量子存储性能及应用分析

王云飞; 周颖; 王英; 颜辉; 朱诗亮

doi:10.7498/aps.72.20231203

摘要

Abstract

作者及机构信息

Authors and contacts

文章全文

1. 引　言
2. 量子存储指标
2.1 存储效率
2.2 存储寿命
2.3 存储保真度
2.4 模式容量
3. 量子存储典型应用
3.1 量子纠缠
3.2 存储辅助增强的多光子过程
3.3 不同粒子的量子干涉
4. 总　结

参考文献

摘要

在量子网络体系中, 光是信息的最好载体. 通过探讨光与物质的相互作用, 可以进一步发展量子存储技术. 这种技术能同步接收和按需获取光量子信息, 是建立大规模量子计算和远距离量子通信的基础. 但是, 量子存储的性能直接影响了其实际应用价值和量子信息技术的进步. 在过去的二十多年里, 多种物理体系和量子信息协议中的量子存储已经得到了深入的研究, 其存储性能也得到了显著的提升, 而且其相关的应用也有了广泛的展示. 本文系统梳理了最近十年来关于量子存储的所有性能指标的研究进展, 并根据冷原子体系和固态掺杂离子晶体系的特性, 详细探讨了存储效率、存储寿命、存储保真度和模式容量等方面的发展情况. 同时, 对近期量子存储在量子纠缠、存储辅助增强的多光子过程以及不同粒子量子干涉等方面的典型应用进行了介绍. 最后, 对量子存储的未来发展进行了展望和总结.

关键词:

Abstract

Light is the best carrier of information in quantum network. By exploring the interaction of light with matter, quantum memory technology can be further developed. Quantum memory can simultaneously receive and obtain optical quantum information on demand, which is the basis for establishing large-scale quantum computing and long-distance quantum communication. However, the performance of quantum memory directly affects its practical application process and the progress of quantum information technology. In the past two decades, quantum memory in various physical systems and quantum information protocols has been intensively studied, its performance has been significantly improved, and its relevant applications have been widely demonstrated. In this paper, we firstly sort the research progress of quantum memory metrics in the past ten years, and discuss the development of efficiency, lifetime, fidelity and mode capacity in detail according to the characteristics of cold atom systems and solid-state doped ion crystal systems. Secondly, the recent typical applications of quantum memory in quantum entanglement, memory-enhanced multi-photon processes, and quantum interference of different particles are introduced. Finally, the future development of quantum storage is prospected and summarized.

Keywords:

PACS:

67.85.-d	(Ultracold gases, trapped gases)
03.67.-a	(Quantum information)
42.50.-p	(Quantum optics)
03.67.Hk	(Quantum communication)

作者及机构信息

1.
华南师范大学物理学院, 原子亚原子结构与量子调控教育部重点实验室, 广州　510006

2.
华南师范大学, 广东省量子调控工程与材料重点实验室, 广州　510006

3.
华南师范大学, 粤港量子物质联合实验室, 广州　510006

通信作者: 王云飞, yunfeiwang2014@126.com

基金项目: 国家自然科学基金(批准号: 12004120)、广东省自然科学基金(批准号: 2022A1515011327, 2020A1515110848)和广东省重点领域研发计划(批准号: 2019B030330001)资助的课题.

Authors and contacts

1.
Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), School of Physics, South China Normal University, Guangzhou 510006, China

2.
Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China

3.
Guangdong-Hong Kong Joint Laboratory of Quantum Matter, South China Normal University, Guangzhou 510006, China

Corresponding author: Wang Yun-Fei, yunfeiwang2014@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12004120), the Natural Science Foundation of Guangdong Province, China (Grant Nos. 2022A1515011327, 2020A1515110848), and the Key-Area Research and Development Program of Guangdong Province, China (Grant No. 2019B030330001).

文章全文

1. 引　言

在量子信息领域, 光子扮演着重要的角色, 主要因其具有传播速度快、抗干扰能力强和信息容量大的特点. 这些优点使其被科学界誉为量子信息的理想载体^[1]. 单光子, 作为光的最小能量单元, 能携带的信息无法复制, 因而被誉为实现量子通信的理想工具^[2–6]. 然而, 光子的强抗干扰性让其难以被控制. 因此, 需通过光与物质的相互作用及非线性过程来操控光子^[7–9]. 在量子通信和量子网络等领域, 利用光与物质的相互作用进行量子信息交换, 具有重要的科学意义^[10–16]. 其中, 由光与物质相互作用派生出来的量子存储技术引起了科研领域的广泛关注. 研究者们致力于将光子携带的量子信息非破坏性地转移至介质, 并在需要的时候提取出来^[17–20]. 量子存储在量子通信和量子网络等相关领域发挥着重要作用. 例如, 在远距离量子通信研究中, 利用量子中继器可以克服远距离传输带来的光子损耗问题, 而量子存储器是量子中继器的核心组件^[4,5,21,22]. 在量子网络中, 节点间的量子态传递和纠缠分发也需借助于量子存储^{[11,12,23,24]}. 并且在多光子产生、多光子干涉以及纠缠交换等实验中, 使用量子存储器可以显著提高单位时间内的成功率^[25,26], 从而节约时间成本.

量子存储主要分为吸收型与DLCZ型两类, 如图1所示^[5]. 吸收型存储能对外部量子信息实现存储, 物理过程是先将外来的光子信息转移到存储介质, 即通过控制介质把光携带的信息存储到介质. 存储一定时间后, 再利用控制场把量子信息恢复到光子并释放, 实现信息的完整存储过程. 吸收型存储不仅可在原子系综、固态掺杂离子晶体和单粒子体系中实现, 也可以同时实现相干光和单光子的存储. 然而, 真正的量子存储需要具备存储单光子并维持良好量子态的能力. 在此, 我们将相干光或单光子水平的存储称为光存储, 对实现真正的单光子存储则称为量子存储. DLCZ型量子存储是只读存储, 其物理过程是首先通过一束写入激光来激发存储介质, 在介质内建立单激发状态的同时释放一个单光子. 存储一定时间后, 再利用读取激光将介质中的激发状态转化为光子释放, 同时保证先后释放的两个光子具有关联性. DLCZ型量子存储器既可以作为光子源, 也可以提供时间同步.

$图 1 (a)吸收型量子存储过程及能级方案. 单光子源产生的光子编码量子信息后, 输入进存储介质中. 待光子完全进入介质, 通过调控控制场将光子信息转化成原子自旋信息, 随后再次调控控制光场恢复光子信息并读取出来. (b) DLCZ型量子存储过程及能级方案. 一束写入激光对原子系综进行单激发, 同时释放一个斯托克斯光子, 随后一束读取激光再次作用到单激发介质上, 释放一个反斯托克斯光子. 两个光子之间的时间延迟可以通过操控写入和读取光的相对时间来控制\r\nFig. 1. The absorptive quantum memory and energy level scheme. The photons generated by the single photon source encode quantum information and are input into the storage medium. After the photons have completely entered the medium, the light quantum information is converted into atomic spin wave by manipulating the control field, and then the light quantum information is read out again by manipulating the control field. (b) DLCZ quantum memory and energy level scheme. A writing laser beam couple the atomic ensemble and simultaneously releases a Stokes photon, and then a reading laser beam couple the medium again to release an anti-Stokes photon. The time delay between two photons can be controlled by manipulating the relative timing of writing and reading laser.$

图 1 (a)吸收型量子存储过程及能级方案. 单光子源产生的光子编码量子信息后, 输入进存储介质中. 待光子完全进入介质, 通过调控控制场将光子信息转化成原子自旋信息, 随后再次调控控制光场恢复光子信息并读取出来. (b) DLCZ型量子存储过程及能级方案. 一束写入激光对原子系综进行单激发, 同时释放一个斯托克斯光子, 随后一束读取激光再次作用到单激发介质上, 释放一个反斯托克斯光子. 两个光子之间的时间延迟可以通过操控写入和读取光的相对时间来控制

Fig. 1. The absorptive quantum memory and energy level scheme. The photons generated by the single photon source encode quantum information and are input into the storage medium. After the photons have completely entered the medium, the light quantum information is converted into atomic spin wave by manipulating the control field, and then the light quantum information is read out again by manipulating the control field. (b) DLCZ quantum memory and energy level scheme. A writing laser beam couple the atomic ensemble and simultaneously releases a Stokes photon, and then a reading laser beam couple the medium again to release an anti-Stokes photon. The time delay between two photons can be controlled by manipulating the relative timing of writing and reading laser.

下载: 全尺寸图片幻灯片

本文介绍了不同类型和体系的量子存储在存储效率、存储寿命、存储保真度和存储模式容量4个关键指标的研究进展, 这些指标直接影响量子存储是否能实现实用化. 随后, 介绍了近期量子存储的一些典型应用, 包括量子纠缠、存储辅助增强的多光子过程、以及不同单粒子的量子干涉等. 最后, 对量子存储的研究发展前景进行了总结与展望.

2. 量子存储指标

量子存储的主要指标包括存储效率、存储寿命、存储保真度、存储模式容量、存储带宽及工作波长等. 不同存储协议和物理体系在应用时要求到达的指标存在差异, 即每个协议和体系都具有独特的指标特性. 以下将介绍在量子中继应用中最关键的几项存储指标的研究进展.

2.1 存储效率

存储效率是量子存储器非常重要的指标, 高效率量子存储是各个研究组都在追求的目标. 2011 年Sangouard等^[21]通过计算发现, 利用量子中继实现远距离纠缠分发, 所需的时间成本会随着存储效率的降低而大大增加, 例如存储效率从90% 降到89% 将造成时间成本增加 10%—14%.

量子存储类型不同, 存储效率定义不一样. 因此, 不同定义下的效率无法进行比较. 对于吸收型量子存储来说, 相干光条件下的存储效率是指读出和存入的光场强度比值. 对于量子存储, 存储效率是单光子存入并读取出来的概率, 或者读出与存入的光子个数比.

$\eta_{m}=\frac{{\displaystyle\int {{{\left| {{\psi _{{\rm{out}}}}\left( \tau \right)} \right|}^2}{\rm{d}}\tau } }}{{\displaystyle\int {{{\left| {{\psi _{{\rm{in}}}}\left( \tau \right)} \right|}^2}{\rm{d}}\tau } }} = \frac{{{N_{{\rm{out}}}}}}{{{N_{{\rm{in}}}}}} ,$

(1)

其中, $\psi _{{\rm{out}}}$ 和 $\psi _{{\rm{in}}}$ 分别是读出和输入光场的时域波函数, $N_{{\rm{out}}}$ 和 $N_{{\rm{in}}}$ 分别是读出和输入的光子个数. 对于DLCZ型量子存储, 存储效率定义的是有斯托克斯光子宣布的情况下能探测到反斯托克斯光子的概率:

$\begin{array}{l} \eta _{{\rm{DLCZ}}}=p_{{\rm{r}}|{\rm{w}}}-p_{{\rm{noise}}}, \end{array}$

(2)

其中, $p_{{\rm{r}}|{\rm{w}}}$ 表示探测到一个写入光子后能符合到读出光子的概率. 由于读取过程会伴随着散射噪声, 因此还要除掉探测到噪声的概率 $p_{{\rm{noise}}}$ .

存储效率的决定因素是光与介质的耦合强度, 耦合强度越大效率就越高. 原子系综因其具有集体增强效应, 与光的耦合可以得到增强, 因此基于原子系综的光存储可以获得较高的存储效率. 反映耦合强弱的指标是介质的光学厚度, 即光学厚度越大存储效率就越高. 基于原子系综的高效率相干光存储已经被若干研究小组利用不同的存储协议实现. 英国Walmsley研究小组^[27–29]采用热原子拉曼存储方案实现了GHz的宽带光存储, 其存储效率达到30%. 2019年, 华东师范大学张卫平研究组^[30]在热原子里面实现了效率82.6%的宽带光存储, 存储带宽77 MHz. 2016年, 澳大利亚国立大学Lam研究组^[31]在获得光学厚度488的冷原子系综基础上, 利用光子回波存储方案实现了效率87%, 寿命1 ms的高性能光存储. 2018年, 台湾省陈应诚研究小组^[32]在获得光学厚度超过1000的冷原子基础上, 利用电磁诱导透明存储方案实现了效率92%的光存储. 在2019 年之前, 大部分研究工作集中于利用相干光或衰减至单光子水平的相干光提升存储的效率和寿命等指标, 而单光子存储的效率始终低于50%的非克隆阈值, 最高的单光子存储效率只达到了49%^[33]. 直到2019年, 华南师范大学朱诗亮、颜辉研究组^[34]采用冷原子电磁诱导透明方案实现了量子存储效率的突破, 单光子存储效率最高达到了90.6%, 对单光子进行任意量子态编码后获得了效率高于85%的单光子偏振量子比特存储, 存储保真度高达99%, 该存储效率目前仍是世界最好水平, 如图2所示. 随后, 2020年法国巴黎第六大学Laraut研究组^[35]利用冷原子量子存储实现了高效率的可逆量子纠缠态转移, 存储效率达到85%.

$图 2 单光子量子存储的实验装置和能级方案　(a)实验方案. 磁光阱1 制备的冷原子系综用于制备时间-频率纠缠光子对, 磁光阱2 制备的冷原子系综用于进行光量子态存储. 磁光阱1 中产生的反斯托克斯光子经半波片和四分之一波片编码成任意偏振态, 然后经过一个偏振光束位移器将其偏振态的两个正交分量H偏振和V偏振分别转换成两条路径信息CHH和CHV. 读取后的光子再次经过反置的偏振光束位移换器重构出偏振态, 随后进行偏振量子态层析. (b)存储过程中的时序及优化后的控制光调制示意. (c)基于电磁诱导透明量子存储的原子能级方案. (d)当水平偏振的输入通道$|H\rangle$具有最优存储效率时, 其输入、EIT慢光以及读取单光子的时域波形情况. (e)光学厚度对存储效率的影响情况. 图中的线均是基于实验采集数据进行的理论拟合, 理论拟合采用的波形为高斯函数. 红色实线表示在存储窗口期间修改控制光的强度以匹配光学深度变化的存储数据, 黑色虚线表示控制光的强度恒定时的数据[34]\r\nFig. 2. Experimental set-up and energy level scheme of the single-photon quantum memory. (a) Schematic of the experimental optical set-up. The cold atoms in the first magneto-optical trap (MOT1) serve as a nonlinear optical medium for producing time-frequency entangled photon pairs, while the cold atoms in the second magneto-optical trap (MOT21) are the medium for the quantum memory. The anti-Stokes photon is coded with an arbitrary polarization state through the qubit manipulation unit (QMU) consisting of a QWP and HWP. After the QMU, the two orthogonal linear polarizations are separated into two beams by a polarization beam displacer (BD) that are coupled into the two balanced spatial channels CHH and CHV of the quantum memory. The memory read-outs are recombined at the second BD and the polarization state is measured by the qubit analyser. (b) The memory operation timing shows the MOT sequence and the optimized control laser intensity time-varying profile in each experimental cycle. (c) The atomic energy level scheme of the quantum memory based on EIT. (d) The input, EIT delayed and retrieved temporal waveforms of the heralded single photons when the quantum memory is optimized for the horizontally polarized input optical channel $|H\rangle$. (e) The storage efficiency as a function of the optical depth of the quantum memory. The solid lines are the best fitted theoretical waveforms by fitting the input waveform using a Gaussian function and then numerically calculating the retrieved waveform based on the measured experimental parameters of the quantum memory. The red line denotes the situation when the intensity of the control light is modified to match the optical depth change during the storage window and the black line denotes the result when the intensity of the control light is constant[34]$

图 2 单光子量子存储的实验装置和能级方案　(a)实验方案. 磁光阱1 制备的冷原子系综用于制备时间-频率纠缠光子对, 磁光阱2 制备的冷原子系综用于进行光量子态存储. 磁光阱1 中产生的反斯托克斯光子经半波片和四分之一波片编码成任意偏振态, 然后经过一个偏振光束位移器将其偏振态的两个正交分量H偏振和V偏振分别转换成两条路径信息CH_H和CH_V. 读取后的光子再次经过反置的偏振光束位移换器重构出偏振态, 随后进行偏振量子态层析. (b)存储过程中的时序及优化后的控制光调制示意. (c)基于电磁诱导透明量子存储的原子能级方案. (d)当水平偏振的输入通道

$|H\rangle$

具有最优存储效率时, 其输入、EIT慢光以及读取单光子的时域波形情况. (e)光学厚度对存储效率的影响情况. 图中的线均是基于实验采集数据进行的理论拟合, 理论拟合采用的波形为高斯函数. 红色实线表示在存储窗口期间修改控制光的强度以匹配光学深度变化的存储数据, 黑色虚线表示控制光的强度恒定时的数据^[34]

Fig. 2. Experimental set-up and energy level scheme of the single-photon quantum memory. (a) Schematic of the experimental optical set-up. The cold atoms in the first magneto-optical trap (MOT₁) serve as a nonlinear optical medium for producing time-frequency entangled photon pairs, while the cold atoms in the second magneto-optical trap (MOT2₁) are the medium for the quantum memory. The anti-Stokes photon is coded with an arbitrary polarization state through the qubit manipulation unit (QMU) consisting of a QWP and HWP. After the QMU, the two orthogonal linear polarizations are separated into two beams by a polarization beam displacer (BD) that are coupled into the two balanced spatial channels CH_H and CH_V of the quantum memory. The memory read-outs are recombined at the second BD and the polarization state is measured by the qubit analyser. (b) The memory operation timing shows the MOT sequence and the optimized control laser intensity time-varying profile in each experimental cycle. (c) The atomic energy level scheme of the quantum memory based on EIT. (d) The input, EIT delayed and retrieved temporal waveforms of the heralded single photons when the quantum memory is optimized for the horizontally polarized input optical channel

$|H\rangle$

. (e) The storage efficiency as a function of the optical depth of the quantum memory. The solid lines are the best fitted theoretical waveforms by fitting the input waveform using a Gaussian function and then numerically calculating the retrieved waveform based on the measured experimental parameters of the quantum memory. The red line denotes the situation when the intensity of the control light is modified to match the optical depth change during the storage window and the black line denotes the result when the intensity of the control light is constant^[34]

下载: 全尺寸图片幻灯片

采用固态掺杂晶体实现高效率存储一般采用加谐振腔或者多次穿过的方案来提升OD, 再进一步提升存储效率^[36–40]. 2013年, 瑞典隆德大学Rippe 研究组^[39,41]采用强增强原子频率梳技术提升了光存储效率, 存储效率达到56%. 2016年, 德国达姆施塔特工业大学Halfmann研究组^[40]设计了一种多次穿过的方案, 利用 ${\rm{Pr}}^{3+}:{\rm{Y}}_{2}{\rm{SiO}}_{5}$ 晶体实现了76%的高效率光存储. 2022年, 该研究组采用电磁诱导透明方案, 在最高效率42%的前提下, 通过ZEFOZ (zero first order Zeeman shifts)技术将存储寿命延长至秒量级^[42].

2.2 存储寿命

存储寿命决定着量子存储对量子态的同步能力, 将直接影响量子中继网络中量子态的传输距离. 受存储介质的退相干效应影响, 存储效率会随着存储时间的延长而降低, 图 3汇总了近10 年存储效率与存储寿命两个关键指标的总体情况, 并与光纤延迟进行了比较. 2013年, 美国佐治亚理工学院Kuzmich研究组^[43]利用超冷原子, 通过实施一维光晶格、魔幻磁场和动力学解耦技术, 实现了16 s的光存储. 同年, 德国达姆施塔特工业大学Halfmann研究组^[44]通过实施动力学解耦和自学习光学制备优化技术, 实现了1 min量级的光存储. 2015 年, 澳大利亚国立大学Sellars研究组^[45]采用动力学解耦和ZEFOZ 的方法, 将 ${\rm{Eu}}^{3+}:{\rm{Y}}_{2}{\rm{SiO}}_{5}$ 晶体基态超精细分裂能级间的相干时间提升到6 h, 这一结果展示了掺杂离子晶体在存储寿命方面的优势和潜力. 2016年, 中国科学技术大学潘建伟研究组^[46,47]通过实施三维光晶格技术, 结合环形腔技术实现了高效率长寿命DLCZ型量子存储, 存储效率达到了75%, 存储寿命0.22 s. 2021年, 中国科学技术大学李传锋研究组^[48]采用ZEFOZ 和动力学解耦技术, 在 ${\rm{Eu}}^{3+}:{\rm{Y}}_{2}{\rm{SiO}}_{5}$ 晶体中实现了超过1 h的光存储.

$图 3 存储效率与存储时间的调研与统计. 图中不同形状的起始点代表不同的存储介质, 其中五角星代表冷原子系综, 三角形代表热原子系综, 正方形代表固体掺杂离子体系. 图中数字对应参考文献序号. 不同线形代表着不同的存储方式, 其中蓝色实线代表相干光存储, 红色实线代表单光子存储, 红色虚线代表DLCZ型量子存储. 作为对比, 图中用灰色实线以及灰色阴影区域标出了1550 nm波长光纤的时间延迟效率, 这里光纤损耗按0.2 dB/km\r\nFig. 3. Statistics on the storage efficiency and storage time. Different storage medium are distinguished by symbols. The star represents the cold atoms, the triangle represents the warm atoms, and the square represents the doped ion crystal. The numbers before the symbols is the reference of the corresponding works. Blue solid line represents coherent light memory, red solid line represents single photon memory, and red dotted line represents DLCZ quantum memory. The transmission of 1550 nm fiber delay line is plotted using solid gray lines with the loss of 0.2 dB/km.$

图 3 存储效率与存储时间的调研与统计. 图中不同形状的起始点代表不同的存储介质, 其中五角星代表冷原子系综, 三角形代表热原子系综, 正方形代表固体掺杂离子体系. 图中数字对应参考文献序号. 不同线形代表着不同的存储方式, 其中蓝色实线代表相干光存储, 红色实线代表单光子存储, 红色虚线代表DLCZ型量子存储. 作为对比, 图中用灰色实线以及灰色阴影区域标出了1550 nm波长光纤的时间延迟效率, 这里光纤损耗按0.2 dB/km

Fig. 3. Statistics on the storage efficiency and storage time. Different storage medium are distinguished by symbols. The star represents the cold atoms, the triangle represents the warm atoms, and the square represents the doped ion crystal. The numbers before the symbols is the reference of the corresponding works. Blue solid line represents coherent light memory, red solid line represents single photon memory, and red dotted line represents DLCZ quantum memory. The transmission of 1550 nm fiber delay line is plotted using solid gray lines with the loss of 0.2 dB/km.

下载: 全尺寸图片幻灯片

2.3 存储保真度

存储保真度定义为读取后和存储之前量子态的重合度(内积):

$F = \frac{{{{\left| {\langle {{\varphi _{{\rm{in}}}}|{\varphi _{{\rm{out}}}}} \rangle } \right|}^2}}}{{\left| {\langle {{\varphi _{{\rm{in}}}}|{\varphi _{{\rm{in}}}}} \rangle } \right|\left| {\langle {{\varphi _{{\rm{out}}}}|{\varphi _{{\rm{out}}}}} \rangle } \right|}}.$

(3)

对于量子存储而言, 存储保真度一定要超过相关的阈值要求. 例如, 对于自旋1/2的自旋态, 阈值要求是2/3, 而对于连续变量, 如相位和振幅等维度, 阈值要求是1/2^[64], 尽管分离变量量子比特和连续变量都能为量子信息提供纠缠态资源, 但迄今为止, 大多数量子存储的实验都是基于分离变量量子比特存储^[17]. 目前, 各研究组在量子存储保真度这一指标均能达到较高的水平, 甚至超过99%^{[34,58,59,65]}.

2.4 模式容量

存储模式有空间、时间和频率等, 这三种模式的复用均可以用于提升量子计算或量子通信的性能. 2007年, 日内瓦大学的Simon等^[22]提出采用多时间模式量子存储器实现量子中继可以显著提升量子中继中纠缠建立的概率, 量子存储的模式数量与量子纠缠成功的概率呈线性关系, 方案如图4(a). 此后, 复用量子存储与中继的研究变得火热起来. 在量子计算方面, 2021年, Gouzien等^[66]指出在解决2048 位RSA (Rivest-Shamir-Adleman)质因数分解这个问题上, 如果将多模量子存储器整合进量子计算机, 对量子比特资源需求量将降低3个数量级, 方案如图4(b). 该方案硬件上可通过整合超导量子计算单元和微波光子量子存储单元来实现^[67–69], 另外也可以借助微波-光波转换接口来整合超导量子计算单元与光量子存储单元^[70–74].

$图 4 (a)利用纠缠光子源和多模量子存储器实现量子中继的方案. 由于量子存储器可以支持同时存储多个光子脉冲, 因此量子纠缠源可以陆续地产生光子, 以节省量子纠缠建立的时间成本. 这里的源和多模量子存储器的组合相当于DLCZ型量子存储器, 但该中继方案具有多模式的功能优势[22]. (b)利用多模量子存储器和量子处理器分解2048位RSA整数的量子计算机体系结构. 研究表明, 在量子存储器支持2800万个空间模式和45个时间模式, 并且存储时间覆盖到2 h的情况下, 处理器只需要13436个物理量子位即可在177天内即可完成任务[66]\r\nFig. 4. (a) Quantum repeater scheme using pair sources and multimode memories. The sources $S_{i}$ can each emit a photon pair into a sequence of time bins. The multimode memories $M_{i}$ can store the sequential photons simultaneously. The combination of source and multimode quantum memory is equivalent to the DLCZ scheme, but with multimode functionality[22]. (b) The quantum computer architecture for factoring a 2048-bit RSA integer with multimode quantum memories and quantum processors. It is shown to be possible in 177 days with 13436 physical qubits and a memory that can store 28 million spatial modes and 45 temporal modes with 2 hours’ storage time[66].$

图 4 (a)利用纠缠光子源和多模量子存储器实现量子中继的方案. 由于量子存储器可以支持同时存储多个光子脉冲, 因此量子纠缠源可以陆续地产生光子, 以节省量子纠缠建立的时间成本. 这里的源和多模量子存储器的组合相当于DLCZ型量子存储器, 但该中继方案具有多模式的功能优势^[22]. (b)利用多模量子存储器和量子处理器分解2048位RSA整数的量子计算机体系结构. 研究表明, 在量子存储器支持2800万个空间模式和45个时间模式, 并且存储时间覆盖到2 h的情况下, 处理器只需要13436个物理量子位即可在177天内即可完成任务^[66]

Fig. 4. (a) Quantum repeater scheme using pair sources and multimode memories. The sources

$S_{i}$

can each emit a photon pair into a sequence of time bins. The multimode memories

$M_{i}$

can store the sequential photons simultaneously. The combination of source and multimode quantum memory is equivalent to the DLCZ scheme, but with multimode functionality^[22]. (b) The quantum computer architecture for factoring a 2048-bit RSA integer with multimode quantum memories and quantum processors. It is shown to be possible in 177 days with 13436 physical qubits and a memory that can store 28 million spatial modes and 45 temporal modes with 2 hours’ storage time^[66].

下载: 全尺寸图片幻灯片

基于稀土离子掺杂晶体的固态存储器因具有存储带宽大和相干寿命长的特点, 在时间和频率及多自由度复用存储能力方面优势明显^[61,75–81]. 中国科学技术大学李传锋研究组^[82,83]首次在 ${\rm{Pr}}^{3+}: {\rm{Y}}_{2}{\rm{SiO}}_{5}$ 晶体中实现了空间、频率和时间三个自由度的复用光存储. 2022年, Businger等^[84]在 ${\rm{Yb}}^{3+}: {\rm{Y}}_{2}{\rm{SiO}}_{5}$ 晶体中, 基于原子频率梳方案实现了1250个时间模式的存储. 近期, 电子科技大学周强研究组^[60]将10 m掺铒石英光纤置于10 mK的低温环境中, 采用时域-频域复用的方式将光存储模式数量提升至1650, 并且该存储器的工作波长处在通信波段, 非常适用于远距离多模量子中继^[85].

冷原子系综凭借着其系综尺寸大和耦合强度高等特点, 在空间复用上具有明显优势, 可以保证较高的效率同时提高空间模式的存储能力. 冷原子空间模式存储的研究主要集中在两方面, 分别是光子轨道角动量(orbital angular momentum, OAM)信息存储和光学通道复用存储. 2013 年, 法国巴黎第六大学Laurat研究组^[86,87]利用相干光编码了OAM信息, 首次实现了冷原子的涡旋光存储. 随后2015年, 中国科学技术大学史保森研究组基于冷原子系综首次实现了OAM纠缠态的量子存储^[88], 并进一步实现了高维量子存储纠缠^[89] 以及多自由度量子纠缠^[90]. 对编码OAM信息的光子进行量子存储相比于单纯的时域波形存储在保真度、效率和寿命等性能提升上有很大的挑战. 例如原子的热运动和环境磁场会导致存储过程中OAM拓扑荷态之间的串扰从而降低保真度, 而绝对静止不动的原子是无法实现的, 绝对干净的磁场环境也是非常大的技术挑战. 编码的OAM信息拓扑荷数越高, 原子系综的有效光学厚度就会越低, 从而严重影响存储效率. 因此实现高维信息的高性能量子存储也是该领域的研究重点之一. 2020年, 西安交通大学高宏研究组^[91]利用冷原子系综实现了高维、高效率光存储, 存储效率最高65%, 存储光的轨道角动量最高拓扑荷数为5, 存储保真度高于98%. 2022年, 中国科学技术大学史保森研究组^[92]通过延长自旋波波长和进行原子钟态制备来抑制原子横向和纵向的退相干, 实现了高维长寿命光存储, 将高维存储寿命提升2个数量级. 在通道复用上, 主流的方法是借助光学元器件来实现, 例如采用光束位移器(beam displacer, BD)实现双通道的复用可以编码偏振量子态, 双BD构建的干涉仪系统具有自稳定的特性, 在量子态保真度的保持上有明显优势^{[55,59,90,93]}. 法国巴黎第六大学Laurat研究组利用BD先后研究了矢量光存储^[93]及高效率任意偏振态存储^[59]. 采用声光移位器(acoustic optical deflectors, AOD)可以通过声光控制的方法实现通道的复用和寻址, 能够大大提升存储的通道数量. 2009年, Kuzmich研究组^[94]首次利用AOD实现了DLCZ型量子存储的多通道空间复用, 当时只是利用单个AOD实现了一维的多路复用. 2017年, 清华大学段路明研究组^[95]利用交叉的AOD 方案实现了二维的多路复用DLCZ型量子存储, 空间复用的模式数量提升到了225. 此后, 进一步将该复用结构拓展到普适型量子存储方案上, 进行了49个空间模式的偏振量子比特存储, 实现了通信光子与复用量子存储的远距离纠缠^[96]. 此外, 也有研究者基于DLCZ方案直接采用多路收集的办法, 提升量子存储的复用容量或实现多通道光子纠缠源^[57,97,98].

3. 量子存储典型应用

3.1 量子纠缠

量子纠缠是量子中继的核心思想, 远距离量子中继网络的实现需解决的首要问题是将最小纠缠单元的距离拉远. 目前, 两个静态量子比特的纠缠已经在多种物理体系实现, 如原子系综^{[23,99–101]}、单原子^[102,103]、NV色心^[104–106]、量子点^[107] 以及囚禁离子^[108]等. 实现远距离量子纠缠需克服的问题包括: 提升物理体系的相干时间, 降低各种光子损耗, 提升系统稳定度以及信噪比等. 2020年, 中国科学技术大学潘建伟研究组^[109]在改善以上问题的基础上, 实现了50 km的量子存储节点纠缠, 如图5(a). 该工作中, 潘建伟等^[46,47]采用了三维光晶格和腔增强技术提升了存储效率和存储寿命, 存储效率最高达到76%, 存储寿命0.22 s. 同时, 利用高效率波长转换器将量子存储释放的795 nm信号光子转换成1342 nm光子来降低信道的光子传输损耗.

$图 5 (a) 潘建伟等[109]借助高效率波长转换器实现了50 km光纤连接的两个DLCZ 量子存储纠缠; (b)李传锋等[56]首次实验演示吸收型量子存储之间的量子纠缠; (c) Riedmatten等[63]实现了两个多模固态量子存储之间的纠缠\r\nFig. 5. (a) 50 km fiber length entanglement of two quantum memories via efficient quantum wavelength converter demonstrated by Pan et al.[109]; (b) experimental demonstration of quantum entanglement between absorbing quantum memories for the first time by Li et al.[56]; (c) experimental demonstration of quantum entanglement between multimode quantum memories by Riedmatten et al.[63].$

图 5 (a) 潘建伟等^[109]借助高效率波长转换器实现了50 km光纤连接的两个DLCZ 量子存储纠缠; (b)李传锋等^[56]首次实验演示吸收型量子存储之间的量子纠缠; (c) Riedmatten等^[63]实现了两个多模固态量子存储之间的纠缠

Fig. 5. (a) 50 km fiber length entanglement of two quantum memories via efficient quantum wavelength converter demonstrated by Pan et al.^[109]; (b) experimental demonstration of quantum entanglement between absorbing quantum memories for the first time by Li et al.^[56]; (c) experimental demonstration of quantum entanglement between multimode quantum memories by Riedmatten et al.^[63].

下载: 全尺寸图片幻灯片

此前实现量子纠缠都是基于发射型物理体系, 即物理体系本身既能发射出光子, 又具有时间同步功能. 2007年, 日内瓦大学的Simon等^[22]首次提出利用纠缠光子源和吸收型量子存储实现量子中继的方案, 科学家可以自由配置不同特性的光子源和存储器来满足不同的需求, 尤其是在多模量子存储方面具有明显优势. 此外, 该方案还可以借助纠缠源作为波长转换接口, 弥补一些量子存储工作波长处于非通信波段的短板. 2021年, 中国科学技术大学李传锋研究组^[56]首次实现了两个吸收型量子存储的纠缠, 如图5(b). 该工作中, 李传锋等^[110]利用一种三明治结构的 ${\rm{Nd}}^{3+}:{\rm{YVO}}_{4}$ 晶体实现了偏振量子比特存储, 同时采用自发参量下转换(SPDC)技术搭配一种干涉仪结构产生了偏振纠缠光子对. 实验中分别将两个光子源产生的信号光子存储到两个量子存储器中, 将闲置光子同时输送到中间站进行联合贝尔态探测, 最终实现了间隔3.5 m的两个固态量子存储纠缠. 同一时间, 西班牙巴塞罗那科学技术学院Riedmatten研究组^[63]采用同样的方案实现了 ${\rm{Pr}}^{3+}:{\rm{Y}}_{2}{\rm{SiO}}_{4}$ 晶体多模量子存储之间的纠缠, 如图5(c). 该工作中研究者还利用SPDC光子源同时产生可存储波长的606 nm光子和通信波长的1436 nm光子, 以光子源作为波长转换接口克服了存储器的工作波长短板^[111].

3.2 存储辅助增强的多光子过程

量子存储器最主要的功能是实现光子或量子信息的同步, 在量子安全通信、量子中继以及多光子产生等方面展现出了明显的优势. 2013年, 英国牛津大学Nunn等^[25]分析了利用多个光子源产生多光子态的过程, 发现借助存储器的时间同步功能辅助实现多光子态产生, 比随机产生所耗费的时间成本可降低12个数量级. 如12 个光子随机同步的时间需要30 年才能实现一次, 而在有存储器辅助的情况下只需要100 μs即可完成. 后续多个工作也验证了量子存储在多光子同步或多光子纠缠态产生方面的增强效果^[112–114]. 2020年, 美国哈佛大学Lukin研究组^[115]基于金刚石纳米腔硅空色心实现了存储辅助增强的量子通信. 2021年, 清华大学段路明研究组^[116]实验验证了量子存储对于量子中继过程中纠缠交换的增强效果, 探索了量子存储性能的提升对于纠缠交换能力的影响. 随后基于同样的实验方案, 展示了量子存储对于多光子非局域图态产生的增强效果^[117]. 同年, 华南师范大学朱诗亮、颜辉研究组^[113]利用高效率量子存储展示了存储增强的双光子同步, 利用概率性的光子源实现了确定性双光子干涉, 如图6. 此外该工作还借助存储中的电磁诱导透明过程, 实现了高效率单光子任意相位调制, 展示了一种同步与相位调制集成的量子存储器.

$图 6 光子同步干涉与相位调制实验方案. 采用暗线磁光阱技术制备三个雪茄形高密度铷85 冷原子系综. 在泵浦光和耦合光共同作用下, 于磁光阱1 (2)中采用四波混频的方法产生斯托克斯光子$\omega_{{\rm{s}}1}$($\omega_{{\rm{s}}2}$)和反斯托克斯光子$\omega_{{\rm{as}}1}$($\omega_{{\rm{as}}2}$)纠缠光子对. $\Delta t_{{\rm{random}}} $表示反斯托克斯光子$\omega_{{\rm{as}}1}$和$\omega_{{\rm{as}}2}$之间的时间差. 磁光阱3是电磁诱导透明存储器, 用于控制$\omega_{{\rm{as}}2}$光子的时间延迟, 实现$\omega_{{\rm{as}}1}$和$\omega_{{\rm{as}}2}$光子的时间同步. 如电磁诱导透明过程能级示意图所示, 光子的存储、读取及相位调制过程完全由控制光决定, 实验上利用声光调制器(AOM)来实现. 同步后的$\omega_{{\rm{as}}1}$和$\omega_{{\rm{as}}2}$光子通过单模光纤传输到由分束器组成的HOM干涉仪中进行干涉, 最终被单光子计数模块A, B, C和D检测. PBS, 偏振分束器; HWP,半波片; QWP, 四分之一波片; HR, 高反射镜[113]\r\nFig. 6. Three cigar-shape dense cold atomic ensembles are prepared by dark-line magneto-optical traps (MOT) of $^{85}$Rb atoms. Single photons $\omega_{{\rm{as}}1}$ ($\omega_{{\rm{as}}2}$) heralded by its counterpart $\omega_{{\rm{s}}1}$ ($\omega_{{\rm{s}}2}$) are generated from MOT$_{1}$ (MOT$_{2}$) with the existence of pump1-coupling1 (pump2-coupling2) laser beams via the spontaneous four-wave-mixing process. Therefore, the timing differences between $\omega_{{\rm{as}}1}$ and $\omega_{{\rm{as}}2}$ are random and denoted by $\Delta t_{{\rm{random}}}$. MOT3 acts as an efficient QM based on EIT that can synchronize the readout single photon $\omega_{{\rm{as}}2}$ to $\omega_{{\rm{as}}1}$ ($\Delta t=0$). As shown by the energy level schematics of EIT two-photon process, a control laser manipulates the storage and readout of single photons $\omega_{{\rm{as}}2}$. The amplitude and phase of the control laser pulse with a complex envelope of Rabi frequency $\Omega_{{\rm{c}}}(t){\rm{e}}^{-{\rm{i}}\phi_{{\rm{c}}}(t)}$ is controlled by an acousto-optic modulator (AOM), by which the readout single photons $\omega_{{\rm{as}}2}$ can be phase modulated accordingly. Single photons $\omega_{{\rm{as}}1}$ and $\omega_{{\rm{as}}2}$ are delivered to a HOM interferometer consisting of a beam splitter (BS) via single mode fibers (SMFs). Photons $\omega_{{\rm{s}}1}$ and $\omega_{{\rm{s}}2}$ are also collected and sent to detectors via SMFs. The generated photons are eventually detected by single photon counting modules (SPCMs) A, B, C and D. Filters are inserted before SPCMs to filter out noisy photons. PBS, polarization beam splitter; HWP, half wave plate; QWP, quarter wave plate; HR, high reflection mirror[113].$

图 6 光子同步干涉与相位调制实验方案. 采用暗线磁光阱技术制备三个雪茄形高密度铷85 冷原子系综. 在泵浦光和耦合光共同作用下, 于磁光阱1 (2)中采用四波混频的方法产生斯托克斯光子

$\omega_{{\rm{s}}1}$

(

$\omega_{{\rm{s}}2}$

)和反斯托克斯光子

$\omega_{{\rm{as}}1}$

(

$\omega_{{\rm{as}}2}$

)纠缠光子对.

$\Delta t_{{\rm{random}}}$

表示反斯托克斯光子

$\omega_{{\rm{as}}1}$

和

$\omega_{{\rm{as}}2}$

之间的时间差. 磁光阱3是电磁诱导透明存储器, 用于控制

$\omega_{{\rm{as}}2}$

光子的时间延迟, 实现

$\omega_{{\rm{as}}1}$

和

$\omega_{{\rm{as}}2}$

光子的时间同步. 如电磁诱导透明过程能级示意图所示, 光子的存储、读取及相位调制过程完全由控制光决定, 实验上利用声光调制器(AOM)来实现. 同步后的

$\omega_{{\rm{as}}1}$

和

$\omega_{{\rm{as}}2}$

光子通过单模光纤传输到由分束器组成的HOM干涉仪中进行干涉, 最终被单光子计数模块A, B, C和D检测. PBS, 偏振分束器; HWP,半波片; QWP, 四分之一波片; HR, 高反射镜^[113]

Fig. 6. Three cigar-shape dense cold atomic ensembles are prepared by dark-line magneto-optical traps (MOT) of

$^{85}$

Rb atoms. Single photons

$\omega_{{\rm{as}}1}$

(

$\omega_{{\rm{as}}2}$

) heralded by its counterpart

$\omega_{{\rm{s}}1}$

(

$\omega_{{\rm{s}}2}$

) are generated from MOT

$_{1}$

(MOT

$_{2}$

) with the existence of pump1-coupling1 (pump2-coupling2) laser beams via the spontaneous four-wave-mixing process. Therefore, the timing differences between

$\omega_{{\rm{as}}1}$

and

$\omega_{{\rm{as}}2}$

are random and denoted by

$\Delta t_{{\rm{random}}}$

. MOT₃ acts as an efficient QM based on EIT that can synchronize the readout single photon

$\omega_{{\rm{as}}2}$

$\omega_{{\rm{as}}1}$

(

$\Delta t=0$

). As shown by the energy level schematics of EIT two-photon process, a control laser manipulates the storage and readout of single photons

$\omega_{{\rm{as}}2}$

. The amplitude and phase of the control laser pulse with a complex envelope of Rabi frequency

$\Omega_{{\rm{c}}}(t){\rm{e}}^{-{\rm{i}}\phi_{{\rm{c}}}(t)}$

is controlled by an acousto-optic modulator (AOM), by which the readout single photons

$\omega_{{\rm{as}}2}$

can be phase modulated accordingly. Single photons

$\omega_{{\rm{as}}1}$

and

$\omega_{{\rm{as}}2}$

are delivered to a HOM interferometer consisting of a beam splitter (BS) via single mode fibers (SMFs). Photons

$\omega_{{\rm{s}}1}$

and

$\omega_{{\rm{s}}2}$

are also collected and sent to detectors via SMFs. The generated photons are eventually detected by single photon counting modules (SPCMs) A, B, C and D. Filters are inserted before SPCMs to filter out noisy photons. PBS, polarization beam splitter; HWP, half wave plate; QWP, quarter wave plate; HR, high reflection mirror^[113].

下载: 全尺寸图片幻灯片

3.3 不同粒子的量子干涉

多粒子量子干涉, 如HOM (Hong-Ou-Mandel)干涉, 揭示了粒子的量子统计性质^[118]. 研究玻色子和费米子量子干涉效应的独特物理现象引起了科研人员的极大兴趣^[26]. 分束器是进行量子干涉研究的基本元件, 它在不同输出端口中创建粒子的叠加状态, 并实现每个端口中粒子的振幅干涉. 量子干涉为多比特量子门提供的单光子非线性过程, 是量子信息处理和量子通信的核心^[119–121]. 此前量子干涉的研究均是在同类型粒子上取得的, 如双光子^[118,122]、双磁子^[123]、双原子等^[124–126], 然而量子干涉的原理并不局限于同质粒子, 只要能够实现单个粒子之间的相干态叠加或转换即可^[127,128]. 因此, 将量子干涉扩展到广义的分束器具有重要的研究意义. 最近, 华南师范大学朱诗亮、颜辉研究组^[129]借助电磁诱导透明存储过程实现了广义的光子与磁子非厄密分束器, 其厄密性可以实现从厄密到非厄密的连续可调, 如图7. 基于该磁子-光子分束器实现了不同单粒子, 即单磁子与单光子之间的量子干涉, 并观察到了干涉后两种不同类型粒子从玻色子到费米子量子统计特性的转变.

$图 7 单磁子与单光子干涉实验方案　(a)磁子-光子HOM干涉仪的理论模型. 磁子$\widehat{\sigma}_{21}$和光子$\widehat{E}$在电磁诱导透明介质中都以暗态极化子的形式存在. 控制光上方的红线显示了实验的时序, 包括磁子的制备$\varOmega_{{\rm{S}}}$、磁子与光子的干涉$\varOmega_{{\rm{BS}}}$和磁子的读取$\varOmega_{{\rm{R}}}$三个过程. 该电磁诱导透明过程的铷85能级方案: $|1\rangle=5 {\rm{S}}_{1/2}, F=2, m_{F}=2$, $|2\rangle=5 {\rm{S}}_{1/2}, F=3, m_{F}=3$, $|3\rangle=5 P_{1/2}, F=3, $$ m_{F}=3$, $\varGamma_{3}$是$|3\rangle$态的自发辐射率, Δ是单光子失谐. (b)磁子和光子HOM干涉的输入和输出态. (c)实验方案. 磁光阱1作为单光子源连续产生单光子, 通过探测斯托克斯光子可宣布反斯托克斯光子的产生. 磁光阱2作为非厄米分束器用于实现光子- 磁子的分束及干涉. PBS, 偏振分束器; QWP, 四分之一波片; SPCM, 单光子计数模块; SMF, 单模光纤[129]\r\nFig. 7. Theoretical and experimental schemes: (a) Theoretical scheme of magnon-photon HOM interferometer. The magnon ($\hat{\sigma}$) and photon ($\hat{E}$) are both in the form of a dark-state polariton (DSP) in an electromagnetically induced transparency (EIT) medium. The red line above the control laser shows the experimental timing sequences: storage of a magnon ($\varOmega _{\rm{S}}$), interference between two DSPs ($\varOmega _{{\rm{BS}}}$) and reading out of the magnon ($\varOmega _{\rm{R}}$). The insert is a $\Lambda$-type EIT energy diagram: $|1\rangle = |5{{\rm{S}}_{1/2}}, $$ F = 2, {m_F} = 2\rangle$, $|2\rangle = |5{{\rm{S}}_{1/2}}, F = 3, {m_F} = 2\rangle$, $|3\rangle = |5{P_{1/2}}, F = 3, {m_F} = 3\rangle$, $\varGamma_{3}$ is the spontaneous decay rate of $|3\rangle$, and $\varDelta$ is single photon detuning. (b) The input and output states of the magnon-photon HOM interferometer. (c) Experimental setup. MOT$_{1}$ is a single photon source. The detection of a Stokes photon ($\omega_{{\rm{s}}i}$) heralded the generation of an anti-Stokes photon ($\omega_{{\rm{as}}i}$). MOT$_{2}$ is the non-Hermitian beam splitter. PBS, polarization beam splitter; QWP, quarter wave plate; SPCM, single photon counting module; SMF, single mode fibre[129].$

图 7 单磁子与单光子干涉实验方案　(a)磁子-光子HOM干涉仪的理论模型. 磁子

$\widehat{\sigma}_{21}$

和光子

$\widehat{E}$

在电磁诱导透明介质中都以暗态极化子的形式存在. 控制光上方的红线显示了实验的时序, 包括磁子的制备

$\varOmega_{{\rm{S}}}$

、磁子与光子的干涉

$\varOmega_{{\rm{BS}}}$

和磁子的读取

$\varOmega_{{\rm{R}}}$

三个过程. 该电磁诱导透明过程的铷85能级方案:

$|1\rangle=5 {\rm{S}}_{1/2}, F=2, m_{F}=2$

$|2\rangle=5 {\rm{S}}_{1/2}, F=3, m_{F}=3$

$|3\rangle=5 P_{1/2}, F=3,$

$m_{F}=3$

$\varGamma_{3}$

是

$|3\rangle$

态的自发辐射率, Δ是单光子失谐. (b)磁子和光子HOM干涉的输入和输出态. (c)实验方案. 磁光阱1作为单光子源连续产生单光子, 通过探测斯托克斯光子可宣布反斯托克斯光子的产生. 磁光阱2作为非厄米分束器用于实现光子- 磁子的分束及干涉. PBS, 偏振分束器; QWP, 四分之一波片; SPCM, 单光子计数模块; SMF, 单模光纤^[129]

Fig. 7. Theoretical and experimental schemes: (a) Theoretical scheme of magnon-photon HOM interferometer. The magnon (

$\hat{\sigma}$

) and photon (

$\hat{E}$

) are both in the form of a dark-state polariton (DSP) in an electromagnetically induced transparency (EIT) medium. The red line above the control laser shows the experimental timing sequences: storage of a magnon (

$\varOmega _{\rm{S}}$

), interference between two DSPs (

$\varOmega _{{\rm{BS}}}$

) and reading out of the magnon (

$\varOmega _{\rm{R}}$

). The insert is a

$\Lambda$

-type EIT energy diagram:

$|1\rangle = |5{{\rm{S}}_{1/2}},$

$F = 2, {m_F} = 2\rangle$

$|2\rangle = |5{{\rm{S}}_{1/2}}, F = 3, {m_F} = 2\rangle$

$|3\rangle = |5{P_{1/2}}, F = 3, {m_F} = 3\rangle$

$\varGamma_{3}$

is the spontaneous decay rate of

$|3\rangle$

, and

$\varDelta$

is single photon detuning. (b) The input and output states of the magnon-photon HOM interferometer. (c) Experimental setup. MOT

$_{1}$

is a single photon source. The detection of a Stokes photon (

$\omega_{{\rm{s}}i}$

) heralded the generation of an anti-Stokes photon (

$\omega_{{\rm{as}}i}$

). MOT

$_{2}$

is the non-Hermitian beam splitter. PBS, polarization beam splitter; QWP, quarter wave plate; SPCM, single photon counting module; SMF, single mode fibre^[129].

下载: 全尺寸图片幻灯片

4. 总　结

本文综合考察了量子存储的一系列关键指标, 如存储效率、存储寿命、存储保真度和模式容量, 并对近期与量子存储相关的典型研究进行了详细介绍. 在过去十年里, 量子存储的各项指标都取得了显著提升. 例如, 存储效率已经超过了90%, 存储寿命最长可达1 h, 保真度更是超过99%, 同时模式容量也达到了 $10^{3}$ 量级. 然而, 尽管取得了这些成果, 但是目前还没有任何体系能够在所有指标上实现全面突破. 各研究组正在努力通过物理创新或技术迭代找到解决方案. 根据2011年Sangouard等^[21]的计算分析, 只有在量子存储的效率、寿命和保真度同时满足确定的标准(如效率超过90%, 寿命达到百秒量级, 保真度超过90%)时, 才能实现量子中继的优势. 在存储模式容量较高的情况下, 其他指标的实际要求可以降低, 如当模式数达到100时, 存储寿命的需求可以降到秒级. 然而, 至今尚未有任何方案能实现这一全面性能目标. 因此, 作为未来量子存储重点发展方向之一, 实现量子存储性能的全面突破将是未来的关键任务.

参考文献

[1]	Walmsley I A 2015 Science 348 525 Google Scholar
[2]	Wootters W K, Zurek W H 1982 Nature 299 802 Google Scholar
[3]	Gisin N, Thew R 2007 Nat. Photonics 1 165 Google Scholar
[4]	Briegel H J, Dür W, Cirac J I, Zoller P 1998 Phys. Rev. Lett. 81 5932 Google Scholar
[5]	Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413 Google Scholar
[6]	Gisin N, Ribordy G, Tittel W, Zbinde H 2002 Rev. Mod. Phys. 74 145 Google Scholar
[7]	Foot C J 2005 Atomic Physics (Oxford: Oxford University Press) pp123–214 Foot C J 2005 Atomic Physics (Oxford: Oxford University Press) pp123–214
[8]	Scully M O, Zubairy M S 1999 Quantum Optics (New York: Cambridge University Press) pp145–217 Scully M O, Zubairy M S 1999 Quantum Optics (New York: Cambridge University Press) pp145–217
[9]	Nielsen, Michael A, I L Chuang 2011 Quantum Computation and Quantum Information: 10th Anniversary Edition (New York: Cambridge University Press) pp277–343 Nielsen, Michael A, I L Chuang 2011 Quantum Computation and Quantum Information: 10th Anniversary Edition (New York: Cambridge University Press) pp277–343
[10]	Hammerer K, SØrensen A S, Polzik E S 2010 Rev. Mod. Phys. 82 1041 Google Scholar
[11]	Kimble H J 2008 Nature 453 1023 Google Scholar
[12]	Wehner S, Elkouss D, Hanson R 2018 Science 362 eaam9288 Google Scholar
[13]	郭光灿 2020 中国科学: 信息科学 50 1395 Google Scholar Guo G C 2020 Sci. Sin. Inform. 50 1395 Google Scholar
[14]	Simon C 2017 Nat. Photonics 11 678 Google Scholar
[15]	Duan L M, Monroe C 2010 Rev. Mod. Phys. 82 1209 Google Scholar
[16]	Yan Z H, Wu L, Jia X J, Xie C D, Peng K C 2021 Adv. Quantum Technol. 4 2100071 Google Scholar
[17]	Afzelius M, Gisin N, De Riedmatten H 2015 Phys. Today 68 42 Google Scholar
[18]	Lvovsky A I, Sanders B C, Tittel W 2009 Nat. Photonics 3 706 Google Scholar
[19]	Bussieres F, Sangouard N, Afzelius M, De Riedmatten H, Simon C, Tittel W 2013 J. Mod. Opt. 60 1519 Google Scholar
[20]	Guo M C, Liu S P, Sun W Y, Ren M M, Wang F D, Zhong M J 2023 Front. Phys. 18 21303 Google Scholar
[21]	Sangouard N, Simon C, De Riedmatten H, Gisin N 2011 Rev. Mod. Phys. 83 33 Google Scholar
[22]	Simon C, De Riedmatten H, Afzelius M, Sangouard N, Zbinden H, Gisin N 2007 Phys. Rev. Lett. 98 190503 Google Scholar
[23]	Chou C W, Laurat J, Deng H, Choi K, De Riedmatten H, Felinto D, Kimble H J 2007 Science 316 1316 Google Scholar
[24]	Wei S H, Jing B, Zhang X Y, Liao J Y, Yuan C Z, Fan B Y, Lyu C, Zhou D L, Wang Y, Deng G W, Song H Z, Oblak D, Guo G C, Zhou Q 2022 Laser Photon. Rev. 16 2100219 Google Scholar
[25]	Nunn J, Langford N K, Kolthammer W S, Champion T F M, Sprague M R, Michelberger P S, Walmsley I A 2013 Phys. Rev. Lett. 110 133601 Google Scholar
[26]	Pan J W, Chen Z B, Lu C Y, Weinfurter H, Zeilinger A, Zukowski M 2012 Rev. Mod. Phys. 84 777 Google Scholar
[27]	Reim K F, Nunn J, Lorenz V O, Sussman B J, Lee K C, Langford N K, Walmsley I A 2010 Nat. Photonics 4 218 Google Scholar
[28]	Reim K F, Michelberger P, Lee K C, Nunn J, Langford N K, Walmsley I A 2011 Phys. Rev. Lett. 107 053603 Google Scholar
[29]	Michelberger P S, Champion T F M, Sprague M R, Kaczmarek K T, Barbieri M, Jin X M, Walmsley I A 2015 New J. Phys. 17 043006 Google Scholar
[30]	Guo J, Feng X, Yang P, Yu Z, Chen L Q, Yuan C H, Zhang W 2019 Nat. Commun. 10 148 Google Scholar
[31]	Cho Y W, Campbell G T, Everett J L, Bernu J, Higginbottom D B, Cao M T, Geng J, Robins N P, Lam P K, Buchler B C 2016 Optica 3 100 Google Scholar
[32]	Hsiao Y F, Tsai P J, Chen H S, Lin S X, Hung C C, Lee C H, Chen Y C 2018 Phys. Rev. Lett. 120 183602 Google Scholar
[33]	Zhou S, Zhang S, Liu C, Chen J F, Wen J, Loy M M T, Du S 2012 Opt. Express 20 24124 Google Scholar
[34]	Wang Y F, Li J F, Zhang S C, Su K Y, Zhou Y R, Liao K Y, Du S W, Yan H, Zhu S L 2019 Nat. Photonics 13 346 Google Scholar
[35]	Cao M, Hoffet F, Qi S, Sheremet A S, Laurat J 2020 Optica 7 1440 Google Scholar
[36]	Davidson J H, Lefebvre P, Zhang J, Oblak D, Tittel W 2020 Phys. Rev. A 101 042333 Google Scholar
[37]	Akhmedzhanov R A, Gushchin L A, Kalachev A A, Nizov N A, Nizov V A, Sobgayda D A, Zelensky I V 2016 Laser Phys. Lett. 13 115203 Google Scholar
[38]	Jobez P, Usmani I, Timoney N, Laplane C, Gisin N, Afzelius M 2014 New J. Phys. 16 083005 Google Scholar
[39]	Sabooni M, Li Q, Kröll S, Rippe L 2013 Phys. Rev. Lett. 110 133604 Google Scholar
[40]	Schraft D, Hain M, Lorenz N, Halfmann T 2016 Phys. Rev. Lett. 116 073602 Google Scholar
[41]	Sabooni M, Kometa S T, Thuresson A, Kröll S, Rippe L 2013 New J. Phys. 15 035025 Google Scholar
[42]	Hain M, Stabel M, Halfmann T 2022 New J. Phys. 24 023012 Google Scholar
[43]	Dudin Y O, Li L, Kuzmich A 2013 Phys. Rev. A 87 031801 Google Scholar
[44]	Heinze G, Hubrich C, Halfmann T 2013 Phys. Rev. Lett. 111 033601 Google Scholar
[45]	Zhong M, Hedges M P, Ahlefeldt R L, Bartholomew J G, Beavan S E, Wittig S M, Sellars M J 2015 Nature 517 177 Google Scholar
[46]	Yang S J, Wang X J, Bao X H, Pan J W 2016 Nat. Photonics 10 381 Google Scholar
[47]	Wang X J, Yang S J, Sun P F, Jing B, Li J, Zhou M T, Pan J W 2021 Phys. Rev. Lett. 126 090501 Google Scholar
[48]	Ma Y, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2021 Nat. Commun. 12 2381 Google Scholar
[49]	Chen Y H, Lee M J, Wang I C, Du S W, Chen Y F, Chen Y C, Yu I A 2013 Phys. Rev. Lett. 110 083601 Google Scholar
[50]	Ma L X, Lei X, Yan J L, Li R Y, Chai T, Yan Z H, Jia X J, Xie C D, Peng K C 2022 Nat. Commun. 13 2368 Google Scholar
[51]	Horvath S P, Alqedra M K, Kinos A, Walther A, Dahlström J M, Stefan Kröll, Rippe L 2021 Phys. Rev. Research 3 023099 Google Scholar
[52]	Mazelanik M, Leszczyński A, Parniak M 2022 Nat. Commun. 13 691 Google Scholar
[53]	Li C, Zhang S, Wu Y K, Jiang N, Pu Y F, Duan L M 2021 Phys. Rev. X 2 040307 Google Scholar
[54]	Dideriksen K B, Schmieg R, Zugenmaier M, Polzik E S 2021 Nat. Commun. 12 3699 Google Scholar
[55]	Ding D S, Zhang W, Zhou Z Y, Shi S, Shi B S, Guo G C 2015 Nat. Photonics 9 332 Google Scholar
[56]	Liu X, Hu J, Li Z F, Li X, Li P Y, Liang P J, Zhou Z Q, Li C F, Guo G C 2021 Nature 594 41 Google Scholar
[57]	Tian L, Xu Z, Chen L, Ge W, Yuan H, Wen Y, Wang H 2017 Phys. Rev. Lett. 119 130505 Google Scholar
[58]	Zhu T X, Liu C, Jin M, Su M X, Liu Y P, Li W J, Guo G C 2022 Phys. Rev. Lett. 128 180501 Google Scholar
[59]	Vernaz-Gris P, Huang K, Cao M, Sheremet A S, Laurat J 2018 Nat. Commun. 9 363 Google Scholar
[60]	Wei S H, Jing B, Zhang X Y, Liao J Y, Li H, You L X, Zhou Q 2022 arXiv: 2209.00802[quant-ph Google Scholar
[61]	Ortu A, Holzäpfel A, Etesse J, Afzelius M 2022 npj Quantum Inform. 8 29 Google Scholar
[62]	Saglamyurek E, Hrushevskyi T, Rastogi A, Cooke L W, Smith B D, LeBlanc L J 2021 New J. Phys. 23 043028 Google Scholar
[63]	Lago-Rivera D, Grandi S, Rakonjac J V, Seri A, de Riedmatten H 2021 Nature 594 37 Google Scholar
[64]	Grosshans F, Grangier P 2001 Phys. Rev. A 64 010301 Google Scholar
[65]	Liu C, Zhu T X, Su M X, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2020 Phys. Rev. Lett. 125 260504 Google Scholar
[66]	Gouzien É, Sangouard N 2021 Phys. Rev. Lett. 127 140503 Google Scholar
[67]	Afzelius M, Sangouard N, Johansson G, Staudt M U, Wilson C M 2013 New J. Phys. 15 065008 Google Scholar
[68]	Ma Y Z, Jin M, Chen D L, Zhou Z Q, Li C F, Guo G C 2021 Nat. Commun. 12 4378 Google Scholar
[69]	周宗权 2022 物理学报 71 070305 Google Scholar Zhou Z Q 2022 Acta. Phys. Sin. 71 070305 Google Scholar
[70]	Mirhosseini M, Sipahigil A, Kalaee M, Painter O 2020 Nature 588 599 Google Scholar
[71]	Tu H T, Liao K Y, Zhang Z X, Liu X H, Zheng S Y, Yang S Z, Zhu S L 2022 Nat. Photonics 16 291 Google Scholar
[72]	Brubaker B M, Kindem J M, Urmey M D, Mittal S, Delaney R D, Burns P S, Regal C A 2022 Phys. Rev. X 12 021062 Google Scholar
[73]	Kumar A, Suleymanzade A, Stone M, Taneja L, Anferov A, Schuster D I, Simon J 2023 Nature 615 614 Google Scholar
[74]	Xu Y, Sayem A A, Fan L, Zou C L, Wang S, Cheng R, Tang H X 2021 Nat. Commun. 12 4453 Google Scholar
[75]	Gündoǧan M, Ledingham P M, Kutluer K, Mazzera M, De Riedmatten H 2015 Phys. Rev. Lett. 114 230501 Google Scholar
[76]	Askarani M F, Das A, Davidson J H, Amaral G C, Sinclair N, Slater J A, Tittel W 2021 Phys. Rev. Lett. 127 220502 Google Scholar
[77]	Tiranov A, Strassmann P C, Lavoie J, Brunner N, Huber M, Verma V B, Gisin N 2016 Phys. Rev. Lett. 117 240506 Google Scholar
[78]	Saglamyurek E, Grimau Puigibert M, Zhou Q, Giner L, Marsili F, Verma V B, Tittel W 2016 Nat. Commun. 7 11202 Google Scholar
[79]	Kutluer K, Distante E, Casabone B, Duranti S, Mazzera M, de Riedmatten H 2019 Phys. Rev. Lett. 123 030501 Google Scholar
[80]	Seri A, Lago-Rivera D, Lenhard A, Corrielli G, Osellame R, Mazzera M, de Riedmatten H 2019 Phys. Rev. Lett. 123 080502 Google Scholar
[81]	Tu Y, Zhang G, Zhai Z, Xu J 2009 Phys. Rev. A 80 033816 Google Scholar
[82]	Yang T S, Zhou Z Q, Hua Y L, Liu X, Li Z F, Li P Y, Liu C, Liang P J, Li X, Xiao Y X, Hu J, Li C F, Guo G C 2018 Nat. Commun. 9 3407 Google Scholar
[83]	Li X, Liu X, Zhou Z Q, Li C F, Guo G C 2020 Phys. Rev. A 101 052330 Google Scholar
[84]	Businger M, Nicolas L, Mejia T S, Ferrier A, Goldner P, Afzelius M 2022 Nat. Commun. 13 6438 Google Scholar
[85]	Zhang X, Zhang B, Wei S, Li H, Liao J, Li C, Deng G, Wang Y, Song H, You L, Jing B, Chen F, Guo G, Zhou Q 2023 Sci. Adv. 9 eadf4587 Google Scholar
[86]	Veissier L, Nicolas A, Giner L, Maxein D, Sheremet A S, Giacobino E, Laurat J 2013 Opt. Lett. 38 712 Google Scholar
[87]	Nicolas A, Veissier L, Giner L, Giacobino E, Maxein D, Laurat J 2014 Nat. Photonics 8 234 Google Scholar
[88]	Ding D S, Zhang W, Zhou Z Y, Shi S, Xiang G Y, Wang X S, Guo G C 2015 Phys. Rev. Lett. 114 050502 Google Scholar
[89]	Ding D S, Zhang W, Shi S, Zhou Z Y, Li Y, Shi B S, Guo G C 2016 Light: Science & Applications 5 e16157 Google Scholar
[90]	Zhang W, Ding D S, Dong M X, Shi S, Wang K, Liu S L, Guo G C 2016 Nat. Commun. 7 13514 Google Scholar
[91]	Wang C, Yu Y, Chen Y, Cao M, Wang J, Yang X, Li F 2021 Quantum Sci. Technol. 6 045008 Google Scholar
[92]	Ye Y H, Zeng L, Dong M X, Zhang W H, Li E Z, Li D C, Guo G C, Ding D S, Shi B S 2022 Phys. Rev. Lett. 129 193601 Google Scholar
[93]	Parigi V, D’Ambrosio V, Arnold C, Marrucci L, Sciarrino F, Laurat J 2015 Nat. Commun. 6 7706 Google Scholar
[94]	Lan S Y, Radnaev A G, Collins O A, Matsukevich D N, Kennedy T A B, Kuzmich A 2009 Opt. Express 17 13639 Google Scholar
[95]	Pu Y F, Jiang N, Chang W, Yang H X, Li C, Duan L M 2017 Nat. Commun. 8 15359 Google Scholar
[96]	Chang W, Li C, Wu Y K, Jiang N, Zhang S, Pu Y F, Duan L M 2019 Phys. Rev. X 9 041033 Google Scholar
[97]	Chrapkiewicz R, Dabrowski M, Wasilewski W 2017 Phys. Rev. Lett. 118 063603 Google Scholar
[98]	Wen Y, Zhou P, Xu Z, Yuan L, Zhang H, Wang S, Wang H 2019 Phys. Rev. A 100 012342 Google Scholar
[99]	Julsgaard B, Kozhekin A, Polzik E S 2001 Nature 413 400 Google Scholar
[100]	Chou C W, De Riedmatten H, Felinto D, Polyakov S V, Van Enk S J, Kimble H J 2005 Nature 438 828 Google Scholar
[101]	Yuan Z S, Chen Y A, Zhao B, Chen S, Schmiedmayer J, Pan J W 2008 Nature 454 1098 Google Scholar
[102]	Hofmann J, Krug M, Ortegel N, Gérard L, Weber M, Rosenfeld W, Weinfurter H 2012 Science 337 72 Google Scholar
[103]	van Leent T, Bock M, Fertig F, Garthoff R, Eppelt S, Zhou Y, Weinfurter H 2022 Nature 607 69 Google Scholar
[104]	Enien H, Hensen B, Pfaff W, Koolstra G, Blok M S, Robledo L, Taminiau T H, Markham M, Twitchen D J, Childress L, Hanson R 2013 Nature 497 86 Google Scholar
[105]	Hensen B, Bernien H, Dréau A E, Reiserer A, Kalb N, Blok M S, Ruitenberg J, Vermeulen R F L, Schouten R N, Abellán C, Amaya W, Pruneri V, Mitchell M W, Markham M, Twitchen D J, Elkouss D, Wehner S, Taminiau T H, Hanson R 2015 Nature 526 682 Google Scholar
[106]	Humphreys P C, Kalb N, Morits J P J, Schouten R N, Vermeulen R F L, Twitchen D J 2018 Nature 558 268 Google Scholar
[107]	Delteil A, Sun Z, Gao W, Togan E, Faelt S, Imamoǧlu A 2016 Nat. Phys. 12 218 Google Scholar
[108]	Moehring D L, Maunz P, Olmschenk S, Younge K C, Matsukevich D N, Duan L M, Monroe C 2007 Nature 449 68 Google Scholar
[109]	Yu Y, Ma F, Luo X Y, Jing B, Sun P F, Fang R Z, Pan J W 2020 Nature 578 240 Google Scholar
[110]	Zhou Z Q, Lin W B, Yang M, Li C F, Guo G C 2012 Phys. Rev. Lett. 108 190505 Google Scholar
[111]	Seri A, Lenhard A, Rieländer D, Gündoǧan M, Ledingham P M, Mazzera M, de Riedmatten H 2017 Phys. Rev. X 7 021028 Google Scholar
[112]	Kaneda F, Xu F, Chapman J, Kwiat P G 2017 Optica 4 1034 Google Scholar
[113]	Su K, Wang Y, Zhang S, Kong Z, Zhong Y, Li J, Zhu S L 2021 Chin. Phys. Lett. 38 094202 Google Scholar
[114]	Meyer-Scott E, Prasannan N, Dhand I, Eigner C, Quiring V, Barkhofen S, Silberhorn C 2022 Phys. Rev. Lett. 129 150501 Google Scholar
[115]	Bhaskar M K, Riedinger R, Machielse B, Levonian D S, Nguyen C T, Knall E N, Lukin M D 2020 Nature 580 60 Google Scholar
[116]	Pu Y F, Zhang S, Wu Y K, Jiang N, Chang W, Li C, Duan L M 2021 Nat. Photonics 15 374 Google Scholar
[117]	Zhang S, Wu Y K, Li C, Jiang N, Pu Y F, Duan L M 2022 Phys. Rev. Lett. 128 080501 Google Scholar
[118]	Hong C K, Ou Z Y, Mandel L 1987 Phys. Rev. Lett. 59 2044 Google Scholar
[119]	Knill E, Laflamme R, Milburn G J 2001 Nature 409 46 Google Scholar
[120]	Kok P , Munro W J, Nemoto K, Ralph T C, Dowling J P, Milburn G J 2007 Rev. Mod. Phys. 79 135 Google Scholar
[121]	Okamoto R, O’Brien J L, Hofmann H F, Takeuchi S 2011 Proc. Natl. Acad. Sci. 108 10067 Google Scholar
[122]	Bouchard F, Sit A, Zhang Y W, Fickler R, Miatto F M, Yao Y, Sciarrino F, Karimi E 2021 Rep. Prog. Phys. 84 012402 Google Scholar
[123]	Li J, Zhou M T, Jing B, Wang X J, Yang S J, Jiang X, Molmer K, Bao X H, Pan J W 2016 Phys. Rev. Lett. 117 180501 Google Scholar
[124]	Fakonas J S, Lee H, Kelaita Y A, Atwater H A 2014 Nat. Photonics 8 317 Google Scholar
[125]	Lopes R, Imanaliev A, Aspect A, Cheneau M, Boiron D, Westbrook C I 2015 Nature 520 66 Google Scholar
[126]	Kaufman A M, Lester B J, Reynolds C M, Wall M L, Foss-Feig M, Hazzard K R A, Rey A M, Regal C A 2014 Science 345 306 Google Scholar
[127]	Wen R, Zou C L, Zhu X, Chen P, Ou Z Y, Chen J F, Zhang W 2019 Phys. Rev. Lett. 122 253602 Google Scholar
[128]	Wang X, Wang J, Ren Z, Wen R, Zou C L, Siviloglou G A, Chen J F 2022 Phys. Rev. Lett. 128 083605 Google Scholar
[129]	Su K Y, Zhong Y, Zhang S C, Li J F, Zou C L, Wang Y F, Yan H, Zhu S L 2022 Phys. Rev. Lett. 129 093604 Google Scholar

图 1 (a)吸收型量子存储过程及能级方案. 单光子源产生的光子编码量子信息后, 输入进存储介质中. 待光子完全进入介质, 通过调控控制场将光子信息转化成原子自旋信息, 随后再次调控控制光场恢复光子信息并读取出来. (b) DLCZ型量子存储过程及能级方案. 一束写入激光对原子系综进行单激发, 同时释放一个斯托克斯光子, 随后一束读取激光再次作用到单激发介质上, 释放一个反斯托克斯光子. 两个光子之间的时间延迟可以通过操控写入和读取光的相对时间来控制

Fig. 1. The absorptive quantum memory and energy level scheme. The photons generated by the single photon source encode quantum information and are input into the storage medium. After the photons have completely entered the medium, the light quantum information is converted into atomic spin wave by manipulating the control field, and then the light quantum information is read out again by manipulating the control field. (b) DLCZ quantum memory and energy level scheme. A writing laser beam couple the atomic ensemble and simultaneously releases a Stokes photon, and then a reading laser beam couple the medium again to release an anti-Stokes photon. The time delay between two photons can be controlled by manipulating the relative timing of writing and reading laser.

下载: 全尺寸图片幻灯片

图 2 单光子量子存储的实验装置和能级方案　(a)实验方案. 磁光阱1 制备的冷原子系综用于制备时间-频率纠缠光子对, 磁光阱2 制备的冷原子系综用于进行光量子态存储. 磁光阱1 中产生的反斯托克斯光子经半波片和四分之一波片编码成任意偏振态, 然后经过一个偏振光束位移器将其偏振态的两个正交分量H偏振和V偏振分别转换成两条路径信息CH_H和CH_V. 读取后的光子再次经过反置的偏振光束位移换器重构出偏振态, 随后进行偏振量子态层析. (b)存储过程中的时序及优化后的控制光调制示意. (c)基于电磁诱导透明量子存储的原子能级方案. (d)当水平偏振的输入通道 $|H\rangle$ 具有最优存储效率时, 其输入、EIT慢光以及读取单光子的时域波形情况. (e)光学厚度对存储效率的影响情况. 图中的线均是基于实验采集数据进行的理论拟合, 理论拟合采用的波形为高斯函数. 红色实线表示在存储窗口期间修改控制光的强度以匹配光学深度变化的存储数据, 黑色虚线表示控制光的强度恒定时的数据^[34]

Fig. 2. Experimental set-up and energy level scheme of the single-photon quantum memory. (a) Schematic of the experimental optical set-up. The cold atoms in the first magneto-optical trap (MOT₁) serve as a nonlinear optical medium for producing time-frequency entangled photon pairs, while the cold atoms in the second magneto-optical trap (MOT2₁) are the medium for the quantum memory. The anti-Stokes photon is coded with an arbitrary polarization state through the qubit manipulation unit (QMU) consisting of a QWP and HWP. After the QMU, the two orthogonal linear polarizations are separated into two beams by a polarization beam displacer (BD) that are coupled into the two balanced spatial channels CH_H and CH_V of the quantum memory. The memory read-outs are recombined at the second BD and the polarization state is measured by the qubit analyser. (b) The memory operation timing shows the MOT sequence and the optimized control laser intensity time-varying profile in each experimental cycle. (c) The atomic energy level scheme of the quantum memory based on EIT. (d) The input, EIT delayed and retrieved temporal waveforms of the heralded single photons when the quantum memory is optimized for the horizontally polarized input optical channel $|H\rangle$ . (e) The storage efficiency as a function of the optical depth of the quantum memory. The solid lines are the best fitted theoretical waveforms by fitting the input waveform using a Gaussian function and then numerically calculating the retrieved waveform based on the measured experimental parameters of the quantum memory. The red line denotes the situation when the intensity of the control light is modified to match the optical depth change during the storage window and the black line denotes the result when the intensity of the control light is constant^[34]

下载: 全尺寸图片幻灯片

图 3 存储效率与存储时间的调研与统计. 图中不同形状的起始点代表不同的存储介质, 其中五角星代表冷原子系综, 三角形代表热原子系综, 正方形代表固体掺杂离子体系. 图中数字对应参考文献序号. 不同线形代表着不同的存储方式, 其中蓝色实线代表相干光存储, 红色实线代表单光子存储, 红色虚线代表DLCZ型量子存储. 作为对比, 图中用灰色实线以及灰色阴影区域标出了1550 nm波长光纤的时间延迟效率, 这里光纤损耗按0.2 dB/km

Fig. 3. Statistics on the storage efficiency and storage time. Different storage medium are distinguished by symbols. The star represents the cold atoms, the triangle represents the warm atoms, and the square represents the doped ion crystal. The numbers before the symbols is the reference of the corresponding works. Blue solid line represents coherent light memory, red solid line represents single photon memory, and red dotted line represents DLCZ quantum memory. The transmission of 1550 nm fiber delay line is plotted using solid gray lines with the loss of 0.2 dB/km.

下载: 全尺寸图片幻灯片

图 4 (a)利用纠缠光子源和多模量子存储器实现量子中继的方案. 由于量子存储器可以支持同时存储多个光子脉冲, 因此量子纠缠源可以陆续地产生光子, 以节省量子纠缠建立的时间成本. 这里的源和多模量子存储器的组合相当于DLCZ型量子存储器, 但该中继方案具有多模式的功能优势^[22]. (b)利用多模量子存储器和量子处理器分解2048位RSA整数的量子计算机体系结构. 研究表明, 在量子存储器支持2800万个空间模式和45个时间模式, 并且存储时间覆盖到2 h的情况下, 处理器只需要13436个物理量子位即可在177天内即可完成任务^[66]

Fig. 4. (a) Quantum repeater scheme using pair sources and multimode memories. The sources $S_{i}$ can each emit a photon pair into a sequence of time bins. The multimode memories $M_{i}$ can store the sequential photons simultaneously. The combination of source and multimode quantum memory is equivalent to the DLCZ scheme, but with multimode functionality^[22]. (b) The quantum computer architecture for factoring a 2048-bit RSA integer with multimode quantum memories and quantum processors. It is shown to be possible in 177 days with 13436 physical qubits and a memory that can store 28 million spatial modes and 45 temporal modes with 2 hours’ storage time^[66].

下载: 全尺寸图片幻灯片

图 5 (a) 潘建伟等^[109]借助高效率波长转换器实现了50 km光纤连接的两个DLCZ 量子存储纠缠; (b)李传锋等^[56]首次实验演示吸收型量子存储之间的量子纠缠; (c) Riedmatten等^[63]实现了两个多模固态量子存储之间的纠缠

Fig. 5. (a) 50 km fiber length entanglement of two quantum memories via efficient quantum wavelength converter demonstrated by Pan et al.^[109]; (b) experimental demonstration of quantum entanglement between absorbing quantum memories for the first time by Li et al.^[56]; (c) experimental demonstration of quantum entanglement between multimode quantum memories by Riedmatten et al.^[63].

下载: 全尺寸图片幻灯片

图 6 光子同步干涉与相位调制实验方案. 采用暗线磁光阱技术制备三个雪茄形高密度铷85 冷原子系综. 在泵浦光和耦合光共同作用下, 于磁光阱1 (2)中采用四波混频的方法产生斯托克斯光子 $\omega_{{\rm{s}}1}$ ( $\omega_{{\rm{s}}2}$ )和反斯托克斯光子 $\omega_{{\rm{as}}1}$ ( $\omega_{{\rm{as}}2}$ )纠缠光子对. $\Delta t_{{\rm{random}}}$ 表示反斯托克斯光子 $\omega_{{\rm{as}}1}$ 和 $\omega_{{\rm{as}}2}$ 之间的时间差. 磁光阱3是电磁诱导透明存储器, 用于控制 $\omega_{{\rm{as}}2}$ 光子的时间延迟, 实现 $\omega_{{\rm{as}}1}$ 和 $\omega_{{\rm{as}}2}$ 光子的时间同步. 如电磁诱导透明过程能级示意图所示, 光子的存储、读取及相位调制过程完全由控制光决定, 实验上利用声光调制器(AOM)来实现. 同步后的 $\omega_{{\rm{as}}1}$ 和 $\omega_{{\rm{as}}2}$ 光子通过单模光纤传输到由分束器组成的HOM干涉仪中进行干涉, 最终被单光子计数模块A, B, C和D检测. PBS, 偏振分束器; HWP,半波片; QWP, 四分之一波片; HR, 高反射镜^[113]

Fig. 6. Three cigar-shape dense cold atomic ensembles are prepared by dark-line magneto-optical traps (MOT) of $^{85}$ Rb atoms. Single photons $\omega_{{\rm{as}}1}$ ( $\omega_{{\rm{as}}2}$ ) heralded by its counterpart $\omega_{{\rm{s}}1}$ ( $\omega_{{\rm{s}}2}$ ) are generated from MOT $_{1}$ (MOT $_{2}$ ) with the existence of pump1-coupling1 (pump2-coupling2) laser beams via the spontaneous four-wave-mixing process. Therefore, the timing differences between $\omega_{{\rm{as}}1}$ and $\omega_{{\rm{as}}2}$ are random and denoted by $\Delta t_{{\rm{random}}}$ . MOT₃ acts as an efficient QM based on EIT that can synchronize the readout single photon $\omega_{{\rm{as}}2}$ to $\omega_{{\rm{as}}1}$ ( $\Delta t=0$ ). As shown by the energy level schematics of EIT two-photon process, a control laser manipulates the storage and readout of single photons $\omega_{{\rm{as}}2}$ . The amplitude and phase of the control laser pulse with a complex envelope of Rabi frequency $\Omega_{{\rm{c}}}(t){\rm{e}}^{-{\rm{i}}\phi_{{\rm{c}}}(t)}$ is controlled by an acousto-optic modulator (AOM), by which the readout single photons $\omega_{{\rm{as}}2}$ can be phase modulated accordingly. Single photons $\omega_{{\rm{as}}1}$ and $\omega_{{\rm{as}}2}$ are delivered to a HOM interferometer consisting of a beam splitter (BS) via single mode fibers (SMFs). Photons $\omega_{{\rm{s}}1}$ and $\omega_{{\rm{s}}2}$ are also collected and sent to detectors via SMFs. The generated photons are eventually detected by single photon counting modules (SPCMs) A, B, C and D. Filters are inserted before SPCMs to filter out noisy photons. PBS, polarization beam splitter; HWP, half wave plate; QWP, quarter wave plate; HR, high reflection mirror^[113].

下载: 全尺寸图片幻灯片

图 7 单磁子与单光子干涉实验方案　(a)磁子-光子HOM干涉仪的理论模型. 磁子 $\widehat{\sigma}_{21}$ 和光子 $\widehat{E}$ 在电磁诱导透明介质中都以暗态极化子的形式存在. 控制光上方的红线显示了实验的时序, 包括磁子的制备 $\varOmega_{{\rm{S}}}$ 、磁子与光子的干涉 $\varOmega_{{\rm{BS}}}$ 和磁子的读取 $\varOmega_{{\rm{R}}}$ 三个过程. 该电磁诱导透明过程的铷85能级方案: $|1\rangle=5 {\rm{S}}_{1/2}, F=2, m_{F}=2$ , $|2\rangle=5 {\rm{S}}_{1/2}, F=3, m_{F}=3$ , $|3\rangle=5 P_{1/2}, F=3,$ $m_{F}=3$ , $\varGamma_{3}$ 是 $|3\rangle$ 态的自发辐射率, Δ是单光子失谐. (b)磁子和光子HOM干涉的输入和输出态. (c)实验方案. 磁光阱1作为单光子源连续产生单光子, 通过探测斯托克斯光子可宣布反斯托克斯光子的产生. 磁光阱2作为非厄米分束器用于实现光子- 磁子的分束及干涉. PBS, 偏振分束器; QWP, 四分之一波片; SPCM, 单光子计数模块; SMF, 单模光纤^[129]

Fig. 7. Theoretical and experimental schemes: (a) Theoretical scheme of magnon-photon HOM interferometer. The magnon ( $\hat{\sigma}$ ) and photon ( $\hat{E}$ ) are both in the form of a dark-state polariton (DSP) in an electromagnetically induced transparency (EIT) medium. The red line above the control laser shows the experimental timing sequences: storage of a magnon ( $\varOmega _{\rm{S}}$ ), interference between two DSPs ( $\varOmega _{{\rm{BS}}}$ ) and reading out of the magnon ( $\varOmega _{\rm{R}}$ ). The insert is a $\Lambda$ -type EIT energy diagram: $|1\rangle = |5{{\rm{S}}_{1/2}},$ $F = 2, {m_F} = 2\rangle$ , $|2\rangle = |5{{\rm{S}}_{1/2}}, F = 3, {m_F} = 2\rangle$ , $|3\rangle = |5{P_{1/2}}, F = 3, {m_F} = 3\rangle$ , $\varGamma_{3}$ is the spontaneous decay rate of $|3\rangle$ , and $\varDelta$ is single photon detuning. (b) The input and output states of the magnon-photon HOM interferometer. (c) Experimental setup. MOT $_{1}$ is a single photon source. The detection of a Stokes photon ( $\omega_{{\rm{s}}i}$ ) heralded the generation of an anti-Stokes photon ( $\omega_{{\rm{as}}i}$ ). MOT $_{2}$ is the non-Hermitian beam splitter. PBS, polarization beam splitter; QWP, quarter wave plate; SPCM, single photon counting module; SMF, single mode fibre^[129].

下载: 全尺寸图片幻灯片

[1]	Walmsley I A 2015 Science 348 525 Google Scholar
[2]	Wootters W K, Zurek W H 1982 Nature 299 802 Google Scholar
[3]	Gisin N, Thew R 2007 Nat. Photonics 1 165 Google Scholar
[4]	Briegel H J, Dür W, Cirac J I, Zoller P 1998 Phys. Rev. Lett. 81 5932 Google Scholar
[5]	Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413 Google Scholar
[6]	Gisin N, Ribordy G, Tittel W, Zbinde H 2002 Rev. Mod. Phys. 74 145 Google Scholar
[7]	Foot C J 2005 Atomic Physics (Oxford: Oxford University Press) pp123–214 Foot C J 2005 Atomic Physics (Oxford: Oxford University Press) pp123–214
[8]	Scully M O, Zubairy M S 1999 Quantum Optics (New York: Cambridge University Press) pp145–217 Scully M O, Zubairy M S 1999 Quantum Optics (New York: Cambridge University Press) pp145–217
[9]	Nielsen, Michael A, I L Chuang 2011 Quantum Computation and Quantum Information: 10th Anniversary Edition (New York: Cambridge University Press) pp277–343 Nielsen, Michael A, I L Chuang 2011 Quantum Computation and Quantum Information: 10th Anniversary Edition (New York: Cambridge University Press) pp277–343
[10]	Hammerer K, SØrensen A S, Polzik E S 2010 Rev. Mod. Phys. 82 1041 Google Scholar
[11]	Kimble H J 2008 Nature 453 1023 Google Scholar
[12]	Wehner S, Elkouss D, Hanson R 2018 Science 362 eaam9288 Google Scholar
[13]	郭光灿 2020 中国科学: 信息科学 50 1395 Google Scholar Guo G C 2020 Sci. Sin. Inform. 50 1395 Google Scholar
[14]	Simon C 2017 Nat. Photonics 11 678 Google Scholar
[15]	Duan L M, Monroe C 2010 Rev. Mod. Phys. 82 1209 Google Scholar
[16]	Yan Z H, Wu L, Jia X J, Xie C D, Peng K C 2021 Adv. Quantum Technol. 4 2100071 Google Scholar
[17]	Afzelius M, Gisin N, De Riedmatten H 2015 Phys. Today 68 42 Google Scholar
[18]	Lvovsky A I, Sanders B C, Tittel W 2009 Nat. Photonics 3 706 Google Scholar
[19]	Bussieres F, Sangouard N, Afzelius M, De Riedmatten H, Simon C, Tittel W 2013 J. Mod. Opt. 60 1519 Google Scholar
[20]	Guo M C, Liu S P, Sun W Y, Ren M M, Wang F D, Zhong M J 2023 Front. Phys. 18 21303 Google Scholar
[21]	Sangouard N, Simon C, De Riedmatten H, Gisin N 2011 Rev. Mod. Phys. 83 33 Google Scholar
[22]	Simon C, De Riedmatten H, Afzelius M, Sangouard N, Zbinden H, Gisin N 2007 Phys. Rev. Lett. 98 190503 Google Scholar
[23]	Chou C W, Laurat J, Deng H, Choi K, De Riedmatten H, Felinto D, Kimble H J 2007 Science 316 1316 Google Scholar
[24]	Wei S H, Jing B, Zhang X Y, Liao J Y, Yuan C Z, Fan B Y, Lyu C, Zhou D L, Wang Y, Deng G W, Song H Z, Oblak D, Guo G C, Zhou Q 2022 Laser Photon. Rev. 16 2100219 Google Scholar
[25]	Nunn J, Langford N K, Kolthammer W S, Champion T F M, Sprague M R, Michelberger P S, Walmsley I A 2013 Phys. Rev. Lett. 110 133601 Google Scholar
[26]	Pan J W, Chen Z B, Lu C Y, Weinfurter H, Zeilinger A, Zukowski M 2012 Rev. Mod. Phys. 84 777 Google Scholar
[27]	Reim K F, Nunn J, Lorenz V O, Sussman B J, Lee K C, Langford N K, Walmsley I A 2010 Nat. Photonics 4 218 Google Scholar
[28]	Reim K F, Michelberger P, Lee K C, Nunn J, Langford N K, Walmsley I A 2011 Phys. Rev. Lett. 107 053603 Google Scholar
[29]	Michelberger P S, Champion T F M, Sprague M R, Kaczmarek K T, Barbieri M, Jin X M, Walmsley I A 2015 New J. Phys. 17 043006 Google Scholar
[30]	Guo J, Feng X, Yang P, Yu Z, Chen L Q, Yuan C H, Zhang W 2019 Nat. Commun. 10 148 Google Scholar
[31]	Cho Y W, Campbell G T, Everett J L, Bernu J, Higginbottom D B, Cao M T, Geng J, Robins N P, Lam P K, Buchler B C 2016 Optica 3 100 Google Scholar
[32]	Hsiao Y F, Tsai P J, Chen H S, Lin S X, Hung C C, Lee C H, Chen Y C 2018 Phys. Rev. Lett. 120 183602 Google Scholar
[33]	Zhou S, Zhang S, Liu C, Chen J F, Wen J, Loy M M T, Du S 2012 Opt. Express 20 24124 Google Scholar
[34]	Wang Y F, Li J F, Zhang S C, Su K Y, Zhou Y R, Liao K Y, Du S W, Yan H, Zhu S L 2019 Nat. Photonics 13 346 Google Scholar
[35]	Cao M, Hoffet F, Qi S, Sheremet A S, Laurat J 2020 Optica 7 1440 Google Scholar
[36]	Davidson J H, Lefebvre P, Zhang J, Oblak D, Tittel W 2020 Phys. Rev. A 101 042333 Google Scholar
[37]	Akhmedzhanov R A, Gushchin L A, Kalachev A A, Nizov N A, Nizov V A, Sobgayda D A, Zelensky I V 2016 Laser Phys. Lett. 13 115203 Google Scholar
[38]	Jobez P, Usmani I, Timoney N, Laplane C, Gisin N, Afzelius M 2014 New J. Phys. 16 083005 Google Scholar
[39]	Sabooni M, Li Q, Kröll S, Rippe L 2013 Phys. Rev. Lett. 110 133604 Google Scholar
[40]	Schraft D, Hain M, Lorenz N, Halfmann T 2016 Phys. Rev. Lett. 116 073602 Google Scholar
[41]	Sabooni M, Kometa S T, Thuresson A, Kröll S, Rippe L 2013 New J. Phys. 15 035025 Google Scholar
[42]	Hain M, Stabel M, Halfmann T 2022 New J. Phys. 24 023012 Google Scholar
[43]	Dudin Y O, Li L, Kuzmich A 2013 Phys. Rev. A 87 031801 Google Scholar
[44]	Heinze G, Hubrich C, Halfmann T 2013 Phys. Rev. Lett. 111 033601 Google Scholar
[45]	Zhong M, Hedges M P, Ahlefeldt R L, Bartholomew J G, Beavan S E, Wittig S M, Sellars M J 2015 Nature 517 177 Google Scholar
[46]	Yang S J, Wang X J, Bao X H, Pan J W 2016 Nat. Photonics 10 381 Google Scholar
[47]	Wang X J, Yang S J, Sun P F, Jing B, Li J, Zhou M T, Pan J W 2021 Phys. Rev. Lett. 126 090501 Google Scholar
[48]	Ma Y, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2021 Nat. Commun. 12 2381 Google Scholar
[49]	Chen Y H, Lee M J, Wang I C, Du S W, Chen Y F, Chen Y C, Yu I A 2013 Phys. Rev. Lett. 110 083601 Google Scholar
[50]	Ma L X, Lei X, Yan J L, Li R Y, Chai T, Yan Z H, Jia X J, Xie C D, Peng K C 2022 Nat. Commun. 13 2368 Google Scholar
[51]	Horvath S P, Alqedra M K, Kinos A, Walther A, Dahlström J M, Stefan Kröll, Rippe L 2021 Phys. Rev. Research 3 023099 Google Scholar
[52]	Mazelanik M, Leszczyński A, Parniak M 2022 Nat. Commun. 13 691 Google Scholar
[53]	Li C, Zhang S, Wu Y K, Jiang N, Pu Y F, Duan L M 2021 Phys. Rev. X 2 040307 Google Scholar
[54]	Dideriksen K B, Schmieg R, Zugenmaier M, Polzik E S 2021 Nat. Commun. 12 3699 Google Scholar
[55]	Ding D S, Zhang W, Zhou Z Y, Shi S, Shi B S, Guo G C 2015 Nat. Photonics 9 332 Google Scholar
[56]	Liu X, Hu J, Li Z F, Li X, Li P Y, Liang P J, Zhou Z Q, Li C F, Guo G C 2021 Nature 594 41 Google Scholar
[57]	Tian L, Xu Z, Chen L, Ge W, Yuan H, Wen Y, Wang H 2017 Phys. Rev. Lett. 119 130505 Google Scholar
[58]	Zhu T X, Liu C, Jin M, Su M X, Liu Y P, Li W J, Guo G C 2022 Phys. Rev. Lett. 128 180501 Google Scholar
[59]	Vernaz-Gris P, Huang K, Cao M, Sheremet A S, Laurat J 2018 Nat. Commun. 9 363 Google Scholar
[60]	Wei S H, Jing B, Zhang X Y, Liao J Y, Li H, You L X, Zhou Q 2022 arXiv: 2209.00802[quant-ph Google Scholar
[61]	Ortu A, Holzäpfel A, Etesse J, Afzelius M 2022 npj Quantum Inform. 8 29 Google Scholar
[62]	Saglamyurek E, Hrushevskyi T, Rastogi A, Cooke L W, Smith B D, LeBlanc L J 2021 New J. Phys. 23 043028 Google Scholar
[63]	Lago-Rivera D, Grandi S, Rakonjac J V, Seri A, de Riedmatten H 2021 Nature 594 37 Google Scholar
[64]	Grosshans F, Grangier P 2001 Phys. Rev. A 64 010301 Google Scholar
[65]	Liu C, Zhu T X, Su M X, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2020 Phys. Rev. Lett. 125 260504 Google Scholar
[66]	Gouzien É, Sangouard N 2021 Phys. Rev. Lett. 127 140503 Google Scholar
[67]	Afzelius M, Sangouard N, Johansson G, Staudt M U, Wilson C M 2013 New J. Phys. 15 065008 Google Scholar
[68]	Ma Y Z, Jin M, Chen D L, Zhou Z Q, Li C F, Guo G C 2021 Nat. Commun. 12 4378 Google Scholar
[69]	周宗权 2022 物理学报 71 070305 Google Scholar Zhou Z Q 2022 Acta. Phys. Sin. 71 070305 Google Scholar
[70]	Mirhosseini M, Sipahigil A, Kalaee M, Painter O 2020 Nature 588 599 Google Scholar
[71]	Tu H T, Liao K Y, Zhang Z X, Liu X H, Zheng S Y, Yang S Z, Zhu S L 2022 Nat. Photonics 16 291 Google Scholar
[72]	Brubaker B M, Kindem J M, Urmey M D, Mittal S, Delaney R D, Burns P S, Regal C A 2022 Phys. Rev. X 12 021062 Google Scholar
[73]	Kumar A, Suleymanzade A, Stone M, Taneja L, Anferov A, Schuster D I, Simon J 2023 Nature 615 614 Google Scholar
[74]	Xu Y, Sayem A A, Fan L, Zou C L, Wang S, Cheng R, Tang H X 2021 Nat. Commun. 12 4453 Google Scholar
[75]	Gündoǧan M, Ledingham P M, Kutluer K, Mazzera M, De Riedmatten H 2015 Phys. Rev. Lett. 114 230501 Google Scholar
[76]	Askarani M F, Das A, Davidson J H, Amaral G C, Sinclair N, Slater J A, Tittel W 2021 Phys. Rev. Lett. 127 220502 Google Scholar
[77]	Tiranov A, Strassmann P C, Lavoie J, Brunner N, Huber M, Verma V B, Gisin N 2016 Phys. Rev. Lett. 117 240506 Google Scholar
[78]	Saglamyurek E, Grimau Puigibert M, Zhou Q, Giner L, Marsili F, Verma V B, Tittel W 2016 Nat. Commun. 7 11202 Google Scholar
[79]	Kutluer K, Distante E, Casabone B, Duranti S, Mazzera M, de Riedmatten H 2019 Phys. Rev. Lett. 123 030501 Google Scholar
[80]	Seri A, Lago-Rivera D, Lenhard A, Corrielli G, Osellame R, Mazzera M, de Riedmatten H 2019 Phys. Rev. Lett. 123 080502 Google Scholar
[81]	Tu Y, Zhang G, Zhai Z, Xu J 2009 Phys. Rev. A 80 033816 Google Scholar
[82]	Yang T S, Zhou Z Q, Hua Y L, Liu X, Li Z F, Li P Y, Liu C, Liang P J, Li X, Xiao Y X, Hu J, Li C F, Guo G C 2018 Nat. Commun. 9 3407 Google Scholar
[83]	Li X, Liu X, Zhou Z Q, Li C F, Guo G C 2020 Phys. Rev. A 101 052330 Google Scholar
[84]	Businger M, Nicolas L, Mejia T S, Ferrier A, Goldner P, Afzelius M 2022 Nat. Commun. 13 6438 Google Scholar
[85]	Zhang X, Zhang B, Wei S, Li H, Liao J, Li C, Deng G, Wang Y, Song H, You L, Jing B, Chen F, Guo G, Zhou Q 2023 Sci. Adv. 9 eadf4587 Google Scholar
[86]	Veissier L, Nicolas A, Giner L, Maxein D, Sheremet A S, Giacobino E, Laurat J 2013 Opt. Lett. 38 712 Google Scholar
[87]	Nicolas A, Veissier L, Giner L, Giacobino E, Maxein D, Laurat J 2014 Nat. Photonics 8 234 Google Scholar
[88]	Ding D S, Zhang W, Zhou Z Y, Shi S, Xiang G Y, Wang X S, Guo G C 2015 Phys. Rev. Lett. 114 050502 Google Scholar
[89]	Ding D S, Zhang W, Shi S, Zhou Z Y, Li Y, Shi B S, Guo G C 2016 Light: Science & Applications 5 e16157 Google Scholar
[90]	Zhang W, Ding D S, Dong M X, Shi S, Wang K, Liu S L, Guo G C 2016 Nat. Commun. 7 13514 Google Scholar
[91]	Wang C, Yu Y, Chen Y, Cao M, Wang J, Yang X, Li F 2021 Quantum Sci. Technol. 6 045008 Google Scholar
[92]	Ye Y H, Zeng L, Dong M X, Zhang W H, Li E Z, Li D C, Guo G C, Ding D S, Shi B S 2022 Phys. Rev. Lett. 129 193601 Google Scholar
[93]	Parigi V, D’Ambrosio V, Arnold C, Marrucci L, Sciarrino F, Laurat J 2015 Nat. Commun. 6 7706 Google Scholar
[94]	Lan S Y, Radnaev A G, Collins O A, Matsukevich D N, Kennedy T A B, Kuzmich A 2009 Opt. Express 17 13639 Google Scholar
[95]	Pu Y F, Jiang N, Chang W, Yang H X, Li C, Duan L M 2017 Nat. Commun. 8 15359 Google Scholar
[96]	Chang W, Li C, Wu Y K, Jiang N, Zhang S, Pu Y F, Duan L M 2019 Phys. Rev. X 9 041033 Google Scholar
[97]	Chrapkiewicz R, Dabrowski M, Wasilewski W 2017 Phys. Rev. Lett. 118 063603 Google Scholar
[98]	Wen Y, Zhou P, Xu Z, Yuan L, Zhang H, Wang S, Wang H 2019 Phys. Rev. A 100 012342 Google Scholar
[99]	Julsgaard B, Kozhekin A, Polzik E S 2001 Nature 413 400 Google Scholar
[100]	Chou C W, De Riedmatten H, Felinto D, Polyakov S V, Van Enk S J, Kimble H J 2005 Nature 438 828 Google Scholar
[101]	Yuan Z S, Chen Y A, Zhao B, Chen S, Schmiedmayer J, Pan J W 2008 Nature 454 1098 Google Scholar
[102]	Hofmann J, Krug M, Ortegel N, Gérard L, Weber M, Rosenfeld W, Weinfurter H 2012 Science 337 72 Google Scholar
[103]	van Leent T, Bock M, Fertig F, Garthoff R, Eppelt S, Zhou Y, Weinfurter H 2022 Nature 607 69 Google Scholar
[104]	Enien H, Hensen B, Pfaff W, Koolstra G, Blok M S, Robledo L, Taminiau T H, Markham M, Twitchen D J, Childress L, Hanson R 2013 Nature 497 86 Google Scholar
[105]	Hensen B, Bernien H, Dréau A E, Reiserer A, Kalb N, Blok M S, Ruitenberg J, Vermeulen R F L, Schouten R N, Abellán C, Amaya W, Pruneri V, Mitchell M W, Markham M, Twitchen D J, Elkouss D, Wehner S, Taminiau T H, Hanson R 2015 Nature 526 682 Google Scholar
[106]	Humphreys P C, Kalb N, Morits J P J, Schouten R N, Vermeulen R F L, Twitchen D J 2018 Nature 558 268 Google Scholar
[107]	Delteil A, Sun Z, Gao W, Togan E, Faelt S, Imamoǧlu A 2016 Nat. Phys. 12 218 Google Scholar
[108]	Moehring D L, Maunz P, Olmschenk S, Younge K C, Matsukevich D N, Duan L M, Monroe C 2007 Nature 449 68 Google Scholar
[109]	Yu Y, Ma F, Luo X Y, Jing B, Sun P F, Fang R Z, Pan J W 2020 Nature 578 240 Google Scholar
[110]	Zhou Z Q, Lin W B, Yang M, Li C F, Guo G C 2012 Phys. Rev. Lett. 108 190505 Google Scholar
[111]	Seri A, Lenhard A, Rieländer D, Gündoǧan M, Ledingham P M, Mazzera M, de Riedmatten H 2017 Phys. Rev. X 7 021028 Google Scholar
[112]	Kaneda F, Xu F, Chapman J, Kwiat P G 2017 Optica 4 1034 Google Scholar
[113]	Su K, Wang Y, Zhang S, Kong Z, Zhong Y, Li J, Zhu S L 2021 Chin. Phys. Lett. 38 094202 Google Scholar
[114]	Meyer-Scott E, Prasannan N, Dhand I, Eigner C, Quiring V, Barkhofen S, Silberhorn C 2022 Phys. Rev. Lett. 129 150501 Google Scholar
[115]	Bhaskar M K, Riedinger R, Machielse B, Levonian D S, Nguyen C T, Knall E N, Lukin M D 2020 Nature 580 60 Google Scholar
[116]	Pu Y F, Zhang S, Wu Y K, Jiang N, Chang W, Li C, Duan L M 2021 Nat. Photonics 15 374 Google Scholar
[117]	Zhang S, Wu Y K, Li C, Jiang N, Pu Y F, Duan L M 2022 Phys. Rev. Lett. 128 080501 Google Scholar
[118]	Hong C K, Ou Z Y, Mandel L 1987 Phys. Rev. Lett. 59 2044 Google Scholar
[119]	Knill E, Laflamme R, Milburn G J 2001 Nature 409 46 Google Scholar
[120]	Kok P , Munro W J, Nemoto K, Ralph T C, Dowling J P, Milburn G J 2007 Rev. Mod. Phys. 79 135 Google Scholar
[121]	Okamoto R, O’Brien J L, Hofmann H F, Takeuchi S 2011 Proc. Natl. Acad. Sci. 108 10067 Google Scholar
[122]	Bouchard F, Sit A, Zhang Y W, Fickler R, Miatto F M, Yao Y, Sciarrino F, Karimi E 2021 Rep. Prog. Phys. 84 012402 Google Scholar
[123]	Li J, Zhou M T, Jing B, Wang X J, Yang S J, Jiang X, Molmer K, Bao X H, Pan J W 2016 Phys. Rev. Lett. 117 180501 Google Scholar
[124]	Fakonas J S, Lee H, Kelaita Y A, Atwater H A 2014 Nat. Photonics 8 317 Google Scholar
[125]	Lopes R, Imanaliev A, Aspect A, Cheneau M, Boiron D, Westbrook C I 2015 Nature 520 66 Google Scholar
[126]	Kaufman A M, Lester B J, Reynolds C M, Wall M L, Foss-Feig M, Hazzard K R A, Rey A M, Regal C A 2014 Science 345 306 Google Scholar
[127]	Wen R, Zou C L, Zhu X, Chen P, Ou Z Y, Chen J F, Zhang W 2019 Phys. Rev. Lett. 122 253602 Google Scholar
[128]	Wang X, Wang J, Ren Z, Wen R, Zou C L, Siviloglou G A, Chen J F 2022 Phys. Rev. Lett. 128 083605 Google Scholar
[129]	Su K Y, Zhong Y, Zhang S C, Li J F, Zou C L, Wang Y F, Yan H, Zhu S L 2022 Phys. Rev. Lett. 129 093604 Google Scholar

[1]	翟晨杰, 王晶, 周俊杰, 王毓, 唐晓明, 周寅, 张灿, 李瑞, 舒晴, 王凯楠, 王双全, 金子骍, 华珊, 孙羿人, 王正豪, 马志祥, 蔡铭豪, 王肖隆, 吴彬, 林强. 基于量子重力仪的航空绝对重力测量. 物理学报, 2025, 74(7): 070302. doi: 10.7498/aps.74.20241621
[2]	梁澎军, 朱天翔, 肖懿鑫, 王奕洋, 韩永建, 周宗权, 李传锋. 浓度依赖的掺铕硅酸钇晶体的光学和自旋非均匀展宽. 物理学报, 2024, 73(10): 100301. doi: 10.7498/aps.73.20240116
[3]	肖懿鑫, 朱天翔, 梁澎军, 王奕洋, 周宗权, 李传锋. 聚焦离子束加工的硅酸钇波导中铕离子的光学与超精细跃迁. 物理学报, 2024, 73(22): 220303. doi: 10.7498/aps.73.20241070
[4]	翟荟. 基于冷原子的非平衡量子多体物理研究. 物理学报, 2023, 72(23): 230701. doi: 10.7498/aps.72.20231375
[5]	张苏钊, 孙雯君, 董猛, 武海斌, 李睿, 张雪姣, 张静怡, 成永军. 基于磁光阱中⁶Li冷原子的真空度测量. 物理学报, 2022, 71(9): 094204. doi: 10.7498/aps.71.20212204
[6]	罗雨晨, 李晓鹏. 相互作用费米子的量子模拟. 物理学报, 2022, 71(22): 226701. doi: 10.7498/aps.71.20221756
[7]	周宗权. 量子存储式量子计算机与无噪声光子回波. 物理学报, 2022, 71(7): 070305. doi: 10.7498/aps.71.20212245
[8]	邢雪燕, 李霞霞, 陈宇辉, 张向东. 基于光子晶体微腔的回波光量子存储. 物理学报, 2022, 71(11): 114201. doi: 10.7498/aps.71.20220083
[9]	周湃, 李霞霞, 邢雪燕, 陈宇辉, 张向东. 基于掺铒晶体的光量子存储和调控. 物理学报, 2022, 71(6): 064203. doi: 10.7498/aps.71.20211803
[10]	李宗峰, 刘端程, 周宗权, 李传锋. 基于EuCl₃·6H₂O晶体的光存储. 物理学报, 2021, 70(16): 160302. doi: 10.7498/aps.70.20210648
[11]	石韬, 吕丽花, 李有泉. 量子中继过程中纠缠态的选择. 物理学报, 2021, 70(23): 230303. doi: 10.7498/aps.70.20211211
[12]	史保森, 丁冬生, 张伟, 李恩泽. 基于拉曼协议的量子存储. 物理学报, 2019, 68(3): 034203. doi: 10.7498/aps.68.20182215
[13]	窦建鹏, 李航, 庞晓玲, 张超妮, 杨天怀, 金贤敏. 量子存储研究进展. 物理学报, 2019, 68(3): 030307. doi: 10.7498/aps.68.20190039
[14]	汪野, 张静宁, 金奇奂. 相干时间超过10 min的单离子量子比特. 物理学报, 2019, 68(3): 030306. doi: 10.7498/aps.68.20181729
[15]	杨天书, 周宗权, 李传锋, 郭光灿. 多模式固态量子存储. 物理学报, 2019, 68(3): 030303. doi: 10.7498/aps.68.20182207
[16]	安子烨, 王旭杰, 苑震生, 包小辉, 潘建伟. 冷原子系综内单集体激发态的相干操纵. 物理学报, 2018, 67(22): 224203. doi: 10.7498/aps.67.20181183
[17]	邓瑞婕, 闫智辉, 贾晓军. 基于电磁诱导透明机制的压缩光场量子存储. 物理学报, 2017, 66(7): 074201. doi: 10.7498/aps.66.074201
[18]	孙颖, 赵尚弘, 东晨. 基于量子存储的长距离测量设备无关量子密钥分配研究. 物理学报, 2015, 64(14): 140304. doi: 10.7498/aps.64.140304
[19]	唐霖, 黄建华, 段正路, 张卫平, 周兆英, 冯焱颖, 朱荣. 冷原子穿越激光束的量子隧穿时间. 物理学报, 2006, 55(12): 6606-6611. doi: 10.7498/aps.55.6606
[20]	罗有华, 黄整, 王育竹. 冷原子在静电势阱中的量子力学效应. 物理学报, 2002, 51(8): 1706-1710. doi: 10.7498/aps.51.1706

计量

文章访问数: 4587
PDF下载量: 173

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板