Research progress of quantum coherence performance and applications of micro/nano scale rare-earth doped crystals

Guo Mu-Cheng; Wang Fu-Dong; Hu Zhao-Gao; Ren Miao-Miao; Sun Wei-Ye; Xiao Wan-Ting; Liu Shu-Ping; Zhong Man-Jin

doi:10.7498/aps.72.20222166

Abstract

Rare-earth ion doped crystals possess stable solid state physicochemical properties and long optical coherence time and spin coherence time, thus showing important development prospect in quantum information science and technology area. Investigations on macroscopic bulk rare-earth single crystals have obtained many promising results, especially in the field of optical quantum memory. With the rapid development of quantum information science, a variety of new functions or multifunctional integrations are found in rare earth crystal systems, such as on chip quantum storage, microwave to optical frequency conversion, scalable quantum single photon sources, and quantum logic gates. As a result, beyond the macroscopic bulk rare-earth single crystals, micro/nano-scale rare-earth crystals have received much attention in recent years and they are regarded as promising candidates in highly integrated hybrid quantum systems and miniaturized quantum devices. Moreover, wet chemical method synthesized micro/nano-scale rare-earth crystals have lower growth difficulty and more flexible manipulation in volume, shape and composition. Therefore, exploring high-performance micro/nano-scale rare-earth crystals and precisely manipulating their quantum states have become one of the important directions in today’s quantum information science and technology research. In this review, we first briefly introduce the basic concepts and high resolution spectroscopic techniques that are commonly used in rare earth ion doped crystals for quantum information science and technologies, such as hole burning technique and photon echo technique. Then we summarize comprehensively recent research status and development trends of rare earth ion doped polycrystalline nanoparticles, thin films, single crystal based micro systems, and some other micro/nano-scale rare earth platforms in terms of material fabrication, quantum coherence property, dephasing mechanisms, and also quantum device explorations. The latest research advances in quantum information applications such as quantum storage, quantum frequency conversion, quantum single photon sources and quantum logic gates are given. Finally, we discuss the possible optimization directions and strategies to improve the component design, material synthesis and quantum performance of micro/nano-scale rare earth crystals and their related quantum devices. This review highlights that the micro/nano-scale rare earth crystals may offer many new possibilities for designing quantum light-matter interfaces, thus are promising quantum systems to develop scalable and integrated quantum devices in the future.

Keywords:

Authors and contacts

1.
Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
2.
Shenzhen International Quantum Academy (SIQA), Shenzhen 518048, China
3.
Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China

Corresponding author: Liu Shu-Ping, liusp@sustech.edu.cn ; Zhong Man-Jin, Zhongmj@sustech.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11904159, 12004168), the Basic and Applied Basic Research Foundation of Guangdong Province, China (Grant No. 2021A1515110191), the “Pearl River Talent Plan” Innovative and Entrepreneurial Research Team Program of Guangdong Province, China (Grant No. 2019ZT08X324), and the Guangdong Provincial Key Laboratory of Quantum Science and Engineering, China (Grant No. 2019B121203002)

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图 1 量子网络技术与固态稀土量子系统研究平台^[59]　 (a)要实现鲁棒性和可扩展的量子网络, 每个小规模局域网络中的量子网络节点均需要装备一整套的高性能量子软硬件设备, 包括用于产生纠缠的量子单光子源、用于网络同步的量子存储器和中继站、用于连接不同量子物理系统(如光波和微波)的量子转换器(适配器), 以及用于处理量子信息和执行纠错操作的量子计算机等; (b)固态稀土离子系统具有丰富且高度相干的4f-4f光学跃迁和自旋跃迁, 是发展上述量子网络中各种关键量子硬件设备的主要物理系统之一; (c) 稀土离子掺杂晶体发展的多条路径, 将目前固态稀土量子系统的研究工作转化为大规模复杂量子网络中可操控部署的技术, 依赖于对材料局限性更深入的理解以及微纳尺度稀土晶体材料制备和合成等方面新的突破

Figure 1. Enabling technologies for quantum networks and rare earth doped crystal platforms^[59]: (a) To realize robust and scalable quantum networks, each network node in small-scale local networks will need to incorporate a suite of quantum technologies. Essential devices include sources of entanglement, quantum memories for network synchronization and repeater stations, converters and transducers to act as adapters for quantum technologies operating in different physical regimes (e.g. microwave and optical), and quantum computers to process information and perform error correction operations. (b) Rare-earth ion crystals possess abundant and highly coherent 4f-4f optical transitions and spin transitions, thus are among the leading material systems to realize the varied devices that are critical to quantum network operation. (c) Multiple avenues for rare earth doped crystal development. Translating current work into deployable technologies in large, complex networks will be accelerated by a deeper understanding of material limitations and new breakthroughs in nanoscale rare earth based material synthesis and fabrication

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图 2 稀土离子掺杂晶体的非均匀线宽($\varGamma_{\mathrm{inh}}$)和均匀线宽($\varGamma_{\mathrm{h}}$)示意图. 晶格中的单个稀土离子只对非常窄的频率范围内的光有共振吸收($\varGamma_{\mathrm{h}}$), 但由于局域环境的不同, 不同位置处稀土离子吸收的频率略有不同, 整体表现为展宽更大的非均匀线宽($\varGamma_{\mathrm{inh}}$)

Figure 2. Inhomogeneous broadening ($\varGamma_{\mathrm{inh}}$) and homogeneous broadening ($\varGamma_{\mathrm{h}}$) of rare earth doped crystals. Single rare earth ion in the lattice has a sharp absorption peak ($\varGamma_{\mathrm{h}}$). Due to the different local environment, rare earth ions at different locations have different absorption frequency. The inhomogeneous absorption profile of an ensemble of ions is the sum of the homogeneous profile of the different individual ions ($\varGamma_{\mathrm{inh}}$)

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图 3 光谱烧孔原理示意图　(a)三种超精细基态能级被均匀占据, 频率为$\omega_{\mathrm{0}}$的激光将中间态离子泵浦到激发态, 被激发的离子可以衰减到任何一种超精细基态, 但重新回到中间态的离子会再次被激光激发, 使得离子都被转移到另外两种超精细基态; (b) 在非均匀展宽上的烧“孔”

Figure 3. Schematic representation of holeburning technique: (a) All three hyperfine ground states are equally populated until a laser with frequency $\omega_{\mathrm{0}}$ pumps the ions in the middle state to a optically excited state. The excited ions can decay to any of the hyperfine ground states, but only those that decay to the middle state will be repumped by the laser. All ions are transferred to the other two hyperfine ground states. (b) A spectral “hole” is burned in the inhomogeneous profile

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图 4 (a)双脉冲回波和(b)三脉冲回波分别对应的脉冲序列及对应的离子态在布洛赫球上的演化

Figure 4. Evolution of ion states on the Bloch sphere and corresponding pulse sequence for (a) two pulse echo and (b) three pulse echo respectively

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图 5 (a)化学刻蚀前后$\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$纳米粉体的光学回波信号衰减曲线. 内附图为对应的纳米粉体的TEM形貌^[81]; (b)$\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$纳米粉体在初次800 ℃煅烧(上左), 二次1200 ℃煅烧(上右)并微波等离子体处理后(下)的TEM形貌^[82]; (c) $\mathrm{Eu}^{3+}$离子$\mathrm{^5 D_{0}}$-$^7\mathrm{F}_{0}$跃迁在不同制备条件下的光学相干时间T₂和非均匀线宽$\varGamma_{\mathrm{inh}}$. 样品在0处的光学跃迁频率为(516.0979 ± 0.0002) THz ((580.8830 ± 0.0001) nm)^[82]

Figure 5. (a) Photon echo decays for initial and etched nanoparticles. The insets are corresponding TEM images^[81]. (b) TEM structural and morphological evolution of the nanoparticles for annealing at 800 ℃ (top-left), a second annealing at 1200 ℃ with microwave excitation power (top-right, lower), respectively^[82]. (c) Coherence time $T_{2}$ and inhomogeneous linewidth $\varGamma_{\mathrm{inh}}$ of $\mathrm{Eu}^{3+}$ ion $^5\mathrm{D}_{0}$-$^7\mathrm{F}_{0}$ transition under different preparation conditions. The optical transition frequency at 0 is (516.0979 ± 0.0002) THz ((580.8830 ± 0.0001) nm)^[82]

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图 6 $\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$纳米粉体的均匀线宽随温度的变化. 黑色、灰色和浅灰色区域分别表示双声子拉曼效应(TPR)、局域无序二能级系统(TSL)以及与温度无关的光谱展宽的贡献. 在主图和插图中, 阴影区域都代表了与温度无关的展宽(最浅)、TLS相互作用展宽和TPR相互作用展宽(最暗)^[92]

Figure 6. Temperature dependence of the homogeneous line width of $\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$ nanoparticles. The black, gray and light-gray regions represent the contribution of two-phonon Raman (TPR) interactions, local disordered two-level system (TSL) interactions and the temperature independent broadening, respectively. In both the main figure and inset the shaded areas represent the temperature independent broadening (lightest), TLS interaction broadening and TPR interaction broadening (darkest)^[92]

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图 7 (a)基于$\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$纳米粉体的SEMM量子存储装置示意图^[97]; (b)存储脉冲序列及输出脉冲幅值随存储时间的函数关系^[97]; (c) $\mathrm{Er}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$纳米粉体与可调谐F-P光学微腔的耦合示意图^[84]; (d) $\mathrm{Er}^{3+}$离子经历的Purcell增强效应, 其中约50%的离子经历大于15的Purcell效应, 至少10%的离子经历大于72的Purcell增强, 腔长度通过施加移动光纤的电压偏移V来控制^[84]

Figure 7. (a) Scheme of SEMM memory based on $\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$ nanoparticles^[97]; (b) storage pulse sequence and output pulse amplitude as a function of the total storage time^[97]; (c) scheme of the tunable fiber-based microcavity with $\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$ nanoparticles^[84]; (d) estimated probability of given ions decay with Purcell factor, which 50% of the ions experience a Purcell factor larger than 15 and 10% larger than 72. The cavity length is controlled by applying a voltage offset V that moves the fiber^[84]

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图 8 (a)退火工艺对$\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$薄膜组分的影响示意图; (b)薄膜组分设计和结构优化(未掺杂底部缓冲层和顶部覆盖层对$\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$进行封装); (c)不同后处理工艺对薄膜非均匀线宽和峰位的影响, 其中N.A.表示未退火处理, STA表示慢速退火处理, RTA表示快速退火处理; (d)制备得到的未后处理较厚$\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$薄膜(样品D)的最窄非均匀线宽; (e)经过1100℃-Ar气氛和600℃-${\rm{O}}_{\mathrm{2}}$气氛两步退火后样品D的光谱烧孔测试, 得到3 K温度下孔的宽度为10 MHz, 即$\mathrm{Eu}^{3+}$的均匀线宽窄至5 MHz^[102]

Figure 8. (a) Effect of annealing for a single $\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$ thin film. (b) Composition design and structure optimization of thin film (Encapsulation of $\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$ by undoped buffer and cap layers). (c) Inhomogeneous linewidth and position for different post-treatments. N.A. stands for not annealed (in green/empty symbol); STA, slow thermal annealing (in blue/filled symbol); RTA, rapid thermal annealing (in orange, half-filled symbols). (d) Inhomogeneous linewidth of the as grown thick film (sample D) revealing the lowest broadening; (e) SHB measurements of a 2 mm-thick multilayer sample (labelled D) with 2-step annealing. The hole width of 10 MHz at 3 K, i.e. the homogeneous broadening narrowed to 5 MHz^[102]

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图 9 (a) $\mathrm{Er}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$-Si光子晶体腔结构示意图以及离子腔耦合协作性和纠缠保真度随腔质量因子的变化^[103]; (b)$\mathrm{Er}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$-石墨烯杂化系统的动态调制示意图^[104]

Figure 9. (a) Schematic of $\mathrm{Er}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$-Si photonic crystal cavity and the ion-cavity coupling cooperativity and entanglement fidelity as a function of cavity quality factor^[103]; (b) concept of dynamic modulation of hybrid $\mathrm{Er}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$-graphene system^[104]

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图 10 基于腔增强的稀土离子单晶微纳系统　(a)稀土离子光子晶体腔^[85]; (b)一维硅光子晶体腔^[72]; (c) F-P腔^[106]; (d)微环腔或回音壁模式(WGM)腔^[107]

Figure 10. Cavity enhanced nanoscale rare earth doped systems: (a) Rare earth ions based photonic crystal cavity^[85]; (b) one-dimensional silicon photonic crystal cavity^[72]; (c) F-P cavity^[106]; (d) microring or whispering gallery modes (WGM) cavity^[107]

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图 11 (a)腔保护的概念说明: 对于具有洛伦兹线性的系综(上), 由于非均匀展宽的Δ, 极化不受保护并发生退相, 即线宽展宽. 而具有高斯线性的系综(下)可以被集体超辐射激发并保护, 不受退相影响. 图中箭头表示每个离子偶极子矢量^[86]. (b)观察到一个不随等待时间$T_{\mathrm{w}}$变化的有效线宽$\varGamma_{\mathrm{eff}}$^[110]. 插图为三脉冲光子回波序列. (c)基于$\mathrm{Er}^{3+}:\mathrm{YSO}$光子晶体腔的片上多模量子存储, (I)存储10个时间多模式2μs; (II)通过双梳过程获得的可见度, 插图为在最大建设性干扰(虚线黑线)和最大破坏性干扰(实红色线)情况下的4个输出脉冲(中间两个重叠)^[87]. (d)激发脉冲后, 单个腔耦合$\mathrm{Er}^{3+}$离子(蓝色)与没有腔增强的荧光寿命比较(橙色)^[72]. (e)在纳米光子腔中进行光学耦合的$^{171}\mathrm{Yb}$量子位元的多体核自旋寄存器示意图^[111]

Figure 11. (a) Conceptual illustration of cavity protection for an ensemble coupled to a cavity mode: For a Lorentzian ensemble (upper), the polaritons are not protected and undergo dephasing (linewidth broadening) due to inhomogeneous broadening Δ. A Gaussian ensemble (lower) can be fully protected with the collective superradiant excitation free of such dephasing. Arrows represent the phasor of each atomic dipole^[86]. (b) A constant effective linewidth $\varGamma_{\mathrm{eff}}$ independent of the waiting time $T_{\mathrm{w}}$ has been observed^[110]. Inset: Three-pulse photon echo sequence. (c) On-chip multimode and coherent storage in the $\mathrm{Er}^{3+}:\mathrm{YSO}$ nanophotonic cavity. (I) Storage of ten temporal modes for 10 μs; (II) visbility curve acquired in a double-comb experiment, and inset is four output pulses (middle two overlapping) in the case of maximally constructive (dashed black line) and maximally destructive (solid red line) interferenc^[87]. (d) Fluorescent lifetime comparison between a single cavity-coupled $\mathrm{Er}^{3+}$ ion (blue) and a bulk ensemble without cavity enhancement (orange)^[72]. (e) Schematic of a many-body nuclear spin register for optically coupled $^{171}\mathrm{Yb}$ qubits in a nanophotonic cavity^[111]

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