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量子存储器是构建未来大规模量子网络的核心器件. 由于具有超长的量子相干寿命, 稀土掺杂晶体逐渐成为最有希望实现实用量子存储的材料之一. 然而掺杂晶体中不可避免的晶格畸变限制了该类材料的吸收深度和存储效率. 纯稀土化合物晶体则同时满足了低晶格畸变和高稀土离子密度的需求, 有望实现高光存储效率. EuCl3·6H2O晶体是目前研究较多的一种纯稀土化合物晶体, 已经实现了低于超精细能级间距的光学非均匀展宽, 并且理论预测的自旋相干寿命可达1000 s, 是一种颇具潜力的量子存储材料. 目前光存储或量子存储功能仅仅在稀土掺杂晶体中实现过, 尚无实验报道纯稀土化合物晶体中的光存储现象. 本文报告了在EuCl3·6H2O晶体中实现了原子频率梳型光存储. 通过降温法生长得到了EuCl3·6H2O单晶, 实验测得其
$^7{\rm{F}}_0 \rightarrow {}^5{\rm D}_0$ 跃迁相干时间为55.7 μs, 存储时间1 μs时的存储效率为1.71%, 展现了这种材料实现光量子存储的原理可行性. 通过分析温度依赖的吸收线频率移动, 指出在这一材料中实现高效率光存储的主要挑战在于高效率的光谱烧孔.Quantum memory is a crucial component for the large-scale quantum networks. Rare-earth-ion doped crystals have been a promising candidate for the practical quantum memory because of its very long coherence time. However, doped ions cause unwanted lattice distortion, and consequently reduce the optical depth and the storage efficiency. The stoichiometric rare-earth crystals have low lattice distortion and high rare earth ion density, and thus are expected to enable high-efficiency storage. EuCl3·6H2O is a promising material for quantum memory applications because its optical inhomogeneous broadening can be smaller than its hyperfine splitting and the theoretically predicted spin coherence time is up to 1000 seconds. Despite the numerous efforts in solid-state quantum memory based on rare-earth ion doped crystals, optical memory and quantum memory have not been implemented with stoichiometric rare-earth crystals yet. Here, we report the atom frequency comb optical storage using a EuCl3·6H2O crystal. A coherence time of 55.7 μs is obtained by photon echo measurements on$^7{\rm{F}}_0 \rightarrow {}^5{\rm{D}}_0$ transition. The two-level atomic frequency comb storage is demonstrated with a storage efficiency of 1.71% at a storage time of 1 μs, showing the potential capability of optical quantum storage of this material. Based on the analysis of the line shift of$^7{\rm{F}}_0 \rightarrow {}^5{\rm{D}}_0$ depending on the sample temperature, we highlight the challenge of achieving high-efficiency optical pumping in this material, which imposes a limit on the achievable efficiency.-
Keywords:
- quantum memory /
- atom frequency comb /
- europium chloride hexahydrate
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图 1 EuCl3·6H2O晶体, 厚度约2 mm, 虚线内为存储实验所用区域. 晶体的三个轴向标示在示意图中, C2轴沿晶体的[010]的方向
Fig. 1. The EuCl3·6H2O crystal used in experiments, with the thickness of 2 mm. The dashed box indicates the area used in the experiment. Crystal’s axes are shown in the lower graph, with the C2 axis along [010] dirction.
图 2 实验装置示意图. 激光器输出的580 nm激光被一个声光调制器(AOM 1)所调制, 并入射到低温系统内的晶体样品(Crystal)上. 输出光场被另一个声光调制器(AOM 2)所调制, 最终由探测器(PD)探测
Fig. 2. Illustration of the experimental setup. The 580 nm laser is modulated by an acousto-optic modulator (AOM 1) and injected into the crystal sample which is cooled down to 3.5 K by a cryostat. The output laser beam is controlled by another AOM (AOM 2) and finally detected by a photodiode (PD).
图 3 EuCl3·6H2O晶体的光子回波幅度随时间的衰减曲线. 拟合得到相干时间(T2)为(55.7 ± 2.3) μs
Fig. 3. The decay curve of two-pulse photon echo amplitude with time in EuCl3·6H2O. The optical coherence time (T2) is (55.7 ± 2.3) μs by fitting the data to a single exponential decay.
图 4 (a) 153Eu3+离子能级结构; (b)在偏离中心频率位置上制备的AFC结构, 其频率中心为517.14873 THz, 插图为放大的AFC光谱结构
Fig. 4. (a) The energy diagram of 153Eu3+. Three beams with center frequency of
$f_1$ ,$f_2$ and$f_3$ are applied in a certain sequence to accomplish the spectral-hole burning for AFC preparation. (b) The prepared AFC structure with the center frequency is 517.14873 THz. Inset: enlarged view of the AFC structure.
图 5 (a) AFC光存储1 μs结果, 存储1 μs时的效率为
$(1.71\pm 0.04)\%$ , 与根据图4(b)得到的AFC参数理论计算值$(1.75\pm 0.11)\%$ 相符; (b)存储时间为0.5—10 μs时AFC存储效率变化, 由四次测量数据平均得到Fig. 5. (a) The AFC memory with a storage time of 1 μs. The storage efficiency at 1 μs is
$(1.71\pm 0.04)\%$ , which agrees with the theoretical efficiency of$(1.75\pm 0.11)\%$ , estimated from the AFC structure shown in Fig.4(b). (b) The storage efficiency with storage time from 0.5 μs to 10 μs. Each data point is averaged by four measurements.
图 6 温度导致的
$^7{\rm{F}}_0 \rightarrow {}^5{\rm{D}}_0$ 跃迁频率偏移及理论拟合Fig. 6. The line shift of
$^7{\rm{F}}_0 \rightarrow {}^5{\rm{D}}_0$ depending on the sample temperature. The curve is fitted using two-phonon Raman-process model[39,40], giving$\alpha = (4.22 \pm 0.57)\;{\rm{cm}}^{-1}$ and$T_{\rm D} = (144.1 \pm 6.2)\;{\rm{K}}$ for this crystal. -
[1] Sangouard N, Simon C, De Riedmatten H, Gisin N 2011 Rev. Mod. Phys. 83 33
Google Scholar
[2] Briegel H J, Dür W, Cirac J, Zoller P 1998 Phys. Rev. Lett. 81 5932
Google Scholar
[3] Yu Y, Ma F, Luo X Y, Jing B, Pan J W 2020 Nature 578 240
Google Scholar
[4] Wang Y, Li J, Zhang S, Su K, Zhou Y, Liao K, Du S, Yan H, Zhu S L 2019 Nat. Photonics 13 346
Google Scholar
[5] Corzo N V, Raskop J, Chandra A, Sheremet A S, Gouraud B 2019 Nature 566 359
Google Scholar
[6] Ritter S, Nolleke C, Hahn C, Reiserer A, Neuzner A, Uphoff M, Mucke M, Figueroa E, Bochmann J, Rempe G 2012 Nature 484 195
Google Scholar
[7] Korber M, Morin O, Langenfeld S, Neuzner A, Ritter S, Rempe G 2018 Nat. Photonics 12 18
Google Scholar
[8] Kalb N, Reiserer A, Humphreys P C, Bakermans J J W, Kamerling S J, Nickerson N H, Benjamin S C, Twitchen D J, Markham M, Hanson R 2017 Science 356 928
Google Scholar
[9] De Riedmatten H, Afzelius M, Staudt M U, Simon C, Gisin N 2008 Nature 456 773
Google Scholar
[10] Hedges M P, Longdell J J, Li Y, Sellars M J 2010 Nature 465 1052
Google Scholar
[11] Zhong M J, Hedges M P, Ahlefeldt R, Bartholomew J G, Beavan S, Wittig S M, Longdell J J, Sellars M 2015 Nature 517 177
Google Scholar
[12] Rancic M, Hedges M P, Ahlefeldt R L, Sellars M J 2018 Nat. Phys. 14 50
Google Scholar
[13] Ma Y, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2021 Nat. Commun. 12 2381
[14] Saglamyurek E, Sinclair N, Jin J, Slater J A, Oblak D, Bussieres F, George M, Ricken R, Sohler W, Tittel W 2011 Nature 469 512
Google Scholar
[15] Saglamyurek E, Puigibert M G, Zhou Q, Giner L, Marsili F, Verma V B, Nam S W, Oesterling L, Nippa D, Oblak D, Tittel W 2016 Nat. Commun. 7 11202
Google Scholar
[16] Tang J S, Zhou Z Q, Wang Y T, Li Y L, Liu X, Hua Y L, Zou Y, Wang S, He D Y, Chen G, Sun Y N, Yu Y, Li M F, Zha G W, Ni H Q, Niu Z C, Li C F, Guo G C 2015 Nat. Commun. 6 8652
Google Scholar
[17] Yang T S, Zhou Z Q, Hua Y L, Liu X, Li Z F, Li P Y, Ma 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
[18] Sinclair N, Saglamyurek E, Mallahzadeh H, Slater J A, George M, Ricken R, Hedges M P, Oblak D, Simon C, Sohler W, Tittel W 2014 Phys. Rev. Lett. 113 053603
Google Scholar
[19] Jobez P, Timoney N, Laplane C, Etesse J, Ferrier A, Goldner P, Gisin N, Afzelius M 2016 Phys. Rev. A 93 032327
Google Scholar
[20] Zhou Z Q, Hua Y L, Liu X, Chen G, Xu J S, Han Y J, Li C F, Guo G C 2015 Phys. Rev. Lett. 115 070502
Google Scholar
[21] Usmani I, Afzelius M, De Riedmatten H, Gisin N 2010 Nat. Commun. 1 12
Google Scholar
[22] Zhong T, Kindem J M, Bartholomew J G, Rochman J, Craiciu I, Miyazono E, Bettinelli M, Cavalli E, Verma V, Nam S W, Marsili F, Shaw M D, Beyer A D, Faraon A 2017 Science 357 1392
Google Scholar
[23] Seri A, Lagorivera D, Lenhard A, Corrielli G, Osellame R, Mazzera M, De Riedmatten H 2019 Phys. Rev. Lett. 123 080502
Google Scholar
[24] Liu C, Zhou Z Q, Zhu T X, Zheng L, Jin M, Liu X, Li P Y, Huang J Y, Ma Y, Tu T, Yang T S, Li C F, Guo G C 2020 Optica 7 192
Google Scholar
[25] Lauritzen B, Minar J, De Riedmatten H, Afzelius M, Sangouard N, Simon C, Gisin N 2010 Phys. Rev. Lett. 104 080502
Google Scholar
[26] Craiciu I, Lei M, Rochman J, Kindem J M, Bartholomew J G, Miyazono E, Zhong T, Sinclair N, Faraon A 2019 Phys. Rev. Appl. 12 024062
Google Scholar
[27] Puigibert M L G, Saglamyurek E, Tittel W, Jin J, Verma V, Marsili F, Nam S W, Oblak D 2015 Phys. Rev. Lett. 115 140501
Google Scholar
[28] Jobez P, Laplane C, Timoney N, Gisin N, Ferrier A, Goldner P, Afzelius M 2015 Phys. Rev. Lett. 114 230502
Google Scholar
[29] Gundogan M, Ledingham P M, Kutluer K, Mazzera M, de Riedmatten H 2015 Phys. Rev. Lett. 114 230501
Google Scholar
[30] Afzelius M, Usmani I, Amari A, Lauritzen B, Walther A, Simon C, Sangouard N, Minar J, de Riedmatten H, Gisin N, Kroll S 2010 Phys. Rev. Lett. 104 040503
Google Scholar
[31] Binnemans K 2015 Coord. Chem. Rev. 295 1
Google Scholar
[32] Ahlefeldt R L, Hutchison W D, Manson N B, Sellars M J 2013 Phys. Rev. B 88 184424
Google Scholar
[33] Ahlefeldt R, Hush M R, Sellars M 2016 Phys. Rev. Lett. 117 250504
Google Scholar
[34] Ahlefeldt R, Manson N B, Sellars M 2013 J. Lumin. 133 152
Google Scholar
[35] Ahlefeldt R, Zhong M, Bartholomew J G, Sellars M 2013 J. Lumin. 143 193
Google Scholar
[36] Ahlefeldt R L, Mcauslan D L, Longdell J J, Manson N B, Sellars M J 2013 Phys. Rev. Lett. 111 240501
Google Scholar
[37] Li Z F, Liu X, Yang T S, Ma Y, Zhou Z Q, Li C F 2021 Phys. Lett. A 399 127295
Google Scholar
[38] Afzelius M, Simon C, Riedmatten H D, Gisin N 2009 Phys. Rev. A 79 052329
Google Scholar
[39] McCumber D E, Sturge M D 1963 J. Appl. Phys. 34 6
Google Scholar
[40] Könz F, Sun Y, Thiel C W, Cone R L, Equall R W, Hutcheson R L, Macfarlane R M 2003 Phys. Rev. B 68 085109
Google Scholar
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