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量子存储是大尺度量子网络的重要组成部分, 基于波导等微纳结构的可集成量子存储可以提供更好的可扩展性并实现更低的光电能耗. 在众多量子存储候选介质中, 151Eu3+:Y2SiO5晶体具有长达6 h的自旋相干寿命和1 h的相干光存储时间, 成为长寿命存储的优异候选材料. 本文通过聚焦离子束在151Eu3+:Y2SiO5晶体表面加工出三角形悬梁臂波导, 波导截面的边长为2 µm, 长度为20 µm, 并对三角形悬梁臂波导中的151Eu3+离子的7F0—5D0光学跃迁以及7F0基态的超精细跃迁开展了研究. 结果显示, 在2 µm尺度的悬梁臂波导中151Eu3+离子基本保持了和块状晶体中151Eu3+离子一致的跃迁展宽及相干寿命, 可以支持量子存储任务的实现. 该工作为实现纳米尺度的151Eu3+离子可集成量子存储器以及单个151Eu3+离子的探测打下基础.Quantum memory is a crucial element in large-scale quantum networks. Integrated quantum memories based on micro-/-nano structures, such as waveguides, can significantly enhance the scalability and reduce the consumption of optical and electrical power. 151Eu3+:Y2SiO5 stands out as an exceptional candidate material for quantum memory, because it possesses a spin coherence lifetime of 6 h and an optical storage lifetime of 1 h. Here we employ focused ion beam technology to fabricate a triangular nanobeam on the surface of a Y2SiO5 crystal. The width and length of the nanobeam are 2 μm and 20 μm, respectively. The optical lifetime and inhomogeneous broadening of 151Eu3+ in the triangular nanobeam are measured by fluorescence spectroscopy. The optical lifetime is (1.9±0.1) ms and the optical inhomogeneous broadening is (1.58±0.05) GHz at a doping level of 0.07% for 151Eu3+. The hyperfine transition spectra are measured by using optically detected magnetic resonance and spin inhomogeneous broadening of (19±3) kHz is obtained. Furthermore, we analyze the coherence properties of optical and hyperfine transitions, respectively, via transient spectral hole burning and spin echo measurement. We obtain an optical homogeneous linewidth down to (22±3) kHz, which is still limited by the instantaneous spectral diffusion. The spin coherence lifetime under the geomagnetic field is (5.1±0.6) ms. The results demonstrate that 151Eu3+ ions embedded within the 2 μm triangular nanobeam essentially retain the same optical and hyperfine transition properties as those observed in bulk crystals. Consequently, this research lays a foundation for studying the integrated quantum memories based on 151Eu3+ ensembles and the detection of the single 151Eu3+ ion based on the focused ion beam technique.
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Keywords:
- rare-earth-doped crystal /
- quantum memory /
- focused ion beam /
- quantum information
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图 1 (a)浓度为0.07%的151Eu3+:Y2SiO5晶体经过聚焦离子束加工后的扫描电子显微镜图像, 在晶体D1×b面的俯视图中, 三角形悬梁臂波导的宽度沿D1轴为2 µm, 长度沿b轴为20 µm, 悬梁臂的输入输出端面为45°斜面. (b) Y2SiO5晶体中的site-1 151Eu3+离子在地磁场环境下的基态7F0和激发态5D0的超精细能级结构图
Fig. 1. (a) Scanning electron microscope (SEM) image of 151Eu3+:Y2SiO5 crystal (doping level: 0.07%) fabricated by focused ion beam milling. In the top view of the D1×b plane, the width (D1 axis) and length (b axis) of the triangular nanobeam structure are 2 µm and 20 µm, respectively. Two slopes at 45° relative to the surface of the crystal are milled at both ends of the triangular nanobeam. (b) Energy-level diagram for the ground state 7F0 and the excited state 5D0 of site-1 151Eu3+ ions in Y2SiO5 crystal at the geomagnetic field.
图 2 实验装置图. 黄色直线代表580 nm激光的路径, 蓝色曲线代表单模光纤, PBS是偏振分束器, BS是非偏振分束器, AOM是声光调制器, AWG是任意波形发生器, SPD是单光子探测器, $ \lambda/2 $是半波片. 激光通过调制光路再由单模光纤传输到耦合光路, 虚线方框以内的部分为笼式系统, 其中发散的白光源(diffuse source)经过BS2照射到晶体表面. 蓝色阴影区代表低温恒温器, 内部装有待测样品与亥姆霍兹线圈. 样品出射的信号光再一次经过笼式系统, 在BS1另一端通过狭缝(slit). 可以通过可翻转的反射镜(flip mirror)反射光场在相机上观察成像, 也可以通过AOM光开关后由SPD进行探测
Fig. 2. Experimental setup. The yellow line represents the transmission path for 580-nm laser and the blue curve represents a single-mode fiber. PBS, polarization beam splitter; BS, beam splitter; AOM, acousto-optic modulator; AWG, arbitrary waveform generator; SPD, single photon detector; $ \lambda/2 $ represents a half-wave plate. The 580-nm laser is modulated by AOMs and collected with a single-mode fiber. The cage system within the dotted box includes a diffuse source which is a white-light source to illuminate the crystal surface through BS2. The blue shadowed area indicates a cryostat with the sample and Helmholtz coils inside. The signal light emitted from the sample is transmitted through the cage system again and spatially filtered by a slit at the another side of BS1. If the flip mirror is turned on then the sample can be imaged on the camera, otherwise, the signal is detected by a SPD after being gated by a double-passed AOM.
图 3 (a) Y2SiO5悬梁臂波导中151Eu3+的7F0 $ \rightarrow $ 5D0跃迁荧光寿命图. 黑色圆点为数据点, 红色曲线是拟合的指数衰减曲线, 误差条表示为一个标准差, 本文中误差条均代表同一含义. (b) Y2SiO5悬梁臂波导中151Eu3+的7F0 $ \rightarrow $ 5D0跃迁荧光激发谱. 黑色圆点为数据点, 红色曲线是由(1)式拟合的pseudo-Voigt型曲线, 中心频率点代表516.8478 THz
Fig. 3. (a) Fluorescence decay for the 7F0 $ \rightarrow $ 5D0 transition of 151Eu3+ in the Y2SiO5 nanobeam. The black dots are the fluorescence data and the red curve is fitted by a single exponential decay. Error bars indicate one standard deviation with the same meaning in whole paper. (b) Fluorescence excitation spectrum for the 7F0 $ \rightarrow $ 5D0 transition of 151Eu3+ in the Y2SiO5 nanobeam. The black dots are fluorescence data, and the red curve is fitted by pseudo-Voigt function according to Eq.(1). The center frequency is 516.8478 THz.
图 4 (a)测试Y2SiO5悬梁臂波导中151Eu3+光学均匀线宽的脉冲时序图. 首先是准备阶段, 其目的是为了初始化布居数. 在准备阶段结束40 ms后, 同时输入三束功率和频率间隔一致且时间宽度0.15 ms的高斯单频激发光. 在10 µs后, 光开关打开一个2 ms的窗口用于测量荧光信号. (b)—(d) 220 nW (b), 440 nW (c)和660 nW (d)的激发光下, 荧光信号随激发光的频率间隔的变化曲线图. 不同颜色的曲线是拟合的洛伦兹曲线
Fig. 4. (a) Pulse sequence for measuring the optical homogeneous linewidth of 151Eu3+ in the Y2SiO5 nanobeam. Preparation process initializes the atomic population for each repeat of measurements. 40 ms after the preparation process, we apply the excitation pulses which are three Gaussian pulses with a duration of 0.15 ms with equal frequency spacing. 10 µs after the excitation, the detection gate opens for 2 ms to detect the fluorescence signal. (b)–(d) Fluorescence signal depending on the frequency spacing of excitation pulses, with excitation powers of 220 nW (b), 440 nW (c) and 660 nW (d). Solid lines are fitted in accordance with Lorentzian lineshape.
图 5 (a)测试Y2SiO5悬梁臂波导中151Eu3+离子的自旋相干寿命的序列图. 在准备阶段后, 通过线圈施加$ \pi/2-\pi-\pi/2 $的自旋回波(spin echo)脉冲序列, 每个射频脉冲的时间间隔τ相等, 射频脉冲的相位依次为$ 0^\circ-90^\circ-0^\circ $. 射频脉冲结束后, 施加一个啁啾带宽3 MHz和时间宽度500 µs的啁啾型光脉冲, 并随后探测2 ms的荧光信号; (b) Y2SiO5悬梁臂波导中151Eu3+离子$ |{\pm1/2}\rangle_{\mathrm{g}} $ $ \leftrightarrow $$ |{\pm3/2}\rangle_{\mathrm{g}} $的spin nutation测试. 红色曲线是拟合的阻尼正弦函数曲线; (c) Y2SiO5悬梁臂波导中151Eu3+离子$ |{\pm1/2}\rangle_{\mathrm{g}} $ $ \leftrightarrow $ $ |{\pm3/2}\rangle_{\mathrm{g}} $的超精细跃迁谱, 橙色曲线是拟合的pseudo-Voigt型曲线; (d)荧光信号随自旋回波序列的总时间的变化图
Fig. 5. (a) Pulse sequence for measuring spin coherence lifetime of 151Eu3+ in the Y2SiO5 nanobeam. The spin-echo sequence (RF pulses $ \pi/2-\pi-\pi/2 $) are applied by the Helmholtz coils after the preparation process. The phases of the RF pulses are $ 0^\circ-90^\circ-0^\circ $. After the RF pulses, the sample is excited by a chirp pulse with a duration of 500 µs and a bandwidth of 3 MHz, and then fluorescence signal is detected with a 2-ms window. (b) Spin nutation measurement on the $ |{\pm1/2}\rangle_{\mathrm{g}} $ $ \leftrightarrow $ $ |{\pm3/2}\rangle_{\mathrm{g}} $ transition of 151Eu3+ in the Y2SiO5 nanobeam. The red curve is fitted by damped sine lineshape. (c) Fluorescence-detected spectrum for $ |{\pm1/2}\rangle_{\mathrm{g}} $ $ \leftrightarrow $ $ |{\pm3/2}\rangle_{\mathrm{g}} $ transition. The orange curve is fitted by pseudo-Voigt lineshape. (d) Fluorescence signal as a function of the total time of the spin-echo sequence.
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