearly polarized light, the generated two-photon state can be written as . Because this structure utilizes the symmetry between two cascading waveguides, it eliminates the degradation of the polarization state caused by polarization drift and propagation loss of the waveguides [112].
偏振是光子纠缠系统中最常被利用的自由度。尽管单个 SFWM 源不能像 I 型或 II 型 SPDC 过程那样直接产生偏振纠缠[ 117, 118],但通过芯片内偏振操纵和随后的相干组合[ 112],有可能纠缠由两个相同芯片共享同一泵源产生的光子对。如图 6 所示,当注入 45°线性偏振光时,所生成的二光子态可写为 。由于这种结构利用了两个级联波导之间的对称性,因此消除了由于波导偏振漂移和传播损耗导致的偏振状态退化[ 112]。
偏振是光子纠缠系统中最常被利用的自由度。尽管单个 SFWM 源不能像 I 型或 II 型 SPDC 过程那样直接产生偏振纠缠[ 117, 118],但通过芯片内偏振操纵和随后的相干组合[ 112],有可能纠缠由两个相同芯片共享同一泵源产生的光子对。如图 6 所示,当注入 45°线性偏振光时,所生成的二光子态可写为
Time-bin entanglement is robust against environment disturbance owing to the fact that all photons have the same properties in all degrees of freedom other than time. This property makes it ideal for entanglement distribution experiments over long distances [100,119]. As energy-time entanglement can be conveniently generated using simple waveguide structures, it has been widely employed in practical implementations [120,121].
时间-bin 缠结对环境干扰是鲁棒的,因为所有光子在除时间之外的所有自由度上都具有相同的属性。这一性质使其非常适合用于长距离遥测分配实验[100,119]。由于能量-时间缠结可以使用简单的波导结构方便地生成,它已被广泛应用于实际实施中[120,121]。
时间-bin 缠结对环境干扰是鲁棒的,因为所有光子在除时间之外的所有自由度上都具有相同的属性。这一性质使其非常适合用于长距离遥测分配实验[100,119]。由于能量-时间缠结可以使用简单的波导结构方便地生成,它已被广泛应用于实际实施中[120,121]。
Energy-time entangled photon pairs can be verified in two ways. The first is to verify entanglement by nonlocal dispersion compensation effects [100,122], using a setup shown in Fig. 7A. Due to the simultaneity of photons in each generated pair, the detected photon pairs will exhibit strong time correlation provided that they are under the same measurement basis [123].
能量-时间纠缠光子对可以通过两种方式进行验证。第一种是通过非局域色散补偿效应来验证纠缠[100,122],使用图 7A 所示的设置。由于每对生成的光子具有同步性,在相同的测量基础下,检测到的光子对将表现出强时间相关性[123]。
能量-时间纠缠光子对可以通过两种方式进行验证。第一种是通过非局域色散补偿效应来验证纠缠[100,122],使用图 7A 所示的设置。由于每对生成的光子具有同步性,在相同的测量基础下,检测到的光子对将表现出强时间相关性[123]。
The second verification method is through Franson interference experiments to detect violations of Bell’s inequality [124]. The principle of this setup is shown in Fig. 7B. The signal and idler photons generated by continuous light pumping pass through an asymmetric Mach–Zehnder interferometer (AMZI) and then detected by single-photon detectors. Due to the simultaneity of the generated photons, three coincidence peaks appear, where the coincidence peak of the zero time difference corresponds to both photons passing through the long arms ∣L, L〉s,i or short arms ∣S, S〉s,i of interferometer, and the two side peaks correspond to one photon passing through the short arm and the other through the long arm, ∣S, L〉s,i and ∣L, S〉s,i. Due to the indistinguishability of which arm the photon actually passes, a time-bin entangled state is post-selected at the central coincidence peak, which can be expressed as where ϕs+i is the phase introduced at the short arms of the AMZI.
第二种验证方法是通过 Franson 干涉实验来检测贝尔不等式的[124]违背。该设置的原理如图 7B 所示。连续光泵浦产生的信号和闲置光子通过不对称的迈赫-塞尔干涉仪(AMZI)然后被单光子探测器检测。由于产生的光子同时性,出现三个同态峰,其中零时间差的同态峰对应两个光子都通过干涉仪的长臂|L,L>s,i 或短臂|S,S>s,i,而两个旁峰对应一个光子通过短臂,另一个通过长臂|S,L>s,i 和|L,S>s,i。由于光子实际通过哪条臂不可辨别,在中央同态峰上事后选择了一个时间 bin 缠结态,可以表示为 e^(i(ϕs+i)),其中ϕs+i 是 AMZI 短臂引入的相位。
第二种验证方法是通过 Franson 干涉实验来检测贝尔不等式的[124]违背。该设置的原理如图 7B 所示。连续光泵浦产生的信号和闲置光子通过不对称的迈赫-塞尔干涉仪(AMZI)然后被单光子探测器检测。由于产生的光子同时性,出现三个同态峰,其中零时间差的同态峰对应两个光子都通过干涉仪的长臂|L,L>s,i 或短臂|S,S>s,i,而两个旁峰对应一个光子通过短臂,另一个通过长臂|S,L>s,i 和|L,S>s,i。由于光子实际通过哪条臂不可辨别,在中央同态峰上事后选择了一个时间 bin 缠结态,可以表示为 e^(i(ϕs+i)),其中ϕs+i 是 AMZI 短臂引入的相位。
Beyond merely the preparation of entanglement source, the applications of on-chip SFWM have gradually become a hot research topic of current research [125–129]. Recently, relevant work has been reported to dynamically control the polarization [130] or phase [131] in the respective SFWM sources to encode different Bell states, which demonstrates its ability to encode through entangled Bell states. Entanglement-based QKD networks have also been realized with SFWM sources on silicon chips. For example, a reconfigurable entanglement distribution network has been demonstrated by integrating several SFWM sources on the same chip and utilizing the quantum interference between the states generated from them [132–134]. Additionally, applications such as multidimensional entanglement, multiple degrees of freedom entanglement, quantum teleportation, and entanglement swapping were also demonstrated using on-chip SFWM sources [125–129].
除了仅仅准备纠缠源之外,片上自发四波混频(SFWM)的应用逐渐成为当前研究的热点话题[125-129]。最近,有相关工作报告动态控制各自 SFWM 源的偏振[130]或相位[131]来编码不同的贝尔态,这展示了它编码通过纠缠贝尔态的能力。基于纠缠的量子密钥分配(QKD)网络也已通过硅芯片上的 SFWM 源实现。例如,通过在同一芯片上集成多个 SFWM 源并利用它们产生的状态之间的量子干涉,实现了可重构的纠缠分配网络[132-134]。此外,还使用片上 SFWM 源展示了多维纠缠、多自由度纠缠、量子隧穿和纠缠交换等应用[125-129]。
除了仅仅准备纠缠源之外,片上自发四波混频(SFWM)的应用逐渐成为当前研究的热点话题[125-129]。最近,有相关工作报告动态控制各自 SFWM 源的偏振[130]或相位[131]来编码不同的贝尔态,这展示了它编码通过纠缠贝尔态的能力。基于纠缠的量子密钥分配(QKD)网络也已通过硅芯片上的 SFWM 源实现。例如,通过在同一芯片上集成多个 SFWM 源并利用它们产生的状态之间的量子干涉,实现了可重构的纠缠分配网络[132-134]。此外,还使用片上 SFWM 源展示了多维纠缠、多自由度纠缠、量子隧穿和纠缠交换等应用[125-129]。
System-level applications
系统级应用程序
As described in the previous sections, many experiments have been conducted to prepare and distribute entangled states at various degrees of freedom through on-chip SFWM. However, integrating the preparation, manipulation, and measurement modules onto a single chip poses new challenges.
正如前几节所述,已经进行了许多实验来通过芯片上的 SFWM 制备和分发各种自由度的纠缠态。然而,将制备、操纵和测量模块集成到单个芯片上会面临新的挑战。
正如前几节所述,已经进行了许多实验来通过芯片上的 SFWM 制备和分发各种自由度的纠缠态。然而,将制备、操纵和测量模块集成到单个芯片上会面临新的挑战。
On-chip manipulation and measurement of entangled states require both high source brightness and integration of active optical components. Silicon platform, due to its CMOS compatibility, offers a wide availability of optical components for realizing large-scale programmable quantum photonic integrated circuits. On this frontier, tremendous experimental progress has been demonstrated, including Mach–Zehnder interferometer (MZI) [135], phase modulators [54,55], tunable wavelength filters [51–53], and single-photon detectors [136]. In particular, tunable filters based on coupled resonator optical waveguide (CROW) were demonstrated to offer over 96 dB of on-chip suppression of pumped light, exceeding the performance of commercially available filters [52]. Rapid development of these on-chip components offers prospects of large-scale integration of quantum photonic circuits [54,137].
芯片上操纵和测量纠缠态需要高亮度源和集成主动光学元件。由于 CMOS 兼容性,硅平台拥有实现大规模可编程量子光子集成电路所需的大量光学元件。在这个前沿,已经取得了巨大的实验进展,包括马赫-曾德尔干涉仪(MZI)[ 135 ]、相位调制器[ 54、55 ]、可调谐波长滤波器[ 51-53 ]和单光子探测器[ 136 ]。特别是,基于耦合共振腔光波导(CROW)的可调谐滤波器已被证明可以提供超过 96 dB 的芯片内泵浦光抑制,超过了商业滤波器的性能[ 52 ]。这些芯片组件的快速发展为量子光子电路的大规模集成提供了前景[ 54、137 ]。
芯片上操纵和测量纠缠态需要高亮度源和集成主动光学元件。由于 CMOS 兼容性,硅平台拥有实现大规模可编程量子光子集成电路所需的大量光学元件。在这个前沿,已经取得了巨大的实验进展,包括马赫-曾德尔干涉仪(MZI)[ 135 ]、相位调制器[ 54、55 ]、可调谐波长滤波器[ 51-53 ]和单光子探测器[ 136 ]。特别是,基于耦合共振腔光波导(CROW)的可调谐滤波器已被证明可以提供超过 96 dB 的芯片内泵浦光抑制,超过了商业滤波器的性能[ 52 ]。这些芯片组件的快速发展为量子光子电路的大规模集成提供了前景[ 54、137 ]。
The above developments make fully integrated applications on chip no longer just imaginations [35,110]. Figure 8 shows several examples of system-level on-chip applications, which all exploit the compactness of spiral waveguides for integration of multiple SFWM sources. Wang et al. [138] demonstrated the first chip-to-chip entanglement distribution using two spirals, and the outputs of which are combined together to form a polarization entanglement (see Fig. 8A). Figure 8B shows an implementation of multidimensional quantum entanglement on a single chip that integrated 16 identical spiral waveguides and over 550 optical components in total, demonstrating maturity and scalability of silicon quantum photonic technology [139]. In comparison with spirals, microring structures have natural advantages of low pump power requirement and high photon purity, making it suitable for systems with high filtering requirements. As shown in Fig. 8C, chip-to-chip quantum teleportation and entanglement swapping have been demonstrated by integrating an array of microring resonators followed by a programmable quantum photonic circuit [9]. Progressing further, interconnection between multiple chips has been recently demonstrated to prove the viability of large-scale quantum networks [140,141].
上述发展使完全集成的片上应用不再仅仅是想象[ 35, 110]。图 8 展示了几个系统级片上应用的例子,它们都利用螺旋形波导的紧凑性来集成多个 SFWM 源。王等人[ 138]演示了第一个使用两个螺旋的芯片到芯片纠缠分配,其输出被组合形成偏振纠缠(见图 8A)。图 8B 展示了在单片集成 16 个相同螺旋波导和 550 多个光学元件的多维量子纠缠实现,展示了硅量子光子技术的成熟性和可扩展性[ 139]。与螺旋相比,微环结构具有低泵浦功率要求和高光子纯度的天然优势,使其适用于有高滤波要求的系统。如图 8C 所示,通过集成一个微环谐振器阵列,并后接一个可编程的量子光子电路,已经实现了芯片到芯片的量子隧穿传输和纠缠交换[ 9]。进一步来说,多芯片之间的互连最近也已经被证明了大规模量子网络的可行性[ 140, 141]。
上述发展使完全集成的片上应用不再仅仅是想象[ 35, 110]。图 8 展示了几个系统级片上应用的例子,它们都利用螺旋形波导的紧凑性来集成多个 SFWM 源。王等人[ 138]演示了第一个使用两个螺旋的芯片到芯片纠缠分配,其输出被组合形成偏振纠缠(见图 8A)。图 8B 展示了在单片集成 16 个相同螺旋波导和 550 多个光学元件的多维量子纠缠实现,展示了硅量子光子技术的成熟性和可扩展性[ 139]。与螺旋相比,微环结构具有低泵浦功率要求和高光子纯度的天然优势,使其适用于有高滤波要求的系统。如图 8C 所示,通过集成一个微环谐振器阵列,并后接一个可编程的量子光子电路,已经实现了芯片到芯片的量子隧穿传输和纠缠交换[ 9]。进一步来说,多芯片之间的互连最近也已经被证明了大规模量子网络的可行性[ 140, 141]。
Along with rapid developments of quantum photonic integration technology, the number of integrated components on a single chip is growing exponentially, with a current record of 2,500 components for monolithic integration [142]. Integrated SPD is the last piece to realize fully integrated quantum information processing. The integration of SPD has been demonstrated on GaAs [143], Si [144], and Si3N4 [145] and can be comparable to the performance of non-integrated detectors.
随着量子光子集成技术的快速发展,单片上集成的组件数量呈指数级增长,目前最高记录为 2,500 个用于单片集成[142]。集成化的单光子探测器是实现完全集成量子信息处理的最后一环。单光子探测器已在 GaAs[143]、Si[144]和 Si3N4[145]上实现集成,性能可与非集成探测器相媲美。
随着量子光子集成技术的快速发展,单片上集成的组件数量呈指数级增长,目前最高记录为 2,500 个用于单片集成[142]。集成化的单光子探测器是实现完全集成量子信息处理的最后一环。单光子探测器已在 GaAs[143]、Si[144]和 Si3N4[145]上实现集成,性能可与非集成探测器相媲美。
Conclusion and Outlook 结论与展望
With rapid progress in photonic integration technologies, on-chip SFWM quantum light sources have reached an exciting stage of development. On the one hand, a variety of platforms and structures have been demonstrated to be viable for their realization. On the other hand, significant challenges remain for the widespread use of the light sources as well as their integration to form a complete on-chip system.
随着光子集成技术的快速进步,芯片上的四波混频量子光源已达到令人兴奋的发展阶段。一方面,已经证明了各种平台和结构都是实现这些光源的可行方式。另一方面,要实现这些光源的广泛应用以及将其集成到完整的芯片系统中,仍然面临着重大挑战。
随着光子集成技术的快速进步,芯片上的四波混频量子光源已达到令人兴奋的发展阶段。一方面,已经证明了各种平台和结构都是实现这些光源的可行方式。另一方面,要实现这些光源的广泛应用以及将其集成到完整的芯片系统中,仍然面临着重大挑战。
One challenge is that the pair generation rate of on-chip SFWM sources remains at a relatively low level, which means that high-power pump laser must be used to generate sufficient number of photon pairs. However, beside introducing more noise, it is difficult to integrate high-power lasers on-chip, whose maximum output power is about 100 mW [146,147]. A long-term solution is likely to be found through further development of integration technology and novel device structures for nonlinear enhancement as well as searching new materials with high χ(3) nonlinearity.
一个挑战是片上 SFWM 源的对生成率相对较低,这意味着必须使用高功率泵浦激光器来产生足够数量的光子对。然而,除了引入更多噪声外,在芯片上集成高功率激光器也很困难,其最大输出功率约为 100 毫瓦[146、147]。长远的解决方案可能是通过进一步发展集成技术和用于非线性增强的新型器件结构,以及寻找具有高 χ(3) 非线性的新材料。
一个挑战是片上 SFWM 源的对生成率相对较低,这意味着必须使用高功率泵浦激光器来产生足够数量的光子对。然而,除了引入更多噪声外,在芯片上集成高功率激光器也很困难,其最大输出功率约为 100 毫瓦[146、147]。长远的解决方案可能是通过进一步发展集成技术和用于非线性增强的新型器件结构,以及寻找具有高 χ(3) 非线性的新材料。
Another challenge is the collection efficiency of photons, which is the main reason for limiting the counting rate and heralding efficiency of heralded single-photon source. It is mainly determined by waveguide transmission loss, coupling loss, channel loss, and detector detection efficiency. With the development of chip preparation technology and superconducting nanowire SPDs [148,149], it is reasonable to expect that the collection efficiency close to unity can be achieved.
另一个挑战是光子的收集效率,这是限制预警单光子源计数率和预警效率的主要原因。其主要由波导传输损耗、耦合损耗、通道损耗和探测器检测效率决定。随着芯片制备技术和超导纳米线单光子探测器的发展[148,149],预计可以实现接近于单位的收集效率。
另一个挑战是光子的收集效率,这是限制预警单光子源计数率和预警效率的主要原因。其主要由波导传输损耗、耦合损耗、通道损耗和探测器检测效率决定。随着芯片制备技术和超导纳米线单光子探测器的发展[148,149],预计可以实现接近于单位的收集效率。
In addition, multiphoton emission is also a challenge for all probabilistic quantum light sources. With the improvement of heralding efficiency and the development of photon number resolution detection technology [150,151], the problem of multiphoton emission from a heralded single-photon source can be resolved, thereby leading to a brighter single-photon source or even Fock photon number sources.
此外,多光子发射对所有概率量子光源来说也是一个挑战。随着信号检测效率的提高和光子数分辨检测技术的发展[150,151],由信号光源产生的多光子发射问题可以解决,从而实现更明亮的单光子源甚至菲克斯光子数源。
此外,多光子发射对所有概率量子光源来说也是一个挑战。随着信号检测效率的提高和光子数分辨检测技术的发展[150,151],由信号光源产生的多光子发射问题可以解决,从而实现更明亮的单光子源甚至菲克斯光子数源。
Acknowledgments 致谢
Competing interests: The authors declare that they have no competing interests.
利益冲突:作者声明他们没有利益冲突。
利益冲突:作者声明他们没有利益冲突。
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Copyright © 2024 Haoyang Wang et al.
Exclusive licensee Beijing Institute of Aerospace Control Devices. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY 4.0).
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- High-quality on-chip entangled photon source with broad tunable range based on coupling compensation, Applied Optics, 63, 16, (4465), (2024).https://doi.org/10.1364/AO.520887
- Suppression of external noise in on-chip photon-pair sources, Journal of the Korean Physical Society, 85, 6, (476-481), (2024).https://doi.org/10.1007/s40042-024-01141-4
- Engineering Quantum Light Sources with Flat Optics, Advanced Materials, 36, 23, (2024).https://doi.org/10.1002/adma.202313589
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