Quantum memory and manipulation based on erbium doped crystals

Zhou Pai; Li Xia-Xia; Xing Xue-Yan; Chen Yu-Hui; Zhang Xiang-Dong

doi:10.7498/aps.71.20211803

Abstract

Quantum information is a rapidly emerging field aiming at combining two of the greatest advances in science and technology of the twentieth century, that is, quantum mechanics and information science. To reliably generate, store, process, and transmit quantum information, diverse systems have been studied. While for specific tasks some of these systems are more suitable than others, no single system can meet all envisioned demands. Erbium doped crystal has optical transition at 1.5 μm and possesses long optical coherence time and spin coherence time, and thus is one of the best candidates in building several essential blocks for quantum information applications. In this review, we summarize the applications of erbium doped crystals in quantum memories, quantum transducers, quantum sources, and quantum manipulations based on erbium-erbium interactions. Finally, the outlooks for near term prospects of the mentioned topics are also given.

Keywords:

Authors and contacts

Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China

Corresponding author: Chen Yu-Hui, stephen.chen@bit.edu.cn ; Zhang Xiang-Dong, zhangxd@bit.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 91850205), the Start-up Fund of Beijing Institute of Technology, China, and the Science and Technology Innovation Project of Beijing Institute of Technology, China.

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Cited By

图 1 若干代表性量子体系的特征参数^[13]. 不同材料在图中的位置是根据该体系本身的相干时间(x轴)和工作频率(y轴)排列的. 例如, 核自旋和电子自旋在低温下具有较长的相干时间; 超导量子比特、量子机械系统和微波光子腔与传统电磁波有很强的耦合作用; 同时通信波段的光子在信息的长距离传输方面具有无可比拟的优势

Figure 1. Blocks of hybrid quantum systems^[13]. Some typical systems with different functionalities are placed in the diagram according to their coherence time (x axis) and their excitation frequencies (y axis). For example, nuclear spins and electron spins feature with their long coherence time; superconducting qubits, quantum mechanical systems and microwave cavities can be strongly coupled to electromagnetic fields in radio or microwave frequencies; and photons at telecom wavelengths are unparalleled in sending information over long distance.

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图 2 晶体材料中磁噪声导致的退相干效应　(a)晶体中的离子本身都具有电子自旋磁矩或者核自旋磁矩. 温度不为零时, 这些磁矩会发生无规则的抖动, 从而改变我们观测的某个离子的局域磁场, 使得它的跃迁频率发生变化$ \Delta \omega $. (b)电子自旋的塞曼效应. 对于自旋$ S = 1/2 $的电子系统, 在外加磁场的情况下, 能级会发生劈裂, 自旋能级之间的跃迁频率ω也是随外加磁场而变化的. 由塞曼效应导致的能级劈裂是线性的. (c)铒离子的超精细能级相互作用. 对于¹⁶⁷Er离子来说, 其电子自旋哈密顿量除了包含塞曼效应项, 还存在电子自旋和核自旋的超精细相互作用项${\boldsymbol{I}}\cdot {\boldsymbol{A}} \cdot {\boldsymbol{S}}$. ¹⁶⁷Er完整的自旋哈密顿量应为$H = \mu_{\rm e} {\boldsymbol{B}}\cdot {\boldsymbol{g}} \cdot {\boldsymbol{S}} +{\boldsymbol{I}}\cdot $$ {\boldsymbol{A}} \cdot {\boldsymbol{S}}+{\boldsymbol{I}}\cdot {\boldsymbol{Q}} \cdot {\boldsymbol{I}}+\mu_{\rm n} {\boldsymbol{B}} \cdot {\boldsymbol{I}}$, 其中${\boldsymbol{g}}$是电子的塞曼矩阵, ${\boldsymbol{Q}}$是电四极矩阵, $g_{\rm n} = -0.1618$是核g因子. 在存在超精细相互作用时, 离子能级结构对外界磁场变化的响应会变成非线性的, 使得在某些特殊的外加磁场下跃迁频率对磁场变化的一阶导数为零, $ \partial{ \omega} / \partial{B} = 0 $

Figure 2. Magnetic decoherence in crystals. (a) Ions that form a crystal possess electron spins or nuclear spins, which are cartooned as small magnets here. With environment temperature above zero, these magnets vibrate around their lattice positions. As a result, a vibrating magnetic field is added to the local field of a targeted ion and its transition frequency is changed by an amount of $ \Delta \omega $. (b) Zeeman effect of electron spins. For electrons with spin $ S = 1/2 $, applying a magnetic field splits the energy levels. The transition frequency ω is linear to the applied magnetic field. (c) Illustration of the hyperfine structure of erbium ions. For ¹⁶⁷Er ions that possess both electron spins and nuclear spins, the spin Hamiltonian is $H = \mu_{\rm e} {\boldsymbol{B}}\cdot {\boldsymbol{g}} \cdot {\boldsymbol{S}} +{\boldsymbol{I}}\cdot $$ {\boldsymbol{A}} \cdot {\boldsymbol{S}}+{\boldsymbol{I}}\cdot {\boldsymbol{Q}} \cdot {\boldsymbol{I}}+\mu_{\rm n} {\boldsymbol{B}} \cdot {\boldsymbol{I}}$, where $\mu_{\rm e}$ is the Bohr magneton, B is the applied magnetic field, g is the Zeeman g-matrix, A is the hyperfine matrix, Q is the electric quadrupole matrix, $\mu_{\rm n}$ is the nuclear magneton, and $g_{\rm n} = -0.1618$ is the nuclear g factor. Due to the hyperfine interactions, the transition frequency ω is no longer a linear function of the applied magnetic field, which leads to $ \partial{ \omega } / \partial{B} = 0 $ at some specific magnetic field.

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图 3 ¹⁶⁷Er:YSO 晶体的基态能级在外加磁场下的变化情况　(a) ¹⁶⁷Er:YSO的16个超精细能级随外加磁场的变化情况, 其中b和c标记了图(b)和(c)对应的区域; (b)箭头b对应区域的能级变化情况; (c)箭头c对应区域的能级变化情况

Figure 3. Hyperfine structure of ¹⁶⁷Er:YSO as a function of applied magnetic field. (a) The ground state of ¹⁶⁷Er:YSO consists of 16 hyperfine energy levels, all of which show nonlinear behaviour around $ B = 0 $. Letter b and c indicate the regime of panel (b) and (c). (b) Zoomed picture of energy level as indicated by b in panel (a). (c) Zoomed picture of energy level as indicated by c in panel (c).

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图 4 基于掺铒晶体可集成量子存储器的主要技术方案　(a) 在铌酸锂晶体材料上通过离子扩散制备波导结构的量子存储器^[37]; (b) 利用聚焦离子束刻蚀技术在 YVO 晶体上制备一维光子晶体结构的存储器^[41]; (c)采用激光直写技术在 YSO 晶体上制备波导结构的存储器^[38]; (d) 在 YSO 晶体上制备硅基光子学结构的存储器^[42]

Figure 4. On-chip erbium quantum memories: (a) Quantum memory based on erbium- and titanium-indiffused lithium-niobate waveguide^[37]; (b) nanophotonic quantum memory by using focued-ion-beam to fabricate a one-dimensional photonic cavity in a YVO crystal^[41]; (c) waveguide memory fabricated by femtosecond-laser micromachining on the surface of a YSO crystal^[38]; (d) quantum memory comprised of an amorphous silicon (αSi) waveguide on a YSO crystal^[42].

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图 5 基于掺铒晶体量子频率转换　(a) 一种实现微波光子到1.5 μm光子的量子转换器. 掺铒晶体提供实现频率转换所必需的电光非线性, 然后分别用光学腔和微波腔来增强在各自波段的光和物质相互作用. 这样一种技术方案原则上可以在低噪声的条件下实现量子效率为100%的频率转换^[63]. (b) 基于掺铒晶体的量子频率转换实验, 实现量子效率为$ 10^{-5} $的频率转换^[68]

Figure 5. Quantum transducer based on erbium doped crystal. (a) Apparatus for quantum conversion between microwave photons and 1.5 μm optical photons. Both a microwave cavity and an optical cavity are used to enhance the light-matter interactions in their corresponding frequency regimes. Together with the large non-linearity provided by erbium ions, a low-noise and 100%-efficiency conversion can be expected ^[63]. (b) Quantum conversion from microwave photons to optical photons^[68]. The quantum efficiency is $ 10^{-5} $

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图 6 基于掺铒晶体的单光子辐射　(a) 空间分辨和光谱分辨相结合的技术方法. 上图, 一般的聚焦光束会和多个铒离子发生相互作用, 不同颜色的铒离子在1.5 μm附近具有不同的辐射波长. 左下图, 利用微纳光学结构可以将光场有效地束缚在微纳尺度, 大大减小和光场发生相互作用的铒离子. 右下图, 在一个微纳光学腔中和光场发生相互作用的铒离子数目仍然很多, 不同发光波长的铒离子构成了该材料的非均匀线宽, 通过利用窄线宽的激光(小于单个铒离子的均匀线宽), 便可以选择性的单独激发红色的铒离子(其他颜色的铒离子由于频率失谐而没有被激发), 从而实现单个铒离子的探测. (b) 上图, 在Er:YSO掺杂晶体上制备硅的光子晶体腔; 下图, 铒离子的单光子辐射, 不同铒离子的辐射频率略有不同^[78]

Figure 6. Single photon sources based on erbium doped crystal. (a) Single ion detection by combining spatial and spectral resolutions. Upper panel, illustration of a large amount of ions inside a crystal interact with a focused laser beam. Dots with different color indicate that erbium ions have slightly different transition frequency around 1.5 μm. Bottom left, using nanophotonic structure to further confine the optical mode can largely reduce the number of interacting ions; bottom right, if at the same time introducing a narrow-frequency window to pick specific ions in the inhomogeneous line, one can isolate single erbium ions, e.g., using a narrow-frequency laser that is resonant with the red ions to saturate the homogeneous line while leaving ions with other colors non-excited. (b) Top, illustration of a silicon waveguide patterned with photonic crystal cavities on the top of a Er:YSO crystal. Bottom, photo-emission spectra of single erbium ions that have slightly different frequency around 1.5 μm^[78]

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图 7 基于铒离子间相互作用的量子调控　(a) 利用空间分辨和光谱分辨技术, 在Er:YSO晶体上实现了对6个铒离子的相干操控^[83]; (b) 由于铒离子间的相互作用而导致的本征光学不稳相^[89].

Figure 7. Quantum manipulation based on erbium-erbium interactions: (a) Combining spatial resolution of nanophotonics and spectral resolution of narrow-frequency laser, six erbium ions can be addressed and controlled independently^[83]; (b) intrinsic optical instability due to ion-ion interactions^[89].

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