Advances in the study of ion trap structures in quantum computation and simulation

Wang Chen-Xu; He Ran; Li Rui-Rui; Chen Yan; Fang Ding; Cui Jin-Ming; Huang Yun-Feng; Li Chuan-Feng; Guo Guang-Can

doi:10.7498/aps.71.20220224

Abstract

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1. 引　言
2. 离子阱基本原理
3. 离子阱基本参数
4. 三维离子阱
4.1 四极杆阱
4.2 刀片阱
4.3 三维芯片阱
5. 二维芯片阱
6. 总　结

References

Cited By

Abstract

Ion trap system is one of the main quantum systems to realize quantum computation and simulation. Various ion trap research groups worldwide jointly drive the continuous enrichment of ion trap structures, and develop a series of high-performance three-dimensional ion trap, two-dimensional ion trap chip, and ion traps with integrated components. The structure of ion trap is gradually developing towards miniaturization, high-optical-access and integration, and is demonstrating its outstanding ability in quantum control. Ion traps are able to trap increasingly more ions and precisely manipulate the quantum state of the system. In this review, we will summarize the evolution history of the ion trap structures in the past few decades, as well as the latest advances of trapped-ion-based quantum computation and simulation. Here we present a selection of representative examples of trap structures. We will summarize the progresses in the processing technology, robustness and versatility of ion traps, and make prospects for the realization of scalable quantum computation and simulation based on ion trap system.

Keywords:

PACS:

37.10.Ty	(Ion trapping)
03.67.Lx	(Quantum computation architectures and implementations)
07.05.Bx	(Computer systems: hardware, operating systems, computer languages, and utilities)

Authors and contacts

1.
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
2.
CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
3.
Department of Physics and Materials Engineering, Hefei Normal University, Hefei 230601, China

Corresponding author: He Ran, heran@ustc.edu.cn ; Cui Jin-Ming, jmcui@ustc.edu.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11734015, 11774335, 11821404)

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1. 引　言

过去一百多年, 量子力学在描述光子、原子、电子、离子等微观粒子的基本性质和运动规律上取得了巨大成功, 已逐渐成为人们理解世界规律和推动科技发展的重要工具, 带来了人类社会的巨大变革. 当今, 量子力学引导的科技革命方兴未艾, 人们正试图实现大规模的可控量子系统, 实现计算能力的巨大飞跃. 这源自二十世纪80年代Feynman^[1]提出的量子模拟的构想: 想要使用经典计算机模拟量子世界, 需要指数级增加的经典算力资源, 而如果使用量子系统模拟量子力学, 则可以大大减少资源消耗. 二十世纪90年代, Shor^[2]提出了著名的Shor算法, 具备破解公开密钥加密方法(RSA加密算法)的潜力, 被认为是量子计算机优越性的代表算法.

随着技术的进步, 构建一台有望超越经典计算机的量子计算机逐渐成为可能. 能够实现量子计算的量子系统必须满足DiVincenzo判据, 即: 1)具有良好表征的量子比特; 2)初态制备; 3)可实施量子纠错的长相干时间; 4)可实现一组通用量子门; 5)结果可以被高效读出; 6)具有可扩展能力^[3]. 多种物理系统都被证明可以满足前5个条件, 如超导量子系统、离子阱系统、冷原子系统、碳化硅系统、氮空位色心、光子体系、核磁共振系统、以及拓扑量子比特等. 而可扩展能力是当前所有系统都面临的最大困难.

离子阱系统是最早用于囚禁单个带电粒子的装置, 被认为是实现量子计算最有潜力的量子硬件之一. Paul^[4]于1953年发明了一种使用射频电场和静电场束缚离子的装置, 被称为Paul阱. Dehmelt^[5]使用一种静磁场和电场相结合的结构, 成功实现了对电子的囚禁, 并将其命名为Penning型离子阱. Paul和Dehmelt二人也因此共同获得了1989年的诺贝尔物理学奖. 两种离子阱的原理不同, 但都能够将单个或多个离子束缚在真空环境中, 如质谱^{[6, 7]}、原子钟^[8–13]、腔量子电动力学^[14–17]、基本物理常数测量^[18]、量子模拟^[19–24]、以及量子计算^[25–31]等. 本文重点论述Paul阱, 关于Penning阱的相关内容, 可以参考文献[32, 33].

二十世纪 80 年代, 美国国家技术标准局(NIST)的Wineland等在Paul阱中实现了单离子的激光冷却^[34], 并且首次将离子冷却到运动基态^[35], 这为激光操作离子的内部量子态提供了基础^[36]. Wineland也因此获得了 2012 年的诺贝尔物理学奖. 1995年, Cirac和Zoller^[25]正式提出离子阱系统可被用于量子计算, 其中单个离子的内部能级被认为是一个量子比特, 离子间由于库仑力而共享的运动模式可以作为相互作用的桥梁, 使用激光可以实现单量子比特操作和双比特操作. 离子阱在满足DiVincenzo前五条判据上取得了一系列重要突破. 近几年, 离子阱中的单比特门保真度已达99.9999%^[37], 基于激光的两比特门的保真度达到0.9989(7), 0.9992(4) 和 0.9994(3) ^[38–40], 基于微波的两比特门保真度高达 $1_{-0.0017}^{+0}$ ^[41]. 单离子的相干时间可达5500 s^[42], 远远超过量子门所需要的时间. 离子阱的可操作比特数目日益增长, 奥地利初创公司Alpine Quantum Technologies (AQT)的商业化离子阱可实现24个离子的Greenberger-Horne-Zeilinger (GHZ)态制备^[43], 美国公司IonQ则实现了上百个离子的囚禁、79个离子的单比特门和11个离子的全连通量子算法^[44]. 离子阱中的保真度指标已经超越了容错量子计算的阈值^[45–47], 人们已经可以实现单个逻辑比特的容错编码和纠错^[48,49]. 除了量子计算, 离子阱也成为重要的量子模拟平台^[50–52], 例如使用原子离子混合系统(hybrid system) ^[53–55]研究冷分子的合成过程及性质^[54,56–59].

当前, 电子计算机的计算能力面临着瓶颈, 进一步减小晶体管的体积越来越困难. 当芯片的加工尺寸达到1 nm左右, 线路中的量子效应将占据主导, 电子的状态将不再稳定, 无法实现准确的计算. 量子计算机则从根本上利用粒子的量子特性实现计算, 有望大幅提升计算能力, 解决目前面临的诸多问题. 量子计算机使用处于叠加状态的量子比特 $\left| 0 \right\rangle$ 和 $\left| 1 \right\rangle$ , 取代经典计算机中只能处于0或1的经典比特. 量子计算机可以自然地实现量子系统的演化, 对于求解和模拟量子系统有着天然的优势. 对于n个量子比特, 其描述的参数空间需要使用 $2^n$ 个经典比特才能够实现. 通用的大规模量子计算是量子计算机发展的最终目标, 要求量子系统能够实现规模上的可扩展(上万个量子比特)和纠正计算中的错误. 虽然当前的离子阱系统距离通用量子计算还有一定距离, 但离子阱系统有望率先实现有噪音的中小规模量子体系, 将在生物制药、交通规划和飞行器设计等复杂问题领域提供应用价值.

实现规模较大的量子计算要求量子比特数目的扩展以及操作能力的提高. 对于离子阱系统而言, 这不仅要求增加离子数目, 还要求激光独立操控能力的提升. 一方面, 一个线性离子阱中离子的数量是有限的, 由于离子之间存在库仑相互作用力, 其间距在几微米左右, 而随着离子数量的增加, 离子链将变得越来越长. 这不仅会使得离子的间距减小, 轴向运动频率降低, 还会使得离子的运动模式越来越复杂, 实现离子间的相互作用越来越困难. 另一方面, 实现离子操作的激光也需要相应的扩展, 而光学的可扩展性也受到激光功率、光电器件的性能、系统的通光性能、相邻离子串扰等因素的限制. 因此, 优化离子阱的结构, 实现离子数目和激光控制的可扩展性是当前离子阱发展的重要问题.

实际上, 离子阱的结构一直在不断改进, 离子阱逐渐从原来的体积大、通光性差且电极简单向着小型化、高通光性和集成化方向发展, 对多离子的囚禁能力和精确控制能力越来越高. 人们陆续发明了线性四极杆阱^[60]、分段式的四极杆阱、线性刀片阱^[61]、分段式线性刀片阱^[62]等具有三维结构的线性离子阱, 由于他们的尺寸都在厘米量级, 因此也被称为宏观离子阱(Macroscope trap). 微纳加工技术的发展为离子阱的小型化和批量生产提供了可能, 人们发明了一种具有不同结构的离子阱—微观离子阱(Microscope trap)^[63–65], 但通常需要放置在低温环境^[66,67]. 除了使用线性离子阱, 还有人使用二维Paul离子阱^[68–72] 或Penning阱^[73–76]来扩展单个离子阱中的离子数量. 为了解决离子阱的可扩展问题, Kielpinski等^[77]提出了量子电荷耦合设备(quantum charge-coupled device, QCCD)的路线图—构造一个具有多个囚禁区域的离子阱结构, 移动离子在不同功能区域间穿梭, 实现不同的操作. 这需要使用具有结连接电极(Junction)结构的三维芯片阱^[78,79]和表面阱芯片^[80]. 尤其是与集成电路、集成光学相结合的表面阱有望为离子阱结构的小型化和可扩展开辟新的道路^[64,81–84]. 第二种扩展路线图是Monroe等^[31]提出的—模块化的离子阱可扩展结构(modular universal scalable ion trap quantum-computer (MUSIQC))—离子阱可以分布在不同的地方, 通过光子飞行比特连接起来, 则可以实现更大规模的量子系统. Monroe等^[31]使用大数值孔径的物镜收集光子, 并实现了不同离子之间概率性的纠缠^[85–87]. 为了提升收集效率和纠缠速率, 可以使用与原子能级共振的法布里-珀罗(Fabry-Pérot, FP)腔^[88–90], 并实现高效率的离子-光子纠缠^[89,91] 以及远距离的光子传输^[92,93]. 但是这仍然面临着光学腔表面杂散电场对囚禁离子稳定性的影响^[94].

综上所述, 离子阱作为一个优秀的量子系统, 为人们使用离子量子比特实现量子信息的处理提供了丰富的操作手段. 但最终实现大规模的量子计算, 离子阱的结构还需要不断地创新. 这些创新来源于全世界不同实验室的共同努力和尝试, 也来源于加工技术的进步和发展. 本文将从实现可扩展量子信息处理为出发点, 论述离子阱设计时需要考虑的主要原则和参数选择, 以一些典型的离子阱为例, 详细论述不同结构的射频离子阱在加工方法、通光性能、可扩展能力、以及量子态操作能力等方面的特点, 以促进未来新型结构的发展和量子硬件的进步.

2. 离子阱基本原理

本节介绍Paul阱的基本原理和主要参数. 如图1所示, 双曲面离子阱结构对称, 射频(radio frequency, RF)电压被施加到射频电极上, 静电压(static electric voltage, DC)被施加到直流电极上, 离子被囚禁在阱的中间. 在Paul阱的双曲面电极上施加电压, 在空间中形成的电势可以写为

$图 1 双曲面离子阱示意图[95]\r\nFig. 1. Schematic of a Paul trap with hyperbolic shaped electrodes[95]$

图 1 双曲面离子阱示意图^[95]

Fig. 1. Schematic of a Paul trap with hyperbolic shaped electrodes^[95]

下载: 全尺寸图片幻灯片

$\begin{align} \varPhi_{{\rm{DC}}}=\frac{U_{{\rm{DC}}}}{2}(\alpha_{{\rm{DC}}}x^{2}+\beta_{{\rm{DC}}}y^{2}+\gamma_{{\rm{DC}}}z^{2}), \end{align}$

(1)

其中, $U_{{\rm{DC}}}$ 为施加的电压, $x$ 和 $y$ 方向为径向, $z$ 方向为轴向. 根据Maxwell方程, $\nabla^{2}U=0$ 要求

$\begin{align} \alpha_{{\rm{DC}}}+\beta_{{\rm{DC}}}+\gamma_{{\rm{DC}}}=0. \end{align}$

(2)

因此单纯使用静电场, 至少有一个方向无法束缚离子. 如果施加射频场(radio frequency field, RF field), 其产生的含时电势为

$\begin{align} \varPhi_{RF}=\frac{U_{{\rm{RF}}}}{2}(\alpha_{{\rm{RF}}}x^{2}+\beta_{{\rm{RF}}}y^{2}+\gamma_{{\rm{RF}}}z^{2})\cos(\varOmega_{{\rm{RF}}}t), \end{align}$

(3)

其中 $U_{{\rm{RF}}}$ 为RF电压, $\varOmega_{{\rm{RF}}}$ 为射频角频率. 同样地^[25],

$\begin{align} \alpha_{{\rm{RF}}}+\beta_{{\rm{RF}}}+\gamma_{{\rm{RF}}}=0. \end{align}$

(4)

对于一维线性离子阱, 取 $\gamma_{{\rm{RF}}}=0$ , $\alpha_{{\rm{RF}}}=-\beta_{{\rm{RF}}}$ , 且 $\alpha_{{\rm{RF}}}\propto1/r_{0}^{2}$ , 其中 $r_{0}$ 为离子到电极的距离. 由于射频电场的时变性, $x$ 和 $y$ 方向交替地改变对离子的作用力方向. 在轴向, 通过施加DC则可以实现束缚作用. 因此, 在合适的参数下, 离子将在电场中作往复运动, 被囚禁在势阱中心. 只考虑 $x$ 一个方向上的电势

$\begin{align} \varPhi_{x}=\frac{1}{2}\left[U_{{\rm{DC}}}\alpha_{{\rm{DC}}}+U_{{\rm{RF}}}\alpha_{{\rm{RF}}}\cos\,(\varOmega_{{\rm{RF}}}t)\right]x^{2}, \end{align}$

(5)

根据牛顿运动方程 $F=ma$ , 对于处于该电场的正电荷 $q$ , 有

$\begin{split} \ddot{x} & = {qE}/{m} \\ & =-\frac{Z\left|e\right|}{m}\left[U_{{\rm{DC}}}\alpha_{{\rm{DC}}}+U_{{\rm{RF}}}\alpha_{{\rm{RF}}}\cos\,(\varOmega_{{\rm{RF}}}t)\right]x, \end{split}$

(6)

其中, $Z$ 为离子所带电荷数, $m$ 为离子质量, $e$ 为单位正电荷 $1.602\times10^{-19}$ $C$ . 这与Mathieu方程

$\frac{{\rm{d}}^{2}x}{{\rm{d}}\xi^{2}}+\left[a_{x}-2q_{x}\cos\,(2\xi)\right]x=0$

形式一致, 只需要做如下替换:

$\begin{split} &\xi=\frac{\varOmega_{{\rm{RF}}}t}{2},\quad a_{x}=\frac{4ZeU_{{\rm{DC}}}\alpha_{{\rm{DC}}}}{m\varOmega_{{\rm{RF}}}^{2}},\\ &q_{x}=\frac{2ZeU_{{\rm{RF}}}\alpha_{RF}}{m\varOmega_{{\rm{RF}}}^{2}}, \end{split}$

(7)

上述方程在一定条件下具有通用的稳定解^{[36, 78]}. 在 $|a_{x}|, \, q_{x}^{2}\ll1$ 时, 可得到离子运动的一阶近似解

$\begin{equation} x(t)\approx2A_{x}\cos\,\left(\beta_{x}\frac{\varOmega_{{\rm{RF}}}}{2}t\right)\left[1-\frac{q_{x}}{2}\cos\,\left(\varOmega_{{\rm{RF}}}t\right)\right], \end{equation}$

(8)

其中, $\beta_{x}\approx\sqrt{a_{x}+q_{x}^{2}/2}$ , $A_{x}$ 为常数, 依赖于初始的边界条件^[36]. 上述结果表明, 离子的运动可以分为两部分, 频率为

$\begin{equation} \omega_{{\rm{secular}}}=\beta_{x}\frac{\varOmega_{{\rm{RF}}}}{2}\ll\varOmega_{{\rm{RF}}}, \end{equation}$

(9)

幅度为 $2 A_{x}$ 的久期运动(secular motion)和频率为 $\varOmega_{{\rm{RF}}}$ , 幅度为 $q_{x}A_{x}$ 的微运动(micromotion). 当 $a_{x}\ll q_{x}^{2}$ 时, 离子的运动频率为

$\begin{align} \omega_{{\rm{secular}}}=q_{x}\varOmega_{{\rm{RF}}}/2\sqrt{2}=\frac{Z\left|e\right|U_{{\rm{RF}}}\alpha_{{\rm{RF}}}}{\sqrt{2}m\varOmega_{{\rm{RF}}}}. \end{align}$

(10)

轴线方向的情况比较简单, 可以直接由

$\begin{align} \frac{{\rm{d}}^{2}z}{{\rm{d}}t^{2}}+\frac{ZeU_{{\rm{DC}}}\gamma_{{\rm{DC}}}}{m}z=0 \end{align}$

(11)

得到轴线运动频率^[25]

$\begin{align} \omega_{z}=\sqrt{\frac{Z\left|e\right|U_{{\rm{DC}}}\gamma_{{\rm{DC}}}}{m}} \end{align}$

(12)

和运动函数

$\begin{align} z(t)=A_{z}\cos\,(\omega_{z}t), \end{align}$

(13)

其中, $A_{z}$ 为运动幅度.

当离子的微运动幅度远小于久期运动幅度时, 离子在径向所感受到的平均势阱近似于一个简谐势:

$\begin{align} \varPhi_{{\rm{pseudo}}}(\boldsymbol{r})=\frac{Z\left|e\right|U_{{\rm{RF}}}^{2}}{4m\varOmega_{{\rm{RF}}}^{2}}(\alpha_{{\rm{RF}}}^{2}x^{2}+\beta_{{\rm{RF}}}^{2}y^{2}), \end{align}$

(14)

称之为赝势(pseudo-potential). 离子的运动可以看作在这个赝势中的简谐振动, 当离子处于赝势的中心附近时, 可以使用量子化的语言描述离子的运动状态, 称之为声子. 声子作为离子的外态, 与离子的内部电子能级所形成的内态共同组成了离子的量子态. 如当离子处于内态的 $\left| 0 \right\rangle$ 态而运动处于基态 $\left| 0 \right\rangle$ 时, 可以表示为直积态 $\left| 00 \right\rangle \equiv \left| 0 \right\rangle \otimes\left| 0 \right\rangle$ . 通过激光可以将二者耦合起来, 实现自旋与声子的耦合. 对于多个离子, 由于库仑相互作用, 离子将在束缚强度较弱的轴向(一般为 $z$ 轴)排成一排, 形成一维离子晶体. 离子的间距由所有离子所受电场力与库仑力平衡位置决定, 一般为几微米, 为使用激光来独立地操作各个离子提供了便利. 此时, 离子的运动模式被所有离子共享, 形成离子间相互作用的纽带. 如对于质心模式而言, 所有离子都同时向同一方向运动, 频率相同. 更多关于多离子运动模式请参考文献[96].

3. 离子阱基本参数

在设计和加工离子阱时, 首先需要确定一些基本参数. 在确保离子稳定囚禁的前提下, 离子的径向声子频率越大越好. 这有几方面的原因, 第一, 原子的能级是有一定线宽的, 而操作离子能级的激光也是存在一定线宽的, 只有当声子频率大于上述的线宽时, 激光才能够分辨不同的运动频率. 第二, 当声子频率较大时, 离子的运动模式更不容易被外界杂散电场激发, 因此具有更低的加热率. 第三, 在一维离子晶体中, 更大的径向声子频率意味着能够容纳更多的离子^[96]. 第四, 大的声子频率还有利于在多普勒冷却时得到更低的初始声子数.

由(10)式可知, 对于特定的离子, 想要增加径向声子频率, 可以通过增加射频电场电压 $U_{{\rm{RF}}}$ , 增加离子阱的结构因子 $\alpha_{{\rm{RF}}}\propto1/r_{0}^{2}$ , 即减小离子到电极的距离 $r_{0}$ , 或减小射频场驱动频率 $\varOmega_{{\rm{RF}}}$ 来实现.

1)增加 $U_{{\rm{RF}}}$ . 离子阱中, 常常使用螺旋谐振腔提供RF所需要的高压射频电场^[97,98]. 螺旋谐振腔可以实现射频电场的电压增益以及阻抗匹配, 同时可以实现对共振频率之外的噪音的滤波. 其输入端的射频功率为 $P$ , 谐振腔的品质因子为 $Q$ , 则其输出的电压幅度为 $U_{{\rm{RF}}}\propto\sqrt{2 PQ}$ . 常温下, 连接到离子阱上的螺旋谐振腔的 $Q$ 值可以达到数百^[97,98], 而在低温下可以达到1000以上^[67]. 进一步提升 $U_{{\rm{RF}}}$ 的方法只能通过增加射频功率 $P$ 来实现, 但提升 $n$ 倍的功率却只能带来 $\sqrt{n}$ 的电压增益, 这不仅受限于电极材料的最大耐压性质, 还受限于离子阱结构的热稳定性^[99].

2)减小离子到电极的距离 $r_{0}$ . 虽然减小 $r_{0}$ 对于增加声子频率效果明显, 但是这会导致离子加热率 $\dot{n}\propto r_{0}^{-4}$ 的急速增加^[100–104], 因此必须选择一个合适的间距.

3)减小射频场驱动频率 $\varOmega_{RF}$ . 根据(9)式, 减小 $\varOmega_{{\rm{{\rm{RF}}}}}$ 会导致 $q_{x}$ 的增加, 不可能一直减小. 在端帽电极为0时, Mathieu方程的稳定解要求 $q_{x}$ 应小于0.908. 但实际上, 大多数的离子阱都会工作在 $q_{x} < 0.5$ 的区域^[36]. 因此减小 $\varOmega_{{\rm{RF}}}$ 会使得稳定囚禁离子的射频电压 $U_{{\rm{RF}}}$ 相应的降低, 与1)冲突.

因此, 需要综合考虑所有因素, 并根据实际目的, 选择一个全局最优的参数. 设计离子阱结构时, 还需要考虑如下因素:

1) 电极所构成的囚禁区域的尺寸、比例、通光角度等几何参数, 这些参数也决定了离子运动频率的大小和主轴方向;

2)电极的材料可以选择金属, 如不锈钢^[61]、钨^[68]、钛^[105,106]等, 也可以选择镀金的绝缘材料, 如陶瓷^[107]、宝石^[108]、熔融石英^[109]等, 材料的选择需要考虑到真空放气率、是否超低温兼容、可加工性、表面粗糙度、电阻率、射频损耗、硬度和热膨胀系数等;

3)良好的电极的连接和固定方法确保结构的牢固性;

4)分段电极的数量、尺寸和加工方法;

5)在具有结连接电极的离子阱中, 结连接的形状和尺寸需要精细的设计, 以减小离子在移动过结点时的加热^[78];

6)固定机械与真空腔体必须有足够的通光性, 确保操作激光的照射, 以及高数值孔径(numerical aperture, NA)物镜用于离子荧光收集;

7)超高真空环境对离子阱至关重要, 能够隔绝空气分子对离子的碰撞^[67], 防止离子从势阱中逃出或形成分子, 因此需要真空腔、真空窗口、真空泵以及真空馈通连接来提供超高真空环境(约 $10^{-11}$ Torr ( $1{\rm{Torr}} \approx 133.322 {\rm{Pa}}$ ));

8)使用低温系统有利于获得更好的真空环境, 以及降低加热率, 但也增加了系统的成本、体积和复杂度.

4. 三维离子阱

4.1 四极杆阱

四极杆阱是一种常用的线性离子阱, 能够囚禁一维离子晶体. 相比于Paul发明的双曲面结构, 四极杆阱的电极更容易制作且具备更高的通光性, 至今仍是离子阱质谱仪领域使用最为广泛的结构. 它由四根主要的圆柱形电极构成, 其中两根作为RF电极, 两根作为DC电极. DC电极不仅作为RF电场的地, 还能够提供偏置电压控制离子位置. 如图2所示, 四极杆阱根据DC电极是否分段可以分为两种结构. 其中不分段的四极杆阱需要使用端帽电极提供轴向束缚, 在陶瓷绝缘支架上, 四根直径0.3 mm的钨棒的中心围成了边长0.6 mm的正方形, 两侧各有一根直径0.2 mm的钨棒作为端帽电极, 相距1.3 mm. 离子距离四个电极距离为0.27 mm, 距离端帽电极0.65 mm. 在其下方还有两根电极, 一个用于补偿微运动, 另一根用于通过射频电流, 驱动离子的磁偶极矩跃迁. 除了使用轴向电极, 还可以使用环形电极等, 防止轴向通光孔径被遮挡^[111]. 而分段的离子阱则将DC电极分段, 可以在轴向开口, 具备轴向通光能力. 在图2(b)的四极杆阱中, 四根长5 cm直径0.79 mm的不锈钢棒围成边长1.25 mm的正方形区域, 其中两根作为RF电极, 两根作为DC电极形成径向的束缚电场, 离子距离电极中心距离为R = 0.5 mm, 距离电极表面 $r_{0}$ = 0.105 mm. 在两根DC电极上共设置四根5 mm长的不锈钢管, 相距2 $Z_{0}$ = 6 mm, 使用25 μm厚的聚酰亚胺作为绝缘材料隔离^[112]. 轴向通光能力有利于使用一束激光照射整个离子链并实施全局操作, 也有利于在轴向设置光学腔等装置^[113]. 然而, 四极杆阱仍然存在一些不足, 如圆柱电极结构仍然限制了径向和轴向的通光孔径, 分段电极的数量难以增加.

$图 2 四极杆离子阱　(a)不分段的四极杆阱需要端帽电极提供轴向束缚[110]; (b)分段的四极杆阱使用分段电极提供轴向束缚[112]\r\nFig. 2. Four-rod trap: (a) Unsegmented four-rod trap requires end cap electrodes to provide axial confinement [110]; (b) segmented four-rod trap uses the segmented electrodes to provide axial confinement[112]$

图 2 四极杆离子阱　(a)不分段的四极杆阱需要端帽电极提供轴向束缚^[110]; (b)分段的四极杆阱使用分段电极提供轴向束缚^[112]

Fig. 2. Four-rod trap: (a) Unsegmented four-rod trap requires end cap electrodes to provide axial confinement ^[110]; (b) segmented four-rod trap uses the segmented electrodes to provide axial confinement^[112]

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4.2 刀片阱

2003年, Innsbruck大学的Rainer Blatt组设计了一种刀片形状的离子阱, 称为刀片阱^[61]. 如图3所示, 四个不锈钢刀片固定在Macor陶瓷支架上, 构成一个刀片阱, 图中的尺寸单位为mm. 轴向一对钼金属制作的端帽电极提供轴向电压(约2000 V), 端帽上突出的圆形结构可以覆盖正对轴线的陶瓷支架的表面, 以减小杂散电场对离子的干扰. 三根不锈钢棒作为补偿电极, 其中一根用于竖直方向, 另外相连的两根用于水平方向. 离子与刀刃间距0.8 mm, $U_{{\rm{RF}}}$ 为1000 V左右, 工作频率23.5 MHz. 这类阱具有很多优点. 如势阱深度达到数个电子伏, 径向声子频率可达2—4 MHz, 能够囚禁数十个离子; 刀片结构使得阱具有更高的通光性能; 具备数个控制电极, 能够补偿离子的微运动; 加热率 < 10 个声子每秒. 这种离子阱由于具有优良的性质获得了巨大的成功, 被称为Innsbruck式的刀片阱. 为了提高系统的通光性和囚禁深度, Rainer Blatt组在2011年做了如下改进: 将离子与刀刃间距缩短至565 μm, 以获得更高的径向声子频率; 在端帽电极中间设置直径0.5 mm的通光孔径, 以便在轴向照射激光, 并将端帽电极间距从5 mm减小为4.5 mm; 使用桥接导线将两个RF电极以串联方式连接^[114], 但桥接导线会产生交流磁场, 影响离子能级. 他们后来又通过改变导线的布线几何结构解决了该问题^[114]. 为了提升该阱的热稳定性和通光性^[99], 在2017年Rainer Blatt组在原有的设计基础上, 又做了如下改进: 使用蓝宝石作为支架, 替换原来的Macor材料; 为匹配宝石的热膨胀系数, 使用钛金属刀片替换原来的不锈钢刀片; 刀片表面电镀10 μm金层, 有利于减小刀片发热产生的黑体辐射^[106], 还有利于降低由于紫外光产生的光电效应(金的逸出功为5.1 eV, 而不锈钢为4.4 eV, 分别对应243 nm和282 nm的光子能量)^[106]. 该类阱在轴向的加热率为1.32(2)至37(2) 个声子每秒. 经过这一系列的改进, Innsbruck式的刀片阱成为一种结构紧凑、性能优良、质量稳定的离子阱结构. 初创公司AQT所提供的商业化离子阱量子计算原型机使用的正是这种设计, 并将所需的激光、射频、光路、控制系统全部集成到两个19英寸机柜中^[43,115].

$图 3 Innsbruck式的刀片阱[61]　(a)组装后的离子阱实物图; (b)离子阱尺寸和结构图\r\nFig. 3. Innsbruck style blade ion trap: (a) Photograph of an assembled blade trap; (b) dimensions and structure of the trap$

图 3 Innsbruck式的刀片阱^[61]　(a)组装后的离子阱实物图; (b)离子阱尺寸和结构图

Fig. 3. Innsbruck style blade ion trap: (a) Photograph of an assembled blade trap; (b) dimensions and structure of the trap

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Maryland大学的Christopher Monroe组在2013年设计了一种分段式的刀片阱, 如图4所示. 他们不使用沿着轴向的端帽电极, 而是将DC刀片分割成五段, 其中最外面的DC电极可以实现轴向束缚. 四个刀片为500 μm厚的陶瓷片, 使用激光切割出四个宽50 μm的缝, 在刀刃处构成250 μm的五段. 电极表面镀金, 先蒸镀10 nm的钛层和1 μm的金层, 也可以采取电镀金产生更厚的金层. 其中RF刀片整体镀金, 五段电极相互连接, 而DC电极只镀一部分, 形成五个独立的电极. 组装时, 四个刀片固定在陶瓷支架上, 每段DC电极都有一个820 pF的陶瓷电容与地相连, 以减小DC刀片上感应的射频信号. 刀片围成的囚禁区域为 $1215\, {\mu {\rm{m}}}\times539\,{\mu {\rm{m}}}$ , 离子电极间距约为660 μm. 这种刀片阱具有在多个方向的通光性, 有利于实现不同要求的光路配置. 在后来的设计中, 最外侧的DC电极长度从250 μm增加至10 mm, 有利于使得RF电场在轴向更均匀, 减小RF的轴向电场分量引起的微运动^[116,117]. 在这个离子阱上, Debnath等^[30]演示了一个全连通的五比特可编程量子计算机.

$图 4 Maryland型刀片阱[62]　(a)分段刀片阱结构图. 分段刀片结构不仅可以提供轴向束缚, 还能够实现非简谐电势, 实现更均匀的离子间距. (b) 在另一个刀片阱中, 将DC最外侧电极的长度从250 μm增加至10 mm, 减小RF在轴向的电场分量[116,117]\r\nFig. 4. Maryland style blade ion trap[62]: (a) Structure of segmented blade ion trap. The segmented blade not only can provide axial confinement, but also generate non-quadratic axial potential to achieve uniform ion distance; (b) in another blade ion trap, the out-most segment is increased to 10 mm from 250 μm in order to reduce the residual RF electric field along the axial direction[116,117]$

图 4 Maryland型刀片阱^[62]　(a)分段刀片阱结构图. 分段刀片结构不仅可以提供轴向束缚, 还能够实现非简谐电势, 实现更均匀的离子间距. (b) 在另一个刀片阱中, 将DC最外侧电极的长度从250 μm增加至10 mm, 减小RF在轴向的电场分量^[116,117]

Fig. 4. Maryland style blade ion trap^[62]: (a) Structure of segmented blade ion trap. The segmented blade not only can provide axial confinement, but also generate non-quadratic axial potential to achieve uniform ion distance; (b) in another blade ion trap, the out-most segment is increased to 10 mm from 250 μm in order to reduce the residual RF electric field along the axial direction^[116,117]

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刀片阱能够在多个方向提供较大的数值孔径, 这对于离子阱来说至关重要. 一方面需要使用大数值孔径的物镜收集离子的荧光, 实现高效的探测和成像. 越大的数值孔径所实现的收集效率越高, 通常使用NA>0.3的物镜, 工作距离在10—40 mm ^[117]. 另一方面, 对单个离子的独立寻址需要使用高数值孔径的物镜将激光聚焦到小于离子间距. 高数值孔径物镜的工作距离要求离子应尽可能地靠近窗口, 而常用的金属真空腔的系统只能够在一个或者两个方向上具有较短的距离. 为此, 人们尝试将物镜放置在真空腔内部^[118]、使用集成的反射镜^[119–121]和衍射器件^[122,123]等措施以增加数值孔径. 但这大大增加了系统的复杂度, 而且置于真空内的器件难以调整和更换. 实验上, 金属真空腔由于易加工、超高真空兼容常用于给离子阱系统提供超高真空环境和机械支撑. 但金属真空腔需要使用光学窗口才可以通光, 因此体积难以进一步缩小. 相比之下, 在冷原子体系中常用的玻璃真空腔同样能够提供超高真空环境^[124,125]. 在玻璃真空腔中制备冷原子系综, 使用光晶格或者光镊束缚单个冷原子阵列都已经是很成熟的技术^[126,127]. 在中国科学技术大学的刀片阱中, 就实现了刀片阱和玻璃真空腔的结合. 如图5所示, 所使用的玻璃真空腔尺寸为 $30\, \mathrm{mm}\times30\, \mathrm{mm}\times100\, \mathrm{mm}$ , 厚度4 mm, 内部尺寸为 $22\, \mathrm{mm}\times22\, \mathrm{mm}\times92\, \mathrm{mm}$ , 离子距离真空腔外界只有15 mm. 所使用的的刀片为熔融石英基底, 表面电镀8 μm金层. DC电极使用激光切割表面金层实现五段电极, 中间三段宽度为250 μm, 每段间隔20 μm. 两个刀片相邻表面夹角为 $82.6°$ 和 $37.4°$ , 对应数值孔径分别为NA = 0.66和NA = 0.32^[109]. 该系统的两个侧面可以用于受激拉曼跃迁操作, 一个方向用于荧光收集, 另一个方向可以实现可寻址的光镊^[128–130]. 该玻璃腔内还保留足够的空间用于实现冷原子系综的制备, 为未来的冷原子实验提供了足够的光学操作空间^[54,56–59].

$图 5 中国科学技术大学的刀片阱[109]　(a)放置于玻璃真空腔中的刀片阱, 在其四周允许同时使用两个NA最大为0.32的物镜和两个NA为0.66的物镜; (b)刀片阱的结构. 该刀片材料为熔融石英, 表面具有8 μm金层, DC电极表面使用激光加工成为五段\r\nFig. 5. The blade ion trap used in University of Science and Technology of China [109]: (a) A blade ion trap is placed in a glass vacuum cell. Two objectives with a maximum NA of 0.32 and another two objectives with a maximum NA of 0.66 are allowed to be used simultaneously. (b) The structure of the blade ion trap. The blades are made from fused silica and coated with a 8 μm gold layer. The surface gold of the DC electrodes is segmented into five using laser cutting$

图 5 中国科学技术大学的刀片阱^[109]　(a)放置于玻璃真空腔中的刀片阱, 在其四周允许同时使用两个NA最大为0.32的物镜和两个NA为0.66的物镜; (b)刀片阱的结构. 该刀片材料为熔融石英, 表面具有8 μm金层, DC电极表面使用激光加工成为五段

Fig. 5. The blade ion trap used in University of Science and Technology of China ^[109]: (a) A blade ion trap is placed in a glass vacuum cell. Two objectives with a maximum NA of 0.32 and another two objectives with a maximum NA of 0.66 are allowed to be used simultaneously. (b) The structure of the blade ion trap. The blades are made from fused silica and coated with a 8 μm gold layer. The surface gold of the DC electrodes is segmented into five using laser cutting

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该离子阱的高通光性结构允许人们更高效地使用光镊, 使得光镊与离子阱更好地结合^[109]. 光镊是一种强会聚的光偶极阱^[128–131], 在冷原子系统中, 光镊可以实现原子的一维到三维排列^{[126,128,129,132–134]}, 而将光镊用于离子阱, 能够实现单个离子的纯光囚禁^[69,135,136], 避免由于微运动造成的加热问题^[137,138]. 最为重要的是, 光镊不仅可以用于增加长离子链的稳定性, 还能够实现同一离子链中不同操作的并行性^[139–142], 有利于增加离子阱的可扩展性.

三维离子阱还给离子阱与光纤腔的结合提供了足够的空间^{[15,91,145–149]}. 将离子阱与光学FP腔结合不仅有助于提升离子荧光的收集效率^[93], 还能够实现离子与腔模的强耦合^[144,150], 用于腔量子电动力学的研究^[147,151]. 然而, 将光纤腔集成在离子阱中仍然十分困难. 虽然大腔镜具有较长的腔长, 可以更方便地放置于真空腔中, 对于离子的扰动较小, 但是较长腔长导致较大的模式体积和较小的耦合系数, 而使用光纤制作的FP腔能够拥有非常小的模式体积, 因此可以实现强耦合. 但是光纤腔的腔长通常只有几百微米, 暴露的介电材料也会对离子的运动产生很大的影响^[94]. 表1中列出了一些离子阱与光学腔结合的案例及相关参数. 图6展示了几种集成光纤腔的离子阱结构. 图6(a)中, Innsbruck大学使用光学腔收集离子发出的854 nm光子, 通过波导将之转换为1550 nm的光子, 在光纤中传播了50 km^[93]. 得益于光学腔的使用, 该系统实现了50%的荧光收集效率和25%的波导转换效率. Sussex大学首次实现了单个离子与光学腔的强耦合^[150], 图6(b)为Sussex大学的离子阱使用了光纤腔, 光纤被一根细金属管包裹着放置于RF电极内部, 内部的金属管可以传递光纤上的电荷, 其上施加的电压可以调节离子的位置. 外圈的RF电极产生的势阱可以天然地将离子囚禁在光纤腔中心附近. 径向的四根电极可以同时施加DC电压和RF电场, 其中RF电场可以将离子精确地移动到腔模中, 以较小的微运动实现离子和腔模的强耦合^[150,152]. 2020年, Aarhus大学的研究团队实现了离子晶体与光学腔的强耦合, 如图6(c)—(e)所示. 他们使用腔长为11.8 mm的光学腔, 腔模可以覆盖三维离子晶体中的一部分, 并通过腔内激光的开关控制与离子的相互作用.

表 1 部分光学腔实验的参数, 来自文献[105]

Table 1. Structural parameters of capillary of different kind of fluid

参考文献	课题组	腔长/μm	凹面半径/μm	模式波长 /nm	束腰/μm	精细度
[153]	Walther	6000	10000	Ca-397	24	3000
[149]	Blatt	21000	25000	Ca-729	54	35000
[146, 147]	Walther	8000	10000	Ca-866	37	49000
[16, 154]	Blatt	19980	10000	Ca-866	13	70000
[148]	Chuang	50000	50000	Sr-422	57.9	25600
[145]	Vuletic	22000	25000	Yb-369	38	12500
[155]	Monroe	2126	25000	Yb-369	25	3790 $\rightarrow$ 1490
[93]	Blatt	19900	9980	Ca-866	12.3	54000
[156]	Kurtsiefer	11000	5500	Rb-780	2.4	603
[157]	Köhl	230	390	Yb-935	7	1000
[158]	Köhl	150	300	Yb-935	6.1	20000
[159]	Köhl	150	200	Yb-935	3.1	1140 $\rightarrow$ 207
[143]	Keller	367	560	Ca-866	8.5	48000

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$图 6 光学腔阱　(a) Innsbruck大学的光学腔阱[93]. 离子发出的854 nm光子有50%的概率被光学腔收集, 并被波导转换为通信波长1550 nm的光子. (b) Sussex大学的光学腔阱. 该装置首次实现了离子与腔模的强耦合[143]. (c) Aarhus大学的离子阱. 一束径向泵浦光(RP)用于Doppler冷却循环, 发光的离子可以在CCD上成像, 光学腔镜(CM)沿轴向放置, 压电平移台(PZT)将腔镜(CM)锁定到与轴向RP光共振. (d)当使用径向RP光时, 整个离子阱中的大约$6, 400 \pm 200$个离子全部发亮. (e)关闭径向的RP光, 只有光学腔中通过RP光时, 处于腔内的$536\pm18$个离子可以正常发光, 而在腔外的离子进入暗态[144]\r\nFig. 6. Ion traps with integrated optical cavities: (a) Integrated optical cavity trap in University of Innsbruck [93]. 50% of the 854-nm photons emitted from the ion can be collected by the cavity, and are converted to a communication wavelength of 1550 nm. (b) Integrated optical cavity trap in Sussex University. This trap demonstrated the first strong coupling between the ions and the cavity mode. (c) Ion trap in Aarhus University. The cavity mirror (CM) is along the axial direction, A pumping beam in the radial direction is used to pump the ions back into the Doppler cooling cycle. These ions can be imaged on the CCD. A Piezo-electric Transducer (PZT) is used to actively lock the optical cavity in resonance with the RP laser. (d) When the radial RP laser is on, the entire crystal of approximately $6, 400\pm200$ ions are all bright. (d) When the radial RP is off, only the $536\pm18$ ions in the cavity are bright. The ions outside the cavity are in dark state [144].$

图 6 光学腔阱　(a) Innsbruck大学的光学腔阱^[93]. 离子发出的854 nm光子有50%的概率被光学腔收集, 并被波导转换为通信波长1550 nm的光子. (b) Sussex大学的光学腔阱. 该装置首次实现了离子与腔模的强耦合^[143]. (c) Aarhus大学的离子阱. 一束径向泵浦光(RP)用于Doppler冷却循环, 发光的离子可以在CCD上成像, 光学腔镜(CM)沿轴向放置, 压电平移台(PZT)将腔镜(CM)锁定到与轴向RP光共振. (d)当使用径向RP光时, 整个离子阱中的大约

$6, 400 \pm 200$

个离子全部发亮. (e)关闭径向的RP光, 只有光学腔中通过RP光时, 处于腔内的

$536\pm18$

个离子可以正常发光, 而在腔外的离子进入暗态^[144]

Fig. 6. Ion traps with integrated optical cavities: (a) Integrated optical cavity trap in University of Innsbruck ^[93]. 50% of the 854-nm photons emitted from the ion can be collected by the cavity, and are converted to a communication wavelength of 1550 nm. (b) Integrated optical cavity trap in Sussex University. This trap demonstrated the first strong coupling between the ions and the cavity mode. (c) Ion trap in Aarhus University. The cavity mirror (CM) is along the axial direction, A pumping beam in the radial direction is used to pump the ions back into the Doppler cooling cycle. These ions can be imaged on the CCD. A Piezo-electric Transducer (PZT) is used to actively lock the optical cavity in resonance with the RP laser. (d) When the radial RP laser is on, the entire crystal of approximately

$6, 400\pm200$

ions are all bright. (d) When the radial RP is off, only the

$536\pm18$

ions in the cavity are bright. The ions outside the cavity are in dark state ^[144].

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4.3 三维芯片阱

刀片阱具备数个控制电极, 只能够实现离子的稳定囚禁, 无法实现离子的频繁移动、分离以及合并. 为了扩展刀片阱控制电极的数量, 丰富电极的结构, 人们设计并搭建了三维芯片阱^[78,79]. 三维芯片阱的尺寸介于宏观(macroscopic)离子阱和微观(microscopic)离子阱中间, 可以被认为是介观(mesoscopic)离子阱. 在绝缘片状材料表面镀金, 使用激光对其进行切割可以制备出分段电极, 将多层分段电极堆叠组装即可形成三维芯片阱, 它具有数十个控制电极以及更精密的电极结构, 能够很好地实现离子链的分离、转移和合并^[160,161]. 但这种离子阱的制作流程较为复杂, 需要手工加工和组装, 因此难以批量制作.

苏黎世联邦理工大学的三维芯片阱如图7所示. 该阱由11片芯片堆叠而成, 分别为: 顶部屏蔽层, 绝缘层1, 上补偿电极层, 绝缘层2, 上控制电极层, 绝缘层3, 下控制电极层, 绝缘层4, 下补偿电极层, 绝缘层5, 底部屏蔽层. 每一层为厚度为127 μm的陶瓷片, 顶部屏蔽层整体镀金且接地, 用于电磁屏蔽和减少原子炉喷出的原子对电极的污染; 绝缘层不做处理, 用于电气隔离, 而其他层都覆盖有平均8 μm厚的金层. 上下补偿电极层分别设置有7个电极, 用于微运动补偿; 上下控制电极层分别设置一个RF电极和15个DC电极, 用于囚禁和移动离子, 电极宽度依次为 1, 1000 μm; 2 和 3, 500 μm; 4, 300 μm; 5 至 7, 155 μm; 8, 300 μm; 9 至 11, 155 μm; 12, 300 μm; 13 和 14, 500 μm; 15, 1000 μm; 电极间距均为 20 μm. 整个三位芯片阱放置于一个陶瓷滤波板上, 并使用电容和电阻为每一条DC电极滤波. 该阱可以同时囚禁 $\mathrm{^{9}Be^{+}}$ 离子和 $\mathrm{^{40}Ca^{+}}$ 离子. 相对于三维刀片阱, 这种阱具备更加丰富的电极结构, 因此能够实现更加复杂的功能. 该阱共有七个功能区, 两个装载区用于将原子炉喷出的原子电离并捕获; 三个实验区用于激光与离子相互作用; 两个移动区电极较窄用于实现离子的分离、合并等操作. 该阱一共有44个DC电极, 其中7对电极用于补偿七个功能区的微运动, 而剩余的15对控制电极用于移动离子. 可以看出, 这种结构的离子阱正满足Kielpinski等^[77]提出的QCCD路线图的需要. 该阱具有十分优良的性能, 能够实现单离子声子态的丰富控制和不同离子的联合操作, 如利用声子实现量子编码^[162]、量子关联的重复读取^[163]等.

$图 7 苏黎世联邦理工大学的三维芯片阱[164]\r\nFig. 7. Three dimensional (3D) microfabricated ion Trap chip in ETH Zurich [164].$

图 7 苏黎世联邦理工大学的三维芯片阱^[164]

Fig. 7. Three dimensional (3D) microfabricated ion Trap chip in ETH Zurich ^[164].

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在一维离子阱中, 离子距离的增加会导致离子之间的相互作用减弱, 离子数目的增加又会使实现其中任意两个离子间的相互作用越来越困难. 在一维线性阱中, 可以通过交换离子的位置来解决上述问题^[65], 但随着离子间距的增加, 这种交换速率会变得越来越慢. 由两个线性离子阱相交产生的结电极结构能够有效解决这个问题. 离子从一个线性区域被移动到结电极中心, 随后进入另一个线性区域. 离子可以在这个区域与其他离子相互作用, 也可以重新回到原来的离子链中并实现离子链的重排. 结电极结构突破了一维离子链的空间限制, 对于实现QCCD结构有着至关重要的作用. 常见的结电极具有T型^[165]、X型^[78,80]、Y型^[63]等. 在结电极交汇处, 原有的一维线性结构被破坏, 轴线上的射频电场分量不再为零, 离子在通过结电极时会受到严重的微运动, 对离子造成加热. 因此在设计结电极时, 必须要优化电极的结构, 以减小这种加热效应.

三维芯片阱中可以实现结电极结构, 但需要精心设计. NIST的三维芯片阱能够以小于一个声子的加热率实现离子穿过结电极^[78,80]. 在该离子阱中, 激光切割的镀金陶瓷片构成电极, 两侧的RF电极通过桥型结构直接相连形成结电极结构. 而在苏黎世联邦理工大学的三维离子阱中, 所具有的X型结电极具有“断桥”结构^[166], 如图8所示. 该离子阱利用飞秒激光和化学刻蚀加工熔融石英, 可以实现1 µm的三维结构加工精度^[167]. 该加工工艺可以实现光滑平整的表面, 用于精确地组装, 两个控制电极层(浅灰色)的直角边缘被放置在绝缘层的斜角边缘面上以此实现固定, 组装误差小于2 μm, 有利于获得更准确更对称的势阱. 该离子阱具有五层芯片, 同样具备控制电极层、绝缘层和补偿电极层, 具有两个X型结, 共142个DC电极. 该阱具有复杂的三维电极结构, 尤其是在结电极处可以实现精确的断桥结构, 这对优化势阱参数, 降低离子通过结点处的加热十分重要.

$图 8 苏黎世联邦理工大学的三维结电极芯片阱[166]. 该离子阱由五层芯片堆叠而成, 具备两个X型结电极结构\r\nFig. 8. Three-dimensional junction trap in ETH Zurich [166]. The ion trap consists of five wafers and has two X-shaped junctions.$

图 8 苏黎世联邦理工大学的三维结电极芯片阱^[166]. 该离子阱由五层芯片堆叠而成, 具备两个X型结电极结构

Fig. 8. Three-dimensional junction trap in ETH Zurich ^[166]. The ion trap consists of five wafers and has two X-shaped junctions.

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5. 二维芯片阱

微纳加工技术的发展为离子阱的小型化和批量生产提供了丰富的技术手段, 也为未来离子阱的规模扩展和功能集成开辟了道路. 基于光刻的微纳加工工艺, 可在绝缘基底上加工出表面金属电极, 实现微米级别的电极结构. 如使用微电子机械系统(micro-electromechanical system, MEMS)制造的离子阱可具备数十个到上百个控制电极, 电极的形状可以灵活设计^[168,169], 离子阱的尺寸因此可以被缩减到毫米量级, 从而可以在同一加工过程中批量化生产芯片, 这对于离子阱的快速迭代升级和降低制造成本具有重要意义. MEMS工艺也可以生产三维芯片阱^[170,171], 但更常用于制作二维表面阱. 二维表面阱的电极结构与三维离子阱不同, 所有电极处于同一平面, 并不具备三维离子阱的对称性, 因此所产生的势阱深度较浅. 离子被囚禁在距离电极表面几十到几百微米的位置, 相比三维离子阱, 表面阱通常面临着严重的加热问题^[100], 或者具有更短的囚禁时间, 因此常常被放置于10 K以下的低温腔中, 可有效降低加热率并延长囚禁时间^[66]. 综述文献[95, 169] 详细介绍了二维芯片阱的设计理念、加工方法, 并回顾了近年来的发展. 本文在此以几个具有代表性的例子, 介绍二维芯片阱的结构和发展方向.

在二维表面阱中, 离子处于表面正上方, 激光平行于表面传播. 对于汇聚的激光光束, 在远离束腰的位置光斑半径逐渐增加, 最终被芯片遮挡. 这限制了光斑半径的进一步降低, 加大了独立寻址和提高激光功率密度的困难. 2016年, IonQ公司发布了HOA2.0 (High Optical Trap 2.0)离子阱, 具有优异的性能^[63], 如图9所示. 为了增加表面阱的通光性, HOA2.0将芯片的线性区域设计成具有狭长的轴向区域、沿着轴线的通孔, 并且放置在另一层芯片上方, 在结构上解决了遮挡的问题. 该芯片中, 离子正下方设计了长通孔, 能够使用垂直于芯片表面的强聚焦激光. 该离子阱还具备两个Y型结电极结构, 但其性能仍需进一步地提升. 在表面阱中实现结电极结构具有很多优势, 例如得益于表面电极加工技术, 电极可以被设计为各种二维形状, 通过数值模拟和优化, 可以优化电极结构使得轴向的射频分量最小, 离子经过结电极结构时的加热最低^[173,174]. 然而, 目前表面阱中结电极的性能还没有超越三维芯片阱, 离子通过结电极被加热的声子数最低为37—150个声子^[175]. 为了减小暴露的绝缘材料的面积, 在布线层将该区域用金属掩盖并接地. 金属层由铝铜合金(99.5%/0.5%)制成, 具有用于垂直互连的通孔. 所有金属层之间都用氧化硅绝缘层进行隔离. 顶部的电极镀了50 nm厚的金层, 并使用钛和铂作为附着层. 离子被束缚在距离电极表面 68 μm的位置. 2019年, 该离子阱演示了150个离子的囚禁, 79个离子的单比特操作和11个离子中任意两个离子的相互作用, 其平均的单比特门保真度为99.5%, 平均两比特门保真度为97.5%^[44]. 如图9所示, 在冷却、初始化和测量过程中, 369和935 nm的激光照亮了所有的 $\mathrm{^{171}Yb}^{+}$ 离子. 每个离子的荧光通过一个NA = 0.6的透镜成像, 其荧光(蓝色线)被收集到光电倍增管阵列上. 两束线偏振、反向传播的355 nm光束照射到离子上, 其中红色所示为同时照射到所有离子的全局光束, 紫色所示为通过物镜和多通道声光调制器(AOM)分别聚焦到每个离子的独立寻址光束^[44].

$图 9 IonQ公司的离子阱芯片HOA [63,172]　(a) HOA离子阱芯片的照片; (b)该表面阱的Y型结电极, 电极的形状已经被优化, 使得沿着轴线的射频电场分量最小, 红线表示离子在不同区域间穿梭的路径; (c)离子阱的内部结构, 该离子阱具有四个金属层, 顶部电极层(M4), 较低的金属布线层(M1, M2和M3); (d)多离子操控的光路图\r\nFig. 9. High-Optical-Access trap from IonQ Inc[63]: (a) Photo of HOA ion trap. It can be clearly seen that the linear trap is located on a higher platform, and has a long and narrow through hole along the axis, and two Y-junction electrode structures. The trap has 94 control DC electrodes. (b) Y-junction of this surface trapl. The shape of the electrodes has been optimized to minimize the RF electric field component along the axis. The red line shows the path the ions transporting between different regions. (c) Inner structure of the ion trap. This ion trap has four metal layers, the top electrode layer (M4), and the lower metal layers (M1, M2 and M3). (d) Optical diagram of the 11-qubit system[44]$

图 9 IonQ公司的离子阱芯片HOA ^[63,172]　(a) HOA离子阱芯片的照片; (b)该表面阱的Y型结电极, 电极的形状已经被优化, 使得沿着轴线的射频电场分量最小, 红线表示离子在不同区域间穿梭的路径; (c)离子阱的内部结构, 该离子阱具有四个金属层, 顶部电极层(M4), 较低的金属布线层(M1, M2和M3); (d)多离子操控的光路图

Fig. 9. High-Optical-Access trap from IonQ Inc^[63]: (a) Photo of HOA ion trap. It can be clearly seen that the linear trap is located on a higher platform, and has a long and narrow through hole along the axis, and two Y-junction electrode structures. The trap has 94 control DC electrodes. (b) Y-junction of this surface trapl. The shape of the electrodes has been optimized to minimize the RF electric field component along the axis. The red line shows the path the ions transporting between different regions. (c) Inner structure of the ion trap. This ion trap has four metal layers, the top electrode layer (M4), and the lower metal layers (M1, M2 and M3). (d) Optical diagram of the 11-qubit system^[44]

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Honeywell公司设计并制作了一种低温线性表面离子阱芯片^[65], 其目标是创建一个基于QCCD架构的高保真的、可扩展的量子计算机. 如图10(a)所示, 该公司提供了一个可以云访问的架构, 系统的信息流(从上到下)依次为: 用户、云端、内部离子分配、机器控制和现场可编程门阵列(FPGA). 线路由编译器处理, 生成控制信号(紫色), 发送到离子阱和光电子器件. 成像系统对自发辐射光子进行计数, 再将结果(绿色)发送回用户或进行实时决策处理. 用户提交一份量子线路程序到云端, 编译器以最小化传输操作数量为原则将量子比特分配给物理离子, 机器根据程序, 控制FPGA产生信号控制离子阱进行一系列传输和逻辑门操作, 并进行测量. 如图10(b)所示, 该离子阱具有线性几何结构, 离子被囚禁在阱表面上方70 $\text{µ} \rm{ m}$ 处, 整体处于12.6 K的低温系统中. 整个离子阱包含198个分段DC电极和两个RF电极, 共分为5个用于实现光与离子相互作用操作区, 2个存储区, 8个用于实现离子置换操作的存储和排序区, 以及1个用于加载离子的装载区, 对离子具有灵活的操作能力. 使用 $^{171}\mathrm{Yb}^{+}$ 离子的超精细结构中的两个能级 $\left| 0 \right\rangle \equiv{}^{2}{\rm{S}}_{1/2}\left|F=0, \thinspace m_{F}=0 \right\rangle$ 和 $\left| 1 \right\rangle \equiv{}^{2}{\rm{S}}_{1/2}\left|F=1, \thinspace m_{F}=0 \right\rangle$ 作为量子比特, 使用 $^{138}\mathrm{Ba}^{+}$ 离子作为协同冷却离子, 始终保持一个 $^{171}\mathrm{Yb}^{+}$ 和一个 $^{138}\mathrm{Ba}^{+}$ 组成离子对, 共同参与移动和操作. 操作激光与表面平行, 由于激光的发散特性, 芯片中心区域以一定高度放置在基座上, 减小芯片对激光的遮挡损耗. 在目前的配置中, 激光没有实现独立寻址, 因此任意两个离子之间的相互作用都需要通过重新排列离子的位置来实现. 离子在轴向的运动频率为0.97 MHz, 加热率为每秒100—500个声子, 径向加热率约为每秒500个声子^[65]. 如图10(c)所示, 该系统演示了一个包含QCCD要素的操作, 包括: 1)囚禁多个离子晶体, 需要使用低温系统^[66,67]; 2)实现离子链的重排列和快速移动, 并尽可能减小加热^[176,177]; 3)离子在不同功能区的状态具有不均匀性, 需要在时钟上实现同步; 4)可能需要同时囚禁两种不同的离子, 一种用于量子门操作, 另一种是在输运后将晶体协同冷却到接近基态^[178]; 5)并行实施离子移动和量子操作. 凭借着良好的性能, Honeywell公司在该平台上用10量子比特实现了利用颜色码的实时容错量子纠错^[49].

$图 10 Honeywell公司的Model H1离子阱[65]　(a)云操作运行结构; (b)离子阱的结构, 该离子阱由16个不同区域组成, 分别为五个门操作区(蓝色)、两个专门用于存储离子的扩展门操作区(橙色)、八个辅助区(黄色)和一个装载区(紫色); (c)基于移动离子实现两个非近邻离子两比特门操作的量子电路, 以及其在该离子阱系统中对应的操作流程\r\nFig. 10. Honeywell's Model H1 ion trap [65]: (a) Structure of cloud operation ionn trap system. (b) The structure of the trap. The trap consists of 16 distinct zones, consisting of five gate zones (blue), two extended gate zones dedicated to ion storage (orange), eight auxiliary zones (yellow), and one loading zone (violet). (c) A quantum circuit for realizing a two-qubit gate operation between two ions that are not adjacent, and its corresponding operation flow in the ion trap system$

图 10 Honeywell公司的Model H1离子阱^[65]　(a)云操作运行结构; (b)离子阱的结构, 该离子阱由16个不同区域组成, 分别为五个门操作区(蓝色)、两个专门用于存储离子的扩展门操作区(橙色)、八个辅助区(黄色)和一个装载区(紫色); (c)基于移动离子实现两个非近邻离子两比特门操作的量子电路, 以及其在该离子阱系统中对应的操作流程

Fig. 10. Honeywell's Model H1 ion trap ^[65]: (a) Structure of cloud operation ionn trap system. (b) The structure of the trap. The trap consists of 16 distinct zones, consisting of five gate zones (blue), two extended gate zones dedicated to ion storage (orange), eight auxiliary zones (yellow), and one loading zone (violet). (c) A quantum circuit for realizing a two-qubit gate operation between two ions that are not adjacent, and its corresponding operation flow in the ion trap system

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表面阱与集成电路、集成光学的结合也给人们实现功能更强大的QCCD结构开辟了新的途径, 如片上集成的光电探测器^[84,179]有助于实现多离子的独立探测, 利用CMOS工艺集成DAC到离子阱芯片上有助于实现控制电路的扩展, 或者集成光波导与表面阱的结合有助于实现操作光路的可扩展^[64,81,82]. 相比之下, 传统的空间光路不仅体积较大、元件众多、可扩展性差, 而且还容易受到振动、温度等因素的影响. 空间光可以满足当前的几十个离子系统的需求, 但是当系统扩展到上百甚至上千个离子时, 激光的扩展性将变得至关重要, 成为限制操作可扩展性的主要因素. 集成光波导与离子阱的结合可以实现片上集成光路, 通过微纳光学器件传导激光, 并最终聚焦到离子上. 片上光学还可以实现电光调制器件, 实现激光幅度、相位的调制, 代替空间光的调制器. 因此, 集成光学与离子阱芯片的结合有望解决操作光路的扩展问题.

麻省理工学院(MIT)最早实现集成波导离子阱芯片^[81], 苏黎世联邦理工大学(ETH)和美国圣地亚(Sandia)国家实验室也陆续开展了相关研究^[64,82,83]. 他们所使用的波导由SiN的波导芯和 $\mathrm{SiO_{2}}$ 包层组成. SiN的折射率为1.95—2.0, 大于 $\mathrm{SiO_{2}}$ 的1.44. 内外层材料折射率的差别较大使得光波在该波导中具有更小的模式, 可以实现更小的弯曲半径和更小的弯曲损耗, 光波的相位和幅度在传播过程中更不容易受到扰动. 但目前所使用的的材料仍然具有较大的损耗, 对于633 nm以上的波长, SiN波导的传输损耗在0.5 dB/cm以下, 但在405 nm的波长下, 损耗增加到约10 dB/cm^[180]. 图11所示为麻省理工大学的集成波导离子阱芯片^[64]. 图11(a)给出了集成光波导的结构和光栅耦合器将激光聚焦到离子上的路径. 表面阱电极下的集成波导(棕色)采用100 nm厚SiN内芯和5 μm的 $\mathrm{SiO_{2}}$ 包层, 内芯的刻蚀深度为40 nm; 上方是铌(Nb)金属制作的控制电极(金色), 下方为Nb金属地层. 图中标注了各个层的厚度. 最上层具有 $20\,{\mu {\rm{m}}}\times 20\,{\mu {\rm{m}}}$ 大小的通光孔, 镀有一层厚20 nm的高导电性的氧化铟锡(ITO)薄膜, 来避免绝缘材料的充电问题. 红色箭头表示通过输出光栅耦合器衍射出来的光的传播方向, 蓝色圆点表示离子的位置, 离子被囚禁在距离表面55 μm处. 图11(b)展示了该芯片最大的特点, 即集成了 $\mathrm{^{88}Sr^{+}}$ 离子所需要的全部6个波长的光, 分别为405, 422, 461, 674, 1033和1092 nm. 6个波长的激光通过边缘耦合的方式耦合到离子阱芯片的SiN集成波导中, 并通过不同的光栅同时聚焦到单个离子上. 图11(c)展示了光纤通过真空馈通进入真空系统内部, 离子阱芯片位于低温腔冷头上. 这种结构天然对振动和光束方向漂移具有鲁棒性, 可以获得比自由空间光束更长的相干时间. 尤其是对于放置于低温系统的表面阱而言, 波导对于低温系统的振动所带来的激光指向抖动问题有着很大的改善. 图11(d)为使用光波导实现单个离子的操作^[64]. 中性 $\mathrm{^{88}Sr}$ 原子被461 nm激光激发到 $\mathrm{P_{1}}$ 态, 再通过405 nm激光电离得到离子. 量子比特编码在 $\mathrm{^{88}Sr^{+}}$ 离子的 $\mathrm{S_{1/2}}$ 和 $\mathrm{D_{5/2}}$ 能级, 使用674 nm激光实现比特翻转. 该系统的光损耗问题十分突出, 光纤和光波导的耦合会产生约10 dB的损耗, 激光从波导经过光栅传输到离子约有10 dB的损耗, 除此之外, 从自由空间激光耦合到光纤、光纤真空馈通、波导传输等损耗也不容忽视. 最终, 该系统中的每种波长都具有26—35 dB的总损耗. 除了光损耗, 芯片上激光出射的方向和聚焦是通过具有一定曲率的衍射光栅实现的, 由于加工误差, 离子并不能恰好落在光斑束腰位置, 因此导致的有效激光功率也小于实际出射的功率. 图11(e)和图11(f)展示了该系统的实物图.

$图 11 麻省理工大学(MIT)集成波导离子阱结构示意图[64]　(a)集成在$ \mathrm{SiO_{2}} $内的光波导和输出光栅耦合器将激光聚焦到离子上; (b)激光从光纤通过边缘耦合进入芯片中的波导; (c)光纤经过光纤真空馈通进入低温真空环境, 芯片放置于7 K冷头上; (d)$ \mathrm{^{88}Sr} $原子和$ \mathrm{^{88}Sr^{+}} $离子的能级图; (e)离子阱中心区域的扫描电子显微镜(SEM)图像, 显示了电极上的方形通光窗口以及周围的RF电极和DC电极分布, 插图: 扫描电镜显示的光栅耦合器, 可以实现光束横向聚焦; (f)集成波导离子阱芯片封装, 插图为1 $ \mathrm{cm^{2}} $左右的离子阱芯片\r\nFig. 11. Ion trap integrated with waveguides used by Massachusetts institute of technology (MIT) [64]: (a) Lasers are propagating in the Optical waveguide and focused to the ion by the grating coupler in $ \mathrm{SiO_{2}} $ substrate. (b) Lasers are coupled from the optical fiber to the on-chip waveguide using the edge coupling method. (c) Optical fibers are fed through the cryostat system using the fiber feedthrough.The ion trap chip is located on the cold head at 7 K. (d) $ \mathrm{^{88}Sr} $ and $ \mathrm{^{88}Sr^{+}} $ ion energy level diagram. (e) The scanning electron microscope (SEM) image of the central region of the ion trap shows the square light-passing window on the electrode and the distribution of RF electrode and DC electrode around it. Inset: A scanning electron microscope shows a grating coupler that enables transverse focusing of a beam. (f) Photonic ion-trap chip packaged. Inset is an ion trap chip around 1 $ \mathrm{cm^{2}} $.$

图 11 麻省理工大学(MIT)集成波导离子阱结构示意图^[64]　(a)集成在

$\mathrm{SiO_{2}}$

内的光波导和输出光栅耦合器将激光聚焦到离子上; (b)激光从光纤通过边缘耦合进入芯片中的波导; (c)光纤经过光纤真空馈通进入低温真空环境, 芯片放置于7 K冷头上; (d)

$\mathrm{^{88}Sr}$

原子和

$\mathrm{^{88}Sr^{+}}$

离子的能级图; (e)离子阱中心区域的扫描电子显微镜(SEM)图像, 显示了电极上的方形通光窗口以及周围的RF电极和DC电极分布, 插图: 扫描电镜显示的光栅耦合器, 可以实现光束横向聚焦; (f)集成波导离子阱芯片封装, 插图为1

$\mathrm{cm^{2}}$

左右的离子阱芯片

Fig. 11. Ion trap integrated with waveguides used by Massachusetts institute of technology (MIT) ^[64]: (a) Lasers are propagating in the Optical waveguide and focused to the ion by the grating coupler in

$\mathrm{SiO_{2}}$

substrate. (b) Lasers are coupled from the optical fiber to the on-chip waveguide using the edge coupling method. (c) Optical fibers are fed through the cryostat system using the fiber feedthrough.The ion trap chip is located on the cold head at 7 K. (d)

$\mathrm{^{88}Sr}$

and

$\mathrm{^{88}Sr^{+}}$

ion energy level diagram. (e) The scanning electron microscope (SEM) image of the central region of the ion trap shows the square light-passing window on the electrode and the distribution of RF electrode and DC electrode around it. Inset: A scanning electron microscope shows a grating coupler that enables transverse focusing of a beam. (f) Photonic ion-trap chip packaged. Inset is an ion trap chip around 1

$\mathrm{cm^{2}}$

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苏黎世联邦理工大学改进了耦合方法, 实现了729 nm激光的高效耦合, 总损耗只有6.4 dB. 该芯片使用片上集成的729 nm操作两个 $\mathrm{^{40}Ca^{+}}$ 离子, 并实现了保真度99.3 %的两比特门^[82]. 圣地亚国家实验室的芯片将 $\mathrm{^{171}Yb}^{+}$ 离子囚禁在表面上20 μm的高度, 并研究了输出耦合器及其形状对离子加热率的影响^[83]. 未来, 进一步提升激光的耦合效率、降低波导的传输损耗、优化光波导与离子的位置匹配精度是使用集成光波导实现可扩展操作需要解决的问题. 同时, 结合电光调制晶体实现片上激光调制, 有利于进一步完善激光的集成.

离子阱系统中, 激光和微波是最主要的操作工具. 由于光子的动量较大, 容易实现离子间的相互作用, 所以人们一般使用激光来驱动离子的运动态. 然而使用激光会面临失谐散射、强度和相位噪音、对振动敏感、难以扩展等问题. 相比之下, 微波的能量要小得多, 无法直接驱动离子的声子状态, 但使用微波可以避免或减小这些因素的影响. 因此需要磁场梯度的辅助. 静磁场梯度可以直接使用静磁铁或者通电线圈产生^[181,182], 而使用近场微波磁场梯度或近场射频磁场梯度^[183,184]有利于实现更强更丰富的磁场梯度. 图12(a)所示为NIST的表面离子阱^[41], 具有若干可以通过射频或者微波电流的电极, 可以产生近场射频或微波磁场梯度. 当该电场的频率满足一定条件时, 可以使用微波来对离子进行寻址操作以及实现多离子门.

$图 12 NIST的集成载流导线离子阱芯片[41]. 图中RF电极(紫色)和DC电极(灰色)用于囚禁离子两个$ \mathrm{^{25}Mg^{+}} $离子, 距表面30 μm. 频率达MHz的射频电流被加载到绿色(编号1到3)的载流电极上, 在离子附近产生垂直于轴的射频磁场和射频磁场梯度. 利用该梯度产生的力, 可以使用微波实现两离子纠缠门. 左上方的小图中, 两个离子偏移轴线而受到不同的射频磁场, 由于AC zeeman移频效应而具有不同的能级, 可以实现离子的独立寻址\r\nFig. 12. NIST’s integrated current-carrying wire(CCW) ion trap chip[41]. RF electrodes (purple) and DC electrodes (gray) are used to trap two $ \mathrm{^{25}Mg^{+}} $ ions, 30 μm from the surface. RF currents at frequencies up to MHz are loaded onto green (numbered 1 to 3) current-carrying electrodes, generating RF magnetic fields and RF magnetic gradients perpendicular to the axis near the ions. Using the forces generated by this gradient, a two-ion entanglement gate can be realized using microwaves. In the small figure on the upper left, two ions with different RF magnetic fields due to their offset axes have different energy levels due to the AC Zeeman frequency shift effect and can achieve independent ion addressing.$

图 12 NIST的集成载流导线离子阱芯片^[41]. 图中RF电极(紫色)和DC电极(灰色)用于囚禁离子两个

$\mathrm{^{25}Mg^{+}}$

离子, 距表面30 μm. 频率达MHz的射频电流被加载到绿色(编号1到3)的载流电极上, 在离子附近产生垂直于轴的射频磁场和射频磁场梯度. 利用该梯度产生的力, 可以使用微波实现两离子纠缠门. 左上方的小图中, 两个离子偏移轴线而受到不同的射频磁场, 由于AC zeeman移频效应而具有不同的能级, 可以实现离子的独立寻址

Fig. 12. NIST’s integrated current-carrying wire(CCW) ion trap chip^[41]. RF electrodes (purple) and DC electrodes (gray) are used to trap two

$\mathrm{^{25}Mg^{+}}$

ions, 30 μm from the surface. RF currents at frequencies up to MHz are loaded onto green (numbered 1 to 3) current-carrying electrodes, generating RF magnetic fields and RF magnetic gradients perpendicular to the axis near the ions. Using the forces generated by this gradient, a two-ion entanglement gate can be realized using microwaves. In the small figure on the upper left, two ions with different RF magnetic fields due to their offset axes have different energy levels due to the AC Zeeman frequency shift effect and can achieve independent ion addressing.

下载: 全尺寸图片幻灯片

6. 总　结

本文综述了离子阱的工作原理和不同的结构. 在过去的几十年里, 离子阱在结构和性能上实现了巨大的发展, 从最初的双曲面型结构, 发展出四极杆阱、刀片阱、光学腔阱、三维芯片阱、二维芯片阱、光学集成的芯片阱等一系列结构. 离子阱能够高水平地完成量子计算所需要的基本要素, 具有明确的可扩展路线图, 是实现大规模量子模拟和量子计算最重要的平台之一. 三维离子阱在势阱深度、加热率、通光性和光学腔集成方面具有许多优秀的性能, 仍然是当前主要使用的离子阱结构之一. 而随着微纳加工技术、低温系统、集成电路和集成光学在离子阱芯片上的成功应用, 二维离子阱芯片也展现出极大的潜力, 使得批量化生产具有高保真度、高集成度和低成本的离子阱产品成为可能. 但是, 离子数目和操控能力的进一步扩展仍然面临着很多问题, 如何在一个离子阱中实现更多离子的操作、具有纠错能力的量子编码、量子逻辑比特间的操作是一个离子阱系统需要解决的主要问题, 而如何实现多个离子阱系统、离子阱系统与其他系统的连接是最终实现大规模量子计算必须要解决的问题. 这不仅对离子阱本身的结构提出了要求, 还需要生产加工水平的不断提升.

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其他类型引用(2)

图 1 双曲面离子阱示意图^[95]

Figure 1. Schematic of a Paul trap with hyperbolic shaped electrodes^[95]

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图 2 四极杆离子阱　(a)不分段的四极杆阱需要端帽电极提供轴向束缚^[110]; (b)分段的四极杆阱使用分段电极提供轴向束缚^[112]

Figure 2. Four-rod trap: (a) Unsegmented four-rod trap requires end cap electrodes to provide axial confinement ^[110]; (b) segmented four-rod trap uses the segmented electrodes to provide axial confinement^[112]

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图 3 Innsbruck式的刀片阱^[61]　(a)组装后的离子阱实物图; (b)离子阱尺寸和结构图

Figure 3. Innsbruck style blade ion trap: (a) Photograph of an assembled blade trap; (b) dimensions and structure of the trap

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Figure 4. Maryland style blade ion trap^[62]: (a) Structure of segmented blade ion trap. The segmented blade not only can provide axial confinement, but also generate non-quadratic axial potential to achieve uniform ion distance; (b) in another blade ion trap, the out-most segment is increased to 10 mm from 250 μm in order to reduce the residual RF electric field along the axial direction^[116,117]

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Figure 5. The blade ion trap used in University of Science and Technology of China ^[109]: (a) A blade ion trap is placed in a glass vacuum cell. Two objectives with a maximum NA of 0.32 and another two objectives with a maximum NA of 0.66 are allowed to be used simultaneously. (b) The structure of the blade ion trap. The blades are made from fused silica and coated with a 8 μm gold layer. The surface gold of the DC electrodes is segmented into five using laser cutting

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Figure 6. Ion traps with integrated optical cavities: (a) Integrated optical cavity trap in University of Innsbruck ^[93]. 50% of the 854-nm photons emitted from the ion can be collected by the cavity, and are converted to a communication wavelength of 1550 nm. (b) Integrated optical cavity trap in Sussex University. This trap demonstrated the first strong coupling between the ions and the cavity mode. (c) Ion trap in Aarhus University. The cavity mirror (CM) is along the axial direction, A pumping beam in the radial direction is used to pump the ions back into the Doppler cooling cycle. These ions can be imaged on the CCD. A Piezo-electric Transducer (PZT) is used to actively lock the optical cavity in resonance with the RP laser. (d) When the radial RP laser is on, the entire crystal of approximately $6, 400\pm200$ ions are all bright. (d) When the radial RP is off, only the $536\pm18$ ions in the cavity are bright. The ions outside the cavity are in dark state ^[144].

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图 7 苏黎世联邦理工大学的三维芯片阱^[164]

Figure 7. Three dimensional (3D) microfabricated ion Trap chip in ETH Zurich ^[164].

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图 8 苏黎世联邦理工大学的三维结电极芯片阱^[166]. 该离子阱由五层芯片堆叠而成, 具备两个X型结电极结构

Figure 8. Three-dimensional junction trap in ETH Zurich ^[166]. The ion trap consists of five wafers and has two X-shaped junctions.

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Figure 9. High-Optical-Access trap from IonQ Inc^[63]: (a) Photo of HOA ion trap. It can be clearly seen that the linear trap is located on a higher platform, and has a long and narrow through hole along the axis, and two Y-junction electrode structures. The trap has 94 control DC electrodes. (b) Y-junction of this surface trapl. The shape of the electrodes has been optimized to minimize the RF electric field component along the axis. The red line shows the path the ions transporting between different regions. (c) Inner structure of the ion trap. This ion trap has four metal layers, the top electrode layer (M4), and the lower metal layers (M1, M2 and M3). (d) Optical diagram of the 11-qubit system^[44]

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Figure 10. Honeywell's Model H1 ion trap ^[65]: (a) Structure of cloud operation ionn trap system. (b) The structure of the trap. The trap consists of 16 distinct zones, consisting of five gate zones (blue), two extended gate zones dedicated to ion storage (orange), eight auxiliary zones (yellow), and one loading zone (violet). (c) A quantum circuit for realizing a two-qubit gate operation between two ions that are not adjacent, and its corresponding operation flow in the ion trap system

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图 11 麻省理工大学(MIT)集成波导离子阱结构示意图^[64]　(a)集成在 $\mathrm{SiO_{2}}$ 内的光波导和输出光栅耦合器将激光聚焦到离子上; (b)激光从光纤通过边缘耦合进入芯片中的波导; (c)光纤经过光纤真空馈通进入低温真空环境, 芯片放置于7 K冷头上; (d) $\mathrm{^{88}Sr}$ 原子和 $\mathrm{^{88}Sr^{+}}$ 离子的能级图; (e)离子阱中心区域的扫描电子显微镜(SEM)图像, 显示了电极上的方形通光窗口以及周围的RF电极和DC电极分布, 插图: 扫描电镜显示的光栅耦合器, 可以实现光束横向聚焦; (f)集成波导离子阱芯片封装, 插图为1 $\mathrm{cm^{2}}$ 左右的离子阱芯片

Figure 11. Ion trap integrated with waveguides used by Massachusetts institute of technology (MIT) ^[64]: (a) Lasers are propagating in the Optical waveguide and focused to the ion by the grating coupler in $\mathrm{SiO_{2}}$ substrate. (b) Lasers are coupled from the optical fiber to the on-chip waveguide using the edge coupling method. (c) Optical fibers are fed through the cryostat system using the fiber feedthrough.The ion trap chip is located on the cold head at 7 K. (d) $\mathrm{^{88}Sr}$ and $\mathrm{^{88}Sr^{+}}$ ion energy level diagram. (e) The scanning electron microscope (SEM) image of the central region of the ion trap shows the square light-passing window on the electrode and the distribution of RF electrode and DC electrode around it. Inset: A scanning electron microscope shows a grating coupler that enables transverse focusing of a beam. (f) Photonic ion-trap chip packaged. Inset is an ion trap chip around 1 $\mathrm{cm^{2}}$ .

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图 12 NIST的集成载流导线离子阱芯片^[41]. 图中RF电极(紫色)和DC电极(灰色)用于囚禁离子两个 $\mathrm{^{25}Mg^{+}}$ 离子, 距表面30 μm. 频率达MHz的射频电流被加载到绿色(编号1到3)的载流电极上, 在离子附近产生垂直于轴的射频磁场和射频磁场梯度. 利用该梯度产生的力, 可以使用微波实现两离子纠缠门. 左上方的小图中, 两个离子偏移轴线而受到不同的射频磁场, 由于AC zeeman移频效应而具有不同的能级, 可以实现离子的独立寻址

Figure 12. NIST’s integrated current-carrying wire(CCW) ion trap chip^[41]. RF electrodes (purple) and DC electrodes (gray) are used to trap two $\mathrm{^{25}Mg^{+}}$ ions, 30 μm from the surface. RF currents at frequencies up to MHz are loaded onto green (numbered 1 to 3) current-carrying electrodes, generating RF magnetic fields and RF magnetic gradients perpendicular to the axis near the ions. Using the forces generated by this gradient, a two-ion entanglement gate can be realized using microwaves. In the small figure on the upper left, two ions with different RF magnetic fields due to their offset axes have different energy levels due to the AC Zeeman frequency shift effect and can achieve independent ion addressing.

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表 1 部分光学腔实验的参数, 来自文献[105]

Table 1. Structural parameters of capillary of different kind of fluid

参考文献	课题组	腔长/μm	凹面半径/μm	模式波长 /nm	束腰/μm	精细度
[153]	Walther	6000	10000	Ca-397	24	3000
[149]	Blatt	21000	25000	Ca-729	54	35000
[146, 147]	Walther	8000	10000	Ca-866	37	49000
[16, 154]	Blatt	19980	10000	Ca-866	13	70000
[148]	Chuang	50000	50000	Sr-422	57.9	25600
[145]	Vuletic	22000	25000	Yb-369	38	12500
[155]	Monroe	2126	25000	Yb-369	25	3790 $\rightarrow$ 1490
[93]	Blatt	19900	9980	Ca-866	12.3	54000
[156]	Kurtsiefer	11000	5500	Rb-780	2.4	603
[157]	Köhl	230	390	Yb-935	7	1000
[158]	Köhl	150	300	Yb-935	6.1	20000
[159]	Köhl	150	200	Yb-935	3.1	1140 $\rightarrow$ 207
[143]	Keller	367	560	Ca-866	8.5	48000

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