浓度依赖的掺铕硅酸钇晶体的光学和自旋非均匀展宽

梁澎军; 朱天翔; 肖懿鑫; 王奕洋; 韩永建; 周宗权; 李传锋

doi:10.7498/aps.73.20240116

摘要

Abstract

作者及机构信息

Authors and contacts

文章全文

1. 引　言
2. 实验内容
2.1 样品准备
2.2 实验装置和测试过程
3. 实验结果与分析
4. 结　论

参考文献

摘要

可移动量子存储器是实现长距离量子通信的一种可行方案, 该方案需要量子存储介质拥有小时量级的存储寿命. 同位素提纯¹⁵¹Eu³⁺:Y₂SiO₅晶体是实现这一应用的重要候选材料, 但其较宽的非均匀展宽对其光存储效率和自旋存储寿命都构成了显著限制. 本文自主生长了不同掺杂浓度的同位素提纯¹⁵¹Eu³⁺:Y₂SiO₅晶体, 讨论了影响非均匀展宽的机制和未来进一步控制非均匀展宽的方法, 为超长寿命可移动量子存储器的实现奠定了基础.

关键词:

Abstract

The transportable quantum memory is a feasible solution for realizing the long-distance quantum communication, which requires a storage lifetime of the order of hours. The isotope-enriched ¹⁵¹Eu³⁺:Y₂SiO₅ crystal is a promising candidate for this application. However, its optical storage efficiency and spin storage lifetime are limited by the wide inhomogeneous linewidth. In this work, we successfully grow isotope-enriched ¹⁵¹Eu³⁺:Y₂SiO₅ crystals with varying doping concentrations by utilizing the Czochralski method. The optical inhomogeneous broadening and spin inhomogeneous broadening are measured by the optical absorption spectroscopy and optically detected magnetic resonance tests, respectively. Notably, in the undoped samples, we identify a baseline level of inhomogeneous linewidths, happening at (390 ± 15) MHz for optical inhomogeneous broadening and (4.6 ± 0.2) kHz for spin inhomogeneous broadening. Our findings reveal that the point defects, induced by the doping ions, significantly contribute to the inhomogeneous broadening. For every increase of 10^–6 in doping concentration, the optical inhomogeneous broadening increases by 0.97 MHz, and the spin inhomogeneous broadening increases by 0.014 kHz. Furthermore, we discuss the influence of dislocations on inhomogeneous broadening and propose potential strategies to further mitigate these effects. These advancements are expected to promote the development of ultra-long-lifetime transportable quantum memory applications.

Keywords:

PACS:

81.15.Gh	(Chemical vapor deposition (including plasma-enhanced CVD, MOCVD, ALD, etc.))
85.60.Gz	(Photodetectors (including infrared and CCD detectors))
81.07.-b	(Nanoscale materials and structures: fabrication and characterization)

作者及机构信息

1.
中国科学技术大学, 中国科学院量子信息重点实验室, 合肥　230026

2.
合肥国家实验室, 合肥　230088

通信作者: 周宗权, zq_zhou@ustc.edu.cn ; 李传锋, cfli@ustc.edu.cn

基金项目: 国家重点研发计划(批准号: 2017YFA0304100)、科技创新2030——“量子通信与量子计算机”重大项目(批准号: 2021ZD0301200)和国家自然科学基金(批准号: 12222411, 11821404)资助的课题.

Authors and contacts

1.
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China

2.
Hefei National Laboratory, Hefei 230088, China

Corresponding author: Zhou Zong-Quan, zq_zhou@ustc.edu.cn ; Li Chuan-Feng, cfli@ustc.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2017YFA0304100), the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0301200), and the National Natural Science Foundation of China (Grant Nos. 12222411, 11821404).

文章全文

1. 引　言

光子是长程量子通信便捷且可靠的物理载体^[1]. 然而, 光子在光纤中的传输面临一个重大挑战: 信号随传输距离指数衰减, 这直接限制了两个节点之间进行量子通信的有效距离^[2,3]. 量子中继方案可以将信号随距离的衰减转变为多项式关系^[2], 而可移动量子存储器方案和卫星量子通信方案则避免了光纤的使用^[4-6]. 量子存储器是实现这些应用的核心器件^[3-7]. 目前, 实现量子存储的系统主要有单原子^[8-12]、冷原子系综^[13-17]、热原子系综^[18-22]和稀土掺杂晶体^[5,23-36]等体系. 作为一种固态系统, 稀土掺杂晶体展现了高保真度^[25]、长寿命^[4,5,30]、多模式^[27,28]、可集成^[36-38]等优势.

考虑到现实交通运输工具的速度, 可移动量子存储器需要有小时量级的存储寿命^[4,5]. 在众多稀土掺杂晶体中, Eu³⁺:Y₂SiO₅晶体因具有长自旋和光学相干寿命而备受关注^[4,39,40]. 目前Eu³⁺:Y₂SiO₅晶体已实现6 h自旋相干寿命^[4]和1 h的相干光存储^[5]以及20 ms的单光子存储^[30]. 长寿命量子存储的实现, 需要使用自旋波存储协议, 并结合零一阶塞曼效应(ZEFOZ)技术和动力学解耦(DD)技术^[4,5]. 由于晶体的非均匀性, Y₂SiO₅晶体中不同位置的Eu³⁺对应的ZEFOZ特征点会有差别, 这限制了ZEFOZ技术对自旋相干寿命的有效延长^[4,41]. 此外, 在DD技术中, 过大的自旋非均匀展宽导致 $\pi$ 脉冲的保真度下降, 也会降低存储效率^[5]. 综上所述, 减小晶体非均匀性是实现超长寿命量子存储器的关键需求之一. 在晶体中, 控制掺杂浓度是一种有效的调控晶体非均匀性的方法, 其主要机制是控制晶体中掺杂缺陷引起的不均匀应力^[40,42].

因此, 本文在相同条件下生长了掺杂浓度为0—10^–3的同位素提纯¹⁵¹Eu³⁺:Y₂SiO₅晶体, 探测了这些样品的光学吸收谱和自旋跃迁谱, 测定了其光学和自旋非均匀展宽, 分析了非均匀展宽对掺杂浓度和位错的依赖性, 并基于实验数据探讨了进一步减小晶体非均匀展宽的可能方法.

2. 实验内容

2.1 样品准备

利用提拉法在相同的生长条件下生长了不同掺杂浓度的同位素提纯的¹⁵¹Eu³⁺:Y₂SiO₅单晶. 所有单晶的生长均采用了纯度为99.9999%的Y₂O₃和SiO₂为原料. 同时, 使用了同位素提纯且纯度大于99.8%的 $^{151}{\rm{Eu}}_2{\rm{O}}_3$ 粉末作为掺杂原料. 生长出的晶体粗胚如图1(c)所示: 晶体的放肩长度为25 mm, 等径长度为75 mm, 等径直径为30 mm. 待测样品选取自与籽晶尾端相距45—55 mm的晶体的中心区域. ¹⁵¹Eu³⁺掺杂浓度分别为0, 3×10^–5,10^–4, 3×10^–4, 7×10^–4, 10^–3. 通过辉光放电质谱测试(GDMS), 确认了掺杂浓度为0的Y₂SiO₅单晶中Eu³⁺的背景浓度低于10^–7. 在实验开始之前, 先确认了取样位置掺杂浓度与初始物料掺杂浓度的比例关系. 向280 g Y₂SiO₅原料中掺入了30 mg $^{151}{\rm{Eu}}_2{\rm{O}}_3$ , 随后提拉生长出了一只单晶. 之后, 在与被测样品相同的位置取样. 样品经过粉碎后, 通过电感耦合等离子体原子发射光谱(ICP-OES)对其浓度进行了测试. 测试结果显示, 该位置浓度为(72.04 ± 2.98) ×10^–6, 这表明实际掺杂浓度与初始物料浓度的比率为0.672 ± 0.028. 由于晶体中的掺杂离子浓度分布由有效分凝系数决定, 且该系数在相同生长条件下保持不变, 因此本文按照0.672 ± 0.028的比率配置了所有晶体的初始物料.

$图 1 (a) Y2SiO5中替位1处的$ {{^{151}{\rm{Eu}}^{3+}}} $在磁场为0时7F0$ \rightarrow $5D0跃迁能级图. f0 = 516.8472 THz, f1 = f0 + 34.5 MHz, f2 = f0 – 20.9 MHz. (b)测试$ { |{\pm1/2}\rangle_{\mathrm{g}}\rightarrow|{\pm3/2}\rangle_{\mathrm{g}}} $自旋跃迁谱的脉冲时序. 准备阶段包括类清理和自旋极化过程, 脉冲频率与图(a)中的相同颜色箭头对应, 准备阶段所有脉冲都是时间宽度为1 ms, 扫频宽度为4 MHz的啁啾脉冲. 在准备阶段结束10 ms之后, 线圈产生一个时间宽度为1 ms的RF高斯脉冲. RF脉冲结束10 µs后, 一个啁啾型泵浦光脉冲被施加到样品上, 其时间宽度为1 ms, 扫频宽度为3.8 MHz. 泵浦光脉冲结束10 µs后, 光开关门被打开, 为单光子探测器提供一个2 ms的探测时间窗口. (c) Y2SiO5晶碇, 样品取自蓝框区域的晶体中心位置\r\nFig. 1. (a) Level structure of 7F0$ \rightarrow $5D0 transition for the $ {{^{151}{\rm{Eu}}^{3+}}} $ at site 1 in the Y2SiO5 under a zero magnetic field. f0 = 516.8472 THz, f1 = f0 + 34.5 MHz, f2 = f0 – 20.9 MHz. (b) Pulse sequence measuring the spin transition $ {|{\pm1/2}\rangle_{\mathrm{g}}\rightarrow|{\pm3/2}\rangle_{\mathrm{g}} } $. The preparation includes the process of class cleaning and polarization. The frequency of these pulses is corresponding to the frequency of the arrows of the same color in Fig (a). Every pulse during the preparation is a chirp pulse with a duration of 1 ms and a bandwidth of 4 MHz. A Gaussian pulse, with a duration of 1 ms, is generated by the Coil 10 ms later after the end of preparation. A chirp pulse, with a duration of 1 ms and a bandwidth of 3.8 MHz, is applied to the sample 10 µs later after the RF pulses. The gate is turned on, 10 µs later after the pumping pulse, to provide a 2 ms detection window for the single photon detector. (c) Y2SiO5 boule, and the sample is taken from the center of the crystal in the blue rectangular area.$

图 1 (a) Y₂SiO₅中替位1处的

${{^{151}{\rm{Eu}}^{3+}}}$

在磁场为0时⁷F₀

$\rightarrow$

⁵D₀跃迁能级图. f₀ = 516.8472 THz, f₁ = f₀ + 34.5 MHz, f₂ = f₀ – 20.9 MHz. (b)测试

${ |{\pm1/2}\rangle_{\mathrm{g}}\rightarrow|{\pm3/2}\rangle_{\mathrm{g}}}$

自旋跃迁谱的脉冲时序. 准备阶段包括类清理和自旋极化过程, 脉冲频率与图(a)中的相同颜色箭头对应, 准备阶段所有脉冲都是时间宽度为1 ms, 扫频宽度为4 MHz的啁啾脉冲. 在准备阶段结束10 ms之后, 线圈产生一个时间宽度为1 ms的RF高斯脉冲. RF脉冲结束10 µs后, 一个啁啾型泵浦光脉冲被施加到样品上, 其时间宽度为1 ms, 扫频宽度为3.8 MHz. 泵浦光脉冲结束10 µs后, 光开关门被打开, 为单光子探测器提供一个2 ms的探测时间窗口. (c) Y₂SiO₅晶碇, 样品取自蓝框区域的晶体中心位置

Fig. 1. (a) Level structure of ⁷F₀

$\rightarrow$

⁵D₀ transition for the

${{^{151}{\rm{Eu}}^{3+}}}$

at site 1 in the Y₂SiO₅ under a zero magnetic field. f₀ = 516.8472 THz, f₁ = f₀ + 34.5 MHz, f₂ = f₀ – 20.9 MHz. (b) Pulse sequence measuring the spin transition

${|{\pm1/2}\rangle_{\mathrm{g}}\rightarrow|{\pm3/2}\rangle_{\mathrm{g}} }$

. The preparation includes the process of class cleaning and polarization. The frequency of these pulses is corresponding to the frequency of the arrows of the same color in Fig (a). Every pulse during the preparation is a chirp pulse with a duration of 1 ms and a bandwidth of 4 MHz. A Gaussian pulse, with a duration of 1 ms, is generated by the Coil 10 ms later after the end of preparation. A chirp pulse, with a duration of 1 ms and a bandwidth of 3.8 MHz, is applied to the sample 10 µs later after the RF pulses. The gate is turned on, 10 µs later after the pumping pulse, to provide a 2 ms detection window for the single photon detector. (c) Y₂SiO₅ boule, and the sample is taken from the center of the crystal in the blue rectangular area.

下载: 全尺寸图片幻灯片

Y₂SiO₅晶体结构属于单斜晶系, C ${ ^6_{2{\rm{h}}}}$ 空间群. ${ ^{151}{\rm{Eu}}^{3+}}$ 取代的Y³⁺在晶体中有两种不同的替位, 替位1和替位2的配位氧离子数分别是7和6^[43,44]. 本文关注的是替位1处的¹⁵¹Eu³⁺, 该处¹⁵¹Eu³⁺与光相互作用更强^[40]. ${ {\rm{Y}}_2{\rm{SiO}}_5}$ 晶体是双折射晶体, 其主轴方向为b, D1, D2^[40]. 样品沿主轴方向D1, D2, b切割, D1D2平面光学抛光. 所有样品在D1和D2方向的尺寸分别为5 mm和4 mm. 为了减少掺杂浓度为10^–3样品在b轴方向由于过强吸收对测试带来的影响, 将其长度取为5 mm, 其他样品长度均保持在10 mm左右.

2.2 实验装置和测试过程

实验装置如图2所示, 激光源是二倍频半导体激光器(Toptica, TA-SHG), 产生580 nm激光. 激光被法布里-珀罗腔锁频在516.8476 THz位置, 线宽在0.3 kHz左右. 二次通过的声光调制器将输入光场频率调节到516.8472 THz附近, 起到调节输入光频率和强度的作用. 两个单通声光调制器组成光开关门, 以保护单光子探测器. 这些声光调制器均由任意波形发生器(AWG)驱动. 样品晶体放在低温恒温器中. 样品周围缠绕7匝线圈. 线圈上的射频(RF)信号由AWG产生, 并经过增益为43 dB的高功率射频放大器放大.

$图 2 实验装置图. 580 nm激光(黄线)经过双次通过声光调制器(AOM)调制, 以控制其频率和强度. 调制后的激光脉冲通过低温恒温腔中的样品. 透过样品的激光通过光电探测器(PD)探测, 用于获得光学吸收谱. 同时, 样品在激光激发下的荧光(红线)经过偏振分束器(PBS)偏振滤波. 反向收集的荧光, 通过由两个声光调制器组成的光开关门, 进入单光子探测器(SPD). 线圈的激励射频信号由AWG产生, 并经射频放大器放大\r\nFig. 2. Diagram of experiment set-up. The 580 nm laser (yellow line) is modulated by a double-pass acousto-optic modulator (AOM) to control its frequency and intensity. The modulated laser pulse passes through the sample in a cryostat. The laser passing through the sample is detected by a photo detector (PD) to measure the absorption spectrum. At the same time, the fluorescence (red line) of the sample excited by the laser is filtered by a polarizing beam splitter (PBS). The fluorescence collected in the reverse direction enters a single-photon detector (SPD) through a gate consisting of two acousto-optic modulators. The radio-frequency excitation signal is generated by an AWG and amplified by a radio frequency amplifier.$

图 2 实验装置图. 580 nm激光(黄线)经过双次通过声光调制器(AOM)调制, 以控制其频率和强度. 调制后的激光脉冲通过低温恒温腔中的样品. 透过样品的激光通过光电探测器(PD)探测, 用于获得光学吸收谱. 同时, 样品在激光激发下的荧光(红线)经过偏振分束器(PBS)偏振滤波. 反向收集的荧光, 通过由两个声光调制器组成的光开关门, 进入单光子探测器(SPD). 线圈的激励射频信号由AWG产生, 并经射频放大器放大

Fig. 2. Diagram of experiment set-up. The 580 nm laser (yellow line) is modulated by a double-pass acousto-optic modulator (AOM) to control its frequency and intensity. The modulated laser pulse passes through the sample in a cryostat. The laser passing through the sample is detected by a photo detector (PD) to measure the absorption spectrum. At the same time, the fluorescence (red line) of the sample excited by the laser is filtered by a polarizing beam splitter (PBS). The fluorescence collected in the reverse direction enters a single-photon detector (SPD) through a gate consisting of two acousto-optic modulators. The radio-frequency excitation signal is generated by an AWG and amplified by a radio frequency amplifier.

下载: 全尺寸图片幻灯片

在执行 $^{151} { {\rm{Eu}}^{3+}}$ 的⁷F₀ $\rightarrow$ ⁵D₀跃迁光学吸收谱的测试时, 低温腔温度设置为18 K. 高斯型光脉冲偏振方向设为D1方向, 沿样品b轴通过, 脉冲周期为100 ms, 脉冲宽度为1 μs. 探测光通过样品后由光电探测器收集. 温度为18 K时, $^{151} { {\rm{Eu}}^{3+}}$ 的自旋弛豫时间为26 ms^[40], 在100 ms的探测周期下, 可以有效避免光谱烧孔带来的探测误差. 吸收系数 $\alpha = {\rm{e}}^{-{{I}}/{{I}}_0}/{{L}}$ , 其中I为透过光光强, ${ {{I}}_0}$ 为频率远失谐晶体基本无吸收时的透过光光强, L为晶体长度. 特别地, 对于零掺杂样品, 由于其吸收系数很小, 无法通过常规吸收测试得到结果, 本文使用荧光方法测试其非均匀展宽, 使用了600 nm长通滤波片, 主要探测从 $^5 {\mathrm{D}}_0$ 能级跃迁到 $^7 {\mathrm{F}}_2$ , $^7{\mathrm{ F}}_3$ , $^7 {\mathrm{F}}_4$ , $^7 {\mathrm{F}}_5$ 和 $^7 {\mathrm{F}}_6$ 能级的荧光.

$^{151} { {\rm{Eu}}^{3+}}$ 的基态 ${ |{\pm1/2}\rangle_{\rm{g}}\rightarrow|{\pm3/2}\rangle_{\rm{g}}}$ 自旋跃迁谱由光探测磁共振方法(ODMR)测试. 实验的时序如所示. 首先进行类清洗和自旋极化^[45], 从光学非均匀展宽中挑选出相应类离子, 并极化到基态 ${ |{\pm3/2}\rangle_{\rm{g}}}$ 能级上, 使 ${ |{\pm1/2}\rangle_{\rm{g}}}$ 能级烧出一个4 MHz的光学烧孔. 随后, 施加一个宽度为1 ms的高斯射频脉冲, 如果射频脉冲的频率在 ${ |{\pm1/2}\rangle_{\rm{g}}\rightarrow|{\pm3/2}\rangle_{\rm{g}}}$ 自旋跃迁的非均匀展宽内, 则会驱动 ${ |{\pm3/2}\rangle_{\rm{g}}}$ 能级上的离子跃迁到 ${ |{\pm1/2}\rangle_{\rm{g}}}$ 能级. 此时施加频率为f₀的泵浦光, 会将 ${ |{\pm1/2}\rangle_{\rm{g}}}$ 能级离子泵浦到激发态 ${ |\pm5/2 \rangle _{\rm{e}}}$ 能级. ${ |\pm5/2 \rangle _{\rm{e}}}$ 能级的离子之后会自发辐射荧光. 在打开光开关门后, 反向传播的荧光会被单光子探测器探测到.

3. 实验结果与分析

在掺杂晶体中, 非均匀展宽线型可以反映晶体中点缺陷和位错对非均匀展宽的贡献^[46]. 其中, 点缺陷产生洛伦兹线型, 而高斯线型主要来自于位错^[42]. 晶体的非均匀展宽线型可以通过洛伦兹函数和高斯函数的卷积来拟合, 如Voigt线型. 这里对数据进行了pseudo-Voigt拟合^[46]:

$V(\omega) = V_0+A[\mu L(\omega)+(1-\mu)G(\omega)],$

(1)

$L(\omega) = \frac{2}{\pi } \frac{\varGamma _{\rm{inh}} }{4(\omega -\omega _0)^2+\varGamma _{\rm{inh}}^2},$

(2)

$G(\omega) = \frac{\sqrt{4 \ln2} }{\sqrt{\pi }\varGamma _{\rm{inh}} } \exp \bigg[{-\dfrac{4 \ln 2}{\varGamma _{\rm{inh}}^2} (\omega -\omega _{0} )^2}\bigg],$

(3)

其中, $V(\omega)$ 为拟合结果函数, $V_0$ 为拟合本底, A为拟合曲线包络面积, $\omega$ 为频率, $\omega _{0}$ 为中心频率, $L(\omega)$ 和 $G(\omega)$ 分别是归一化的洛伦兹和高斯函数, µ为拟合时洛伦兹部分的权重, $\varGamma _{\rm{inh}}$ 为非均匀展宽. 以下用µ1表示光学非均匀展宽拟合的洛伦兹权重, µ2表示自旋非均匀展宽拟合的洛伦兹权重, $\varGamma _{ {\rm{opt}}-{\rm{inh}}}$ 表示光学非均匀展宽, $\varGamma _{\text{spin-inh}}$ 表示自旋非均匀展宽.

图3展示了¹⁵¹Eu³⁺:Y₂SiO₅中替位1处¹⁵¹Eu³⁺离子⁷F₀ $\rightarrow$ ⁵D₀跃迁光学吸收谱随浓度的变化关系. 样品的浓度高于10^–4时, 浓度每增加10^–6, 光学非均匀展宽增加0.97 MHz, 这可以反映点缺陷对展宽的贡献. 非同位素提纯样品中相应的增长率为2.1 MHz^[40], 这个值高于同位素提纯的样品. 这种增加的展宽可能源于同位素质量差异引起的跃迁频移(isotope shift)^[47,48]. 要对这一现象进行更加具体的解释, 需要做进一步的数值拟合验证. 浓度低于10^–4样品, 每增加10^–6浓度的展宽增长为2.89 MHz, 比0.97 MHz高出1.92 MHz. 这个1.92 MHz的贡献主要来源于位错, 在Y₂SiO₅生长过程中, 掺杂离子会引入局部点阵失常, 进而诱导了位错的增加, 这种位错和点缺陷共同导致了较高的展宽增长率. 然而, 当掺杂浓度超过一定值时, 掺杂离子本身开始对位错形成产生抑制作用, 使位错数量不再增加. 此时, 展宽增长率贡献主要来自于点缺陷. 这种掺杂对位错的抑制作用在半导体工业中已被广泛研究, 成为制备无位错少位错半导体的一种有效手段^[49]. 这一现象也可以从拟合时洛伦兹权重的变化分析得到. 表1中, 从零掺杂样品到掺杂浓度为3×10^–5样品位错的增加造成了洛伦兹权重µ1和µ2的减小. 随后, 随着浓度增加, 点缺陷贡献逐渐增大, 导致µ1和µ2逐渐增加.

$图 3 (a) Y2SiO5中替位1处不同掺杂浓度下Eu3+离子7F0$ \rightarrow $5D0跃迁光学吸收谱. (b) 零掺杂样品的7F0$ \rightarrow $5D0跃迁荧光激发谱, 黑色方块为数据点, 红色曲线是拟合曲线. (c) 151Eu3+:Y2SiO5光学非均匀展宽与掺杂浓度拟合图. $ [^{151} {\rm{Eu}} ^{3+}] $表示151Eu3+掺杂浓度. $ \varGamma_\text{{\rm{opt}}-{\rm{inh}}} $表示光学非均匀展宽. 黑色方块为数据点, 红色线和蓝色线分别是0—10–4和10–4—10–3的线性拟合. 拟合方程展示在图中, 并由箭头指向各自曲线\r\nFig. 3. (a) Optical absorption spectrum for the 7F0$ \rightarrow $5D0 transition of Eu3+ ions at site 1 in Y2SiO5 with variable doping concentrations. (b) Fluorescence excitation spectrum for the 7F0$ \rightarrow $5D0 transition of the 0 ppm sample, and the black squares represent the data points, red curve is the fitting curve. (c) Optical inhomogeneous linewidth fitted as a function of 151Eu3+ concentrations. $ [^{151} {\rm{Eu}} ^{3+}]$ is the concentration of 151Eu3+ ions. $ \varGamma_\text{{\rm{opt}}-{\rm{inh}}} $ is the optical inhomogeneous linewidth. Black squares stand for the data points. Red and blue lines represent linear fits of 0–10–4 and 10–4–10–3, respectively. The fitting equations are depicted in the graph, accompanied by arrows indicating their corresponding lines.$

图 3 (a) Y₂SiO₅中替位1处不同掺杂浓度下Eu³⁺离子⁷F₀

$\rightarrow$

⁵D₀跃迁光学吸收谱. (b) 零掺杂样品的⁷F₀

$\rightarrow$

⁵D₀跃迁荧光激发谱, 黑色方块为数据点, 红色曲线是拟合曲线. (c) ¹⁵¹Eu³⁺:Y₂SiO₅光学非均匀展宽与掺杂浓度拟合图.

$[^{151} {\rm{Eu}} ^{3+}]$

表示¹⁵¹Eu³⁺掺杂浓度.

$\varGamma_\text{{\rm{opt}}-{\rm{inh}}}$

表示光学非均匀展宽. 黑色方块为数据点, 红色线和蓝色线分别是0—10^–4和10^–4—10^–3的线性拟合. 拟合方程展示在图中, 并由箭头指向各自曲线

Fig. 3. (a) Optical absorption spectrum for the ⁷F₀

$\rightarrow$

⁵D₀ transition of Eu³⁺ ions at site 1 in Y₂SiO₅ with variable doping concentrations. (b) Fluorescence excitation spectrum for the ⁷F₀

$\rightarrow$

⁵D₀ transition of the 0 ppm sample, and the black squares represent the data points, red curve is the fitting curve. (c) Optical inhomogeneous linewidth fitted as a function of ¹⁵¹Eu³⁺ concentrations.

$[^{151} {\rm{Eu}} ^{3+}]$

is the concentration of ¹⁵¹Eu³⁺ ions.

$\varGamma_\text{{\rm{opt}}-{\rm{inh}}}$

is the optical inhomogeneous linewidth. Black squares stand for the data points. Red and blue lines represent linear fits of 0–10^–4and 10^–4–10^–3, respectively. The fitting equations are depicted in the graph, accompanied by arrows indicating their corresponding lines.

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表 1 Y₂SiO₅中同位素提纯¹⁵¹Eu³⁺中不同掺杂浓度下拟合结果参数表.

$[^{151} {\rm{Eu}} ^{3+}]$

表示¹⁵¹Eu³⁺掺杂浓度,

$\varGamma_{ {\rm{opt}}\text-{\rm{inh}}}$

表示光学非均匀展宽,

$\varGamma_{\text{spin-inh}}$

表示自旋非均匀展宽, µ1和µ2分别表示光学吸收谱和自旋跃迁谱pseudo-Voigt拟合洛伦兹部分的权重

Table 1. Parameter table of the fitting results for variable doping concentrations of isotope-enriched ¹⁵¹Eu³⁺ ions in the Y₂SiO₅.

$\varGamma_{ \text{opt-inh}}$

represents the optical inhomogeneous linewidth.

$\varGamma_{\text{spin-inh}}$

stands for the spin inhomogeneous linewidth. The weights µ1 and µ2 represent the contributions of the Lorentzian component in the pseudo-Voigt fitting, corresponding to the optical absorption and spin transition, respectively.

$[^{151} {\rm{Eu}} ^{3+}]$ /10^–6	$\varGamma_{\text{\rm opt-inh}}$ /MHz	$\varGamma_{\text{spin-inh}}$ /kHz	µ1	µ2
0	392 ± 15	4.6 ± 0.2	0.65 ± 0.18	0.69 ± 0.15
30	483 ± 15	5.3 ± 0.2	0.54 ± 0.13	0.47 ± 0.14
100	677 ± 8	7.0 ± 0.3	0.74 ± 0.04	0.64 ± 0.16
300	915 ± 9	10.4 ± 0.3	0.83 ± 0.03	0.74 ± 0.12
700	1319 ± 24	15.4 ± 0.4	1 ± 0.05	0.89 ± 0.09
1000	1561 ± 21	19.7 ± 0.2	1 ± 0.03	0.89 ± 0.03

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| 显示表格

图4展示了¹⁵¹Eu³⁺:Y₂SiO₅中Eu³⁺离子基态 ${ |{\pm1/2}\rangle_{\rm{g}}\rightarrow|{\pm3/2}\rangle_{\rm{g}}}$ 自旋跃迁谱随浓度的变化关系. 浓度高于10^–4时, 浓度每增加10^–6, 自旋非均匀展宽有一个0.014 kHz的增长. 浓度低于10^–4时, 该展宽增长为0.023 kHz, 其中位错的贡献为0.009 kHz.

$图 4 (a) Y2SiO5中不同掺杂浓度下151Eu3+离子基态$ { |{\pm1/2}\rangle_{\rm{g}}\rightarrow|{\pm3/2}\rangle_{\rm{g}}} $自旋跃迁谱. (b)自旋非均匀展宽随浓度变化的拟合曲线. $ [^{151} {\rm{Eu}} ^{3+}] $表示151Eu3+掺杂浓度. $ \varGamma_{\text{spin-inh}} $表示自旋非均匀展宽. 黑色方块是数据点, 红色和蓝色线分别是从0—10–4和10–4—10–3的线性拟合曲线. 图中各曲线给出了对应的拟合方程\r\nFig. 4. (a) Spin transition spectrum for the ground-state $ { |{\pm1/2}\rangle_{\rm{g}}\rightarrow|{\pm3/2}\rangle_{\rm{g}}} $ transition of 151Eu3+ ions in Y2SiO5 with variable doping concentrations. (b) Fitting curve of concentration-dependent variation in the spin inhomogeneous broadening. $ [^{151} {\rm{Eu}} ^{3+}] $ stands for the concentration of 151Eu3+ ions. $ \varGamma_{\text{spin-inh}} $ represents the spin inhomogeneous linewidth. Black squares are the data points, and the red and blue lines represent linear fits ranging from 0–10–4 and from 10–4–10–3, respectively. Fitted equations are illustrated for their respective lines in the graph.$

图 4 (a) Y₂SiO₅中不同掺杂浓度下¹⁵¹Eu³⁺离子基态

${ |{\pm1/2}\rangle_{\rm{g}}\rightarrow|{\pm3/2}\rangle_{\rm{g}}}$

自旋跃迁谱. (b)自旋非均匀展宽随浓度变化的拟合曲线.

$[^{151} {\rm{Eu}} ^{3+}]$

表示¹⁵¹Eu³⁺掺杂浓度.

$\varGamma_{\text{spin-inh}}$

表示自旋非均匀展宽. 黑色方块是数据点, 红色和蓝色线分别是从0—10^–4和10^–4—10^–3的线性拟合曲线. 图中各曲线给出了对应的拟合方程

Fig. 4. (a) Spin transition spectrum for the ground-state

${ |{\pm1/2}\rangle_{\rm{g}}\rightarrow|{\pm3/2}\rangle_{\rm{g}}}$

transition of ¹⁵¹Eu³⁺ ions in Y₂SiO₅ with variable doping concentrations. (b) Fitting curve of concentration-dependent variation in the spin inhomogeneous broadening.

$[^{151} {\rm{Eu}} ^{3+}]$

stands for the concentration of ¹⁵¹Eu³⁺ ions.

$\varGamma_{\text{spin-inh}}$

represents the spin inhomogeneous linewidth. Black squares are the data points, and the red and blue lines represent linear fits ranging from 0–10^–4 and from 10^–4–10^–3, respectively. Fitted equations are illustrated for their respective lines in the graph.

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本文测到的零掺杂晶体的光学非均匀展宽和自旋非均匀展宽分别是(390 ± 15) MHz和(4.6 ± 0.2) kHz. 根据之前的分析, 掺杂离子点缺陷对样品的光学非均匀展宽贡献为每增加10^–6的掺杂浓度, 展宽增长为0.97 MHz. 从表1得知, 掺杂浓度为10^–4的样品展现了677 MHz的光学非均匀展宽. 其中, 97 MHz的展宽归因于点缺陷. 剩余的580 MHz的展宽比零掺杂样品的390 MHz大出190 MHz. 这一额外的展宽主要源于位错. 通过改进晶体生长方法, 有望消除由位错引起的展宽, 使得掺杂浓度为10^–4的样品在去除掺杂离子点缺陷的影响后, 展宽接近390 MHz. 我们未来的研究将专注于消除由位错引起的额外展宽, 并进一步减少零掺杂样品的展宽.

4. 结　论

本文研究了相同生长条件下, 不同掺杂浓度的同位素提纯的¹⁵¹Eu³⁺:Y₂SiO₅的⁷F₀ $\rightarrow$ ⁵D₀光学跃迁吸收光谱和 ${ |{\pm1/2}\rangle_{\rm{g}}\rightarrow|{\pm3/2}\rangle_{\rm{g}}}$ 基态跃迁谱. 分析了晶体光学和自旋非均匀展宽的浓度依赖性. 通过分析发现, 除了掺杂离子本身的点缺陷外, 位错的增加是造成晶体展宽的重要因素. 进一步减小晶体非均匀展宽, 需要采取措施抑制位错, 这可以通过改变生长方向、优化生长界面、稳定生长环境等手段来实现^[49,50].

窄的自旋非均匀展宽可以使晶体获得更长的自旋相干寿命^[4,5,11], 可以提高DD技术脉冲作用效率以提高存储效率^[5], 另外还能通过降低上能级消相位速率提高无噪声光子回波(NLPE)方案的存储效率^[31,51]. 同时, 相同浓度下, 窄的光学展宽也可以提高有效的光学吸收深度, 实现光存储效率的增强. 目前, 我们在零掺杂样品中观察到了一个非均匀展宽的极限值. 基于这一极限值, 我们未来的研究将专注于两个主要目标: 首先, 在较高掺杂浓度条件下, 使展宽在去除点缺陷的贡献后逼近该极限值; 其次, 探索方法以进一步缩减这一非均匀展宽的极限.

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图 1 (a) Y₂SiO₅中替位1处的 ${{^{151}{\rm{Eu}}^{3+}}}$ 在磁场为0时⁷F₀ $\rightarrow$ ⁵D₀跃迁能级图. f₀ = 516.8472 THz, f₁ = f₀ + 34.5 MHz, f₂ = f₀ – 20.9 MHz. (b)测试 ${ |{\pm1/2}\rangle_{\mathrm{g}}\rightarrow|{\pm3/2}\rangle_{\mathrm{g}}}$ 自旋跃迁谱的脉冲时序. 准备阶段包括类清理和自旋极化过程, 脉冲频率与图(a)中的相同颜色箭头对应, 准备阶段所有脉冲都是时间宽度为1 ms, 扫频宽度为4 MHz的啁啾脉冲. 在准备阶段结束10 ms之后, 线圈产生一个时间宽度为1 ms的RF高斯脉冲. RF脉冲结束10 µs后, 一个啁啾型泵浦光脉冲被施加到样品上, 其时间宽度为1 ms, 扫频宽度为3.8 MHz. 泵浦光脉冲结束10 µs后, 光开关门被打开, 为单光子探测器提供一个2 ms的探测时间窗口. (c) Y₂SiO₅晶碇, 样品取自蓝框区域的晶体中心位置

Fig. 1. (a) Level structure of ⁷F₀ $\rightarrow$ ⁵D₀ transition for the ${{^{151}{\rm{Eu}}^{3+}}}$ at site 1 in the Y₂SiO₅ under a zero magnetic field. f₀ = 516.8472 THz, f₁ = f₀ + 34.5 MHz, f₂ = f₀ – 20.9 MHz. (b) Pulse sequence measuring the spin transition ${|{\pm1/2}\rangle_{\mathrm{g}}\rightarrow|{\pm3/2}\rangle_{\mathrm{g}} }$ . The preparation includes the process of class cleaning and polarization. The frequency of these pulses is corresponding to the frequency of the arrows of the same color in Fig (a). Every pulse during the preparation is a chirp pulse with a duration of 1 ms and a bandwidth of 4 MHz. A Gaussian pulse, with a duration of 1 ms, is generated by the Coil 10 ms later after the end of preparation. A chirp pulse, with a duration of 1 ms and a bandwidth of 3.8 MHz, is applied to the sample 10 µs later after the RF pulses. The gate is turned on, 10 µs later after the pumping pulse, to provide a 2 ms detection window for the single photon detector. (c) Y₂SiO₅ boule, and the sample is taken from the center of the crystal in the blue rectangular area.

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图 3 (a) Y₂SiO₅中替位1处不同掺杂浓度下Eu³⁺离子⁷F₀ $\rightarrow$ ⁵D₀跃迁光学吸收谱. (b) 零掺杂样品的⁷F₀ $\rightarrow$ ⁵D₀跃迁荧光激发谱, 黑色方块为数据点, 红色曲线是拟合曲线. (c) ¹⁵¹Eu³⁺:Y₂SiO₅光学非均匀展宽与掺杂浓度拟合图. $[^{151} {\rm{Eu}} ^{3+}]$ 表示¹⁵¹Eu³⁺掺杂浓度. $\varGamma_\text{{\rm{opt}}-{\rm{inh}}}$ 表示光学非均匀展宽. 黑色方块为数据点, 红色线和蓝色线分别是0—10^–4和10^–4—10^–3的线性拟合. 拟合方程展示在图中, 并由箭头指向各自曲线

Fig. 3. (a) Optical absorption spectrum for the ⁷F₀ $\rightarrow$ ⁵D₀ transition of Eu³⁺ ions at site 1 in Y₂SiO₅ with variable doping concentrations. (b) Fluorescence excitation spectrum for the ⁷F₀ $\rightarrow$ ⁵D₀ transition of the 0 ppm sample, and the black squares represent the data points, red curve is the fitting curve. (c) Optical inhomogeneous linewidth fitted as a function of ¹⁵¹Eu³⁺ concentrations. $[^{151} {\rm{Eu}} ^{3+}]$ is the concentration of ¹⁵¹Eu³⁺ ions. $\varGamma_\text{{\rm{opt}}-{\rm{inh}}}$ is the optical inhomogeneous linewidth. Black squares stand for the data points. Red and blue lines represent linear fits of 0–10^–4and 10^–4–10^–3, respectively. The fitting equations are depicted in the graph, accompanied by arrows indicating their corresponding lines.

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图 4 (a) Y₂SiO₅中不同掺杂浓度下¹⁵¹Eu³⁺离子基态 ${ |{\pm1/2}\rangle_{\rm{g}}\rightarrow|{\pm3/2}\rangle_{\rm{g}}}$ 自旋跃迁谱. (b)自旋非均匀展宽随浓度变化的拟合曲线. $[^{151} {\rm{Eu}} ^{3+}]$ 表示¹⁵¹Eu³⁺掺杂浓度. $\varGamma_{\text{spin-inh}}$ 表示自旋非均匀展宽. 黑色方块是数据点, 红色和蓝色线分别是从0—10^–4和10^–4—10^–3的线性拟合曲线. 图中各曲线给出了对应的拟合方程

(a) Spin transition spectrum for the ground-state ${ |{\pm1/2}\rangle_{\rm{g}}\rightarrow|{\pm3/2}\rangle_{\rm{g}}}$ transition of ¹⁵¹Eu³⁺ ions in Y₂SiO₅ with variable doping concentrations. (b) Fitting curve of concentration-dependent variation in the spin inhomogeneous broadening. $[^{151} {\rm{Eu}} ^{3+}]$ stands for the concentration of ¹⁵¹Eu³⁺ ions. $\varGamma_{\text{spin-inh}}$ represents the spin inhomogeneous linewidth. Black squares are the data points, and the red and blue lines represent linear fits ranging from 0–10^–4 and from 10^–4–10^–3, respectively. Fitted equations are illustrated for their respective lines in the graph.

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表 1 Y₂SiO₅中同位素提纯¹⁵¹Eu³⁺中不同掺杂浓度下拟合结果参数表. $[^{151} {\rm{Eu}} ^{3+}]$ 表示¹⁵¹Eu³⁺掺杂浓度, $\varGamma_{ {\rm{opt}}\text-{\rm{inh}}}$ 表示光学非均匀展宽, $\varGamma_{\text{spin-inh}}$ 表示自旋非均匀展宽, µ1和µ2分别表示光学吸收谱和自旋跃迁谱pseudo-Voigt拟合洛伦兹部分的权重

Table 1. Parameter table of the fitting results for variable doping concentrations of isotope-enriched ¹⁵¹Eu³⁺ ions in the Y₂SiO₅. $\varGamma_{ \text{opt-inh}}$ represents the optical inhomogeneous linewidth. $\varGamma_{\text{spin-inh}}$ stands for the spin inhomogeneous linewidth. The weights µ1 and µ2 represent the contributions of the Lorentzian component in the pseudo-Voigt fitting, corresponding to the optical absorption and spin transition, respectively.

$[^{151} {\rm{Eu}} ^{3+}]$ /10^–6	$\varGamma_{\text{\rm opt-inh}}$ /MHz	$\varGamma_{\text{spin-inh}}$ /kHz	µ1	µ2
0	392 ± 15	4.6 ± 0.2	0.65 ± 0.18	0.69 ± 0.15
30	483 ± 15	5.3 ± 0.2	0.54 ± 0.13	0.47 ± 0.14
100	677 ± 8	7.0 ± 0.3	0.74 ± 0.04	0.64 ± 0.16
300	915 ± 9	10.4 ± 0.3	0.83 ± 0.03	0.74 ± 0.12
700	1319 ± 24	15.4 ± 0.4	1 ± 0.05	0.89 ± 0.09
1000	1561 ± 21	19.7 ± 0.2	1 ± 0.03	0.89 ± 0.03

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浓度依赖的掺铕硅酸钇晶体的光学和自旋非均匀展宽