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基于光子晶体微腔的回波光量子存储

邢雪燕 李霞霞 陈宇辉 张向东

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基于光子晶体微腔的回波光量子存储

邢雪燕, 李霞霞, 陈宇辉, 张向东

Optical echo memory based on photonic crystal cavities

Xing Xue-Yan, Li Xia-Xia, Chen Yu-Hui, Zhang Xiang-Dong
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  • 充分发掘量子计算机的应用潜力需要将大量分立的量子节点连接起来, 组建一个与互联网类似的全量子网络. 高性能的可集成光量子存储器是解决不同量子节点间信号同步问题的核心器件, 直接关系到量子网络的实现规模和整体性能. 然而, 目前的微纳量子存储器还存在可集成性和存储性能难以兼容的问题, 还不能满足构建全量子网络的需求. 本文提出在掺铒硅材料上设计通信波段的光子晶体微腔, 不仅可利用光学微腔的角动量共振模式来实现基于光子回波的量子存储, 还可利用光学微腔来增强光和物质相互作用, 有望实现高存储效率的可集成量子存储器.
    Like internet, connecting quantum computers together to build a full quantum network will enhance the ability to process quantum information. On-chip quantum memories can possess the essential functionalities in building a quantum network, including synchronizing a large number of quantum computers and implementing long-distance quantum communication. However, owning mainly to the constraints imposed by the micro-photonic structures themselves, on-chip quantum memories cannot satisfy the requirement for constructing the full quantum network for the incompatibility of their memory property and integration property. We here propose to build an on-chip quantum memory by using spatial-phase-mismatching effect in photonic crystal cavities. In this scenario, not only is the large orbital angular momentum of photonic crystal cavities utilized to realize photon-echo type memory, but also the light-matter enhancement of a photonic cavity is used to achieve a high-efficiency quantum storage.
      通信作者: 陈宇辉, stephen.chen@bit.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 62105033, 12174026)、北京理工大学学术启动计划和北京理工大学科技创新计划资助的课题.
      Corresponding author: Chen Yu-Hui, stephen.chen@bit.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62105033, 12174026), the Start-up Fund of Beijing Institute of Technology, China, and the Science and Technology Innovation Project of Beijing Institute of Technology, China.
    [1]

    Lvovsky A I, Sanders B C, Tittel W 2009 Nat. Photonics 3 706Google Scholar

    [2]

    Sangouard N, Simon C, Riedmatten H D, Gisin N 2011 Rev. Mod. Phys. 83 33Google Scholar

    [3]

    Heshami K, England D G, Humphreys P C, Bustard P J, Acosta V M, Nunn J, Sussman B J 2016 J. Mod. Opt. 63 2005Google Scholar

    [4]

    Simon C 2017 Nat. Photonics 11 678Google Scholar

    [5]

    Kimble H J 2008 Nature 453 1023Google Scholar

    [6]

    Bussieres F, Sangouard N, Afzelius M, Riedmatten H D, Tittel W 2013 J. Mod. Opt. 60 1519Google Scholar

    [7]

    Saglamyurek E, Sinclair N, Jin J, Slater J A, Oblak D, Bussieres F, George M, Ricken R, Sohler W, Tittel W 2011 Nature 469 512Google Scholar

    [8]

    Liu C, Zhu T X, Su M X, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2020 Phys. Rev. Lett. 125 260504Google Scholar

    [9]

    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

    [10]

    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 1392Google Scholar

    [11]

    Craiciu I, Lei M, Rochman J, Bartholomew J G, Faraon A 2021 Optica 8 114

    [12]

    Hétet G, Longdell J J, Alexander A L, Lam P K, Sellars M J 2008 Phys. Rev. Lett. 100 23601Google Scholar

    [13]

    Moiseev S A, Kröll S 2001 Phys. Rev. Lett. 87 173601

    [14]

    Kraus B, Tittel W, Gisin N, Nilsson M, Kröll S, Cirac J I Phys. Rev. A 73 020302

    [15]

    Alexander A L, Longdell J J, Sellars M J, Manson N B 2006 Phys. Rev. Lett. 96 043602Google Scholar

    [16]

    Riedmatten H D, AfZelius M, Staudt M U, Simon C, Gisin N 2008 Nature 456 07607

    [17]

    Mcauslan D L, Ledingham P M, Naylor W R, Beavan S E, Longdell J J 2011 Phys. Rev. A 84 022309Google Scholar

    [18]

    Afzelius M, Simon C, Riedmatten H De, Gisin N 2009 Phys. Rev. A 79 052329Google Scholar

    [19]

    Chanelière T, Hétet G 2015 Opt. Lett. 40 1294Google Scholar

    [20]

    McDonald H C 2016 Ph. D. Dissertation (Otago: University of Otago)

    [21]

    Ma Y Z, Jin M, Chen D L, Zhou Z Q, Li C F, Guo G C 2021 Nat. Commun. 12 4378Google Scholar

    [22]

    Damon V, Bonarota M, Louchet-Chauvet A, Chaneliere T, Le Gouët J L 2011 New J. Phys. 13 093031Google Scholar

    [23]

    Dajczgewand J, Le Gouët J L, Louchet-Chauvet A, Chanelière T 2014 Opt. Lett. 39 2711Google Scholar

    [24]

    Fu Y, Wang M F, Zheng Y Z 2014 Opt. Commun. 321 162Google Scholar

    [25]

    Fan S, Villeneuve P R, Joannopoulos J D, Haus H A 1998 Opt. Express 3 4

    [26]

    Afzelius1 M, Simon C 2010 Phys. Rev. A 82 022310

    [27]

    Wang J, Sciarrino F, Laing A, Thompson M G 2020 Nat. Photonics 14 273Google Scholar

    [28]

    Zhong T, Goldner P 2019 Nanophotonics 8 2003Google Scholar

    [29]

    Hughes M A, Panjwani N A, Urdampilleta M, Homewood K P, Murdin B, Carey J D 2021 Appl. Phys. Lett. 118 194001Google Scholar

    [30]

    Yin C, Rancic M, Boo G G, Stavrias N, McCallum J C, Sellars M J, Rogge S 2013 Nature 497 91Google Scholar

  • 图 1  $ \pi $脉冲作用下的光子回波静默和再现操作 (a)双$ \pi $脉冲光子回波技术的脉冲序列, 输入信号光的空间相位分布为$ \phi_0(r) $, 第一个$ \pi $脉冲对应的空间相位分布为$ \phi_1(r) $, 并且$ \phi_1(r) \neq \phi_0(r) $, 第二个$ \pi $脉冲对应的空间相位分布为$ \phi_2(r) $; (b)在自由空间的ROSE存储技术中, $ \phi_1(r) \neq \phi_0(r) $可通过控制脉冲光和控制脉冲的入射方向来实现. 例如, 图中的信号脉冲从左侧入射$ \phi_0 = {\rm{i}} k r $, $ \pi $脉冲从右侧入射$ \phi_1 = \phi_2 = -{\rm{ i }}k r $

    Fig. 1.  The silence and revival of two-$ \pi $-pulse photon echo: (a) Pulse sequence of two-$ \pi $-pulse photon echo. The phase distribution of the input pulse is $ \phi_0(r) $, that of the first $ \pi $ pulse is $ \phi_1(r) $, where $ \phi_1(r) \neq \phi_0(r) $, and that of the second $ \pi $ pulse is $ \phi_2(r) $. (b) In free space ROSE, $ \phi_1(r) $ differs from $ \phi_0(r) $ due to the different propagating directions of the signal pluse and the $ \pi $ pulses. In panel (b), the signal pulse incoming from the left has $ \phi_0 = {\rm{i}} k r $, and the $ \pi $ pulses incoming from the right have $ \phi_1 = \phi_2 = -{\rm{ i}} k r $.

    图 2  拟采用的光子晶体结构 (a)光子晶体结构, 光子晶体为正方晶格结构, 周期为500 nm, 其中蓝色柱子为掺铒的硅材料, 直径$ D = 200 $ nm; (b)计算得到的光子晶体能带图, 带隙在$1.21 — 1.78\;\text{µ} {\rm{m}}$范围内

    Fig. 2.  Photonic crystal: (a) Structurre of the photonic crystal. The photonic crystal has a square lattice, whose period is 500 nm. The circles stands for the silicon pillars with a diameter of $ D = 200 $ nm. (b) Energy band of the photonic crystal in panel (a), showing a bandgap within 1.21–1.78$\;\text{µ} {\rm{m}}$

    图 3  两种不同的光子晶体微腔. 单极子谐振模式 (a)在光子晶体中去掉一个硅柱子可以形成一个缺陷态微腔. 这样一种腔支持单极子的谐振模式, 如图(c)所示. 入射光从左上方的光子晶体波导入射耦合到光子晶体腔中, 如图(e)所示. 由于单极子谐振模式是一种类似于驻波的谐振模式, 因此无法通过调节阻抗匹配实现100%的单端输出. 六极子谐振模式: (b)把光子晶体中间的硅柱子直径增加为$ d_1 = 700 $ nm, 并且将边沿的一个硅柱子直径减小为$ d_2 = 150 $ nm, 可以形成另一种光学微腔. 这样一种光学腔支持六极子的谐振模式, 其场分布如图(d)所示. 当入射光同样从左上方的光子晶体波导耦合到光子晶体腔时, 如图(f)所示, 六单极子谐振模式类似于一个顺时针旋转的回音壁模式, 可以通过调节阻抗匹配实现能量接近100%地从左下角的端口输出

    Fig. 3.  Two photonic-crystal cavities. Monopole resonace: (a) Removing a rod in the photonic crystal forms a defect cavity. One of the resonances of the structure (a) is a monopole resonance, the field distribution of which is shown in panel (c). Such a monopole mode is analogous to standing-wave resonance, and has a constant phase in space. This means that single-port output to one end of the waveguides can not be realized bu tuning the waveguide-cavity coupling, as shown in panel (e). Hexapole resonance: (b) By increasing the diameter of the central rod to 700 nm and reducing the rods at the edge to $ d_2 = 150 $ nm, one can make another kind of cavity that supports hexapole resonance. The field distribution is shown in panel (d). In such a structure the coupling between waveguides and the cavity are impedance matched, as shown in panel (f), therefore one can transfer the input light to the down-right port with an efficiency close to 100%

    图 4  基于光子晶体微腔的ROSE回波量子存储 (a)用于ROSE存储的光子晶体结构; (b)信号光脉冲从左侧入射, 如图 3(d)所示, 可以在原子系统中激发出一种$ \phi_0(r) $为“顺时针”旋转的集体极化; (c)控制$ \pi $脉冲从右侧入射, 因此其激发的腔模具有的相位分布$ \phi_1(r) $为“逆时针”旋转方向; (d) 当第二个控制$ \pi $脉冲也从右侧入射后, 根据(13)式和(15)式, 原子系统的集体激发再次具有$ \phi_0(r) $的相位分布, 在$ t = 2 t_2 - 2 t_1 + t_0 $时刻会向右边的端口外辐射出一个光子回波

    Fig. 4.  Protocol of ROSE quantum memory based on photonic crystal structures: (a) One photonic crystal structure that is suitable for ROSE technique; (b) a signal pulse is input from the left, and the collective atomic polarization thus has a “clockwise” spatial phase distribution $ \phi_0(r) $; (c) control $ \pi $ pulses are input from the right, therefore have a “anti-clockwise” spatial phase distribution $ \phi_1(r) $; (d) after the second $ \pi $ pulse, according the Eqs. (13) and (15), the collective atomic polarization has a phase distribution of $ \phi_0(r) $ and then emit a photon echo to the right port

  • [1]

    Lvovsky A I, Sanders B C, Tittel W 2009 Nat. Photonics 3 706Google Scholar

    [2]

    Sangouard N, Simon C, Riedmatten H D, Gisin N 2011 Rev. Mod. Phys. 83 33Google Scholar

    [3]

    Heshami K, England D G, Humphreys P C, Bustard P J, Acosta V M, Nunn J, Sussman B J 2016 J. Mod. Opt. 63 2005Google Scholar

    [4]

    Simon C 2017 Nat. Photonics 11 678Google Scholar

    [5]

    Kimble H J 2008 Nature 453 1023Google Scholar

    [6]

    Bussieres F, Sangouard N, Afzelius M, Riedmatten H D, Tittel W 2013 J. Mod. Opt. 60 1519Google Scholar

    [7]

    Saglamyurek E, Sinclair N, Jin J, Slater J A, Oblak D, Bussieres F, George M, Ricken R, Sohler W, Tittel W 2011 Nature 469 512Google Scholar

    [8]

    Liu C, Zhu T X, Su M X, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2020 Phys. Rev. Lett. 125 260504Google Scholar

    [9]

    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

    [10]

    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 1392Google Scholar

    [11]

    Craiciu I, Lei M, Rochman J, Bartholomew J G, Faraon A 2021 Optica 8 114

    [12]

    Hétet G, Longdell J J, Alexander A L, Lam P K, Sellars M J 2008 Phys. Rev. Lett. 100 23601Google Scholar

    [13]

    Moiseev S A, Kröll S 2001 Phys. Rev. Lett. 87 173601

    [14]

    Kraus B, Tittel W, Gisin N, Nilsson M, Kröll S, Cirac J I Phys. Rev. A 73 020302

    [15]

    Alexander A L, Longdell J J, Sellars M J, Manson N B 2006 Phys. Rev. Lett. 96 043602Google Scholar

    [16]

    Riedmatten H D, AfZelius M, Staudt M U, Simon C, Gisin N 2008 Nature 456 07607

    [17]

    Mcauslan D L, Ledingham P M, Naylor W R, Beavan S E, Longdell J J 2011 Phys. Rev. A 84 022309Google Scholar

    [18]

    Afzelius M, Simon C, Riedmatten H De, Gisin N 2009 Phys. Rev. A 79 052329Google Scholar

    [19]

    Chanelière T, Hétet G 2015 Opt. Lett. 40 1294Google Scholar

    [20]

    McDonald H C 2016 Ph. D. Dissertation (Otago: University of Otago)

    [21]

    Ma Y Z, Jin M, Chen D L, Zhou Z Q, Li C F, Guo G C 2021 Nat. Commun. 12 4378Google Scholar

    [22]

    Damon V, Bonarota M, Louchet-Chauvet A, Chaneliere T, Le Gouët J L 2011 New J. Phys. 13 093031Google Scholar

    [23]

    Dajczgewand J, Le Gouët J L, Louchet-Chauvet A, Chanelière T 2014 Opt. Lett. 39 2711Google Scholar

    [24]

    Fu Y, Wang M F, Zheng Y Z 2014 Opt. Commun. 321 162Google Scholar

    [25]

    Fan S, Villeneuve P R, Joannopoulos J D, Haus H A 1998 Opt. Express 3 4

    [26]

    Afzelius1 M, Simon C 2010 Phys. Rev. A 82 022310

    [27]

    Wang J, Sciarrino F, Laing A, Thompson M G 2020 Nat. Photonics 14 273Google Scholar

    [28]

    Zhong T, Goldner P 2019 Nanophotonics 8 2003Google Scholar

    [29]

    Hughes M A, Panjwani N A, Urdampilleta M, Homewood K P, Murdin B, Carey J D 2021 Appl. Phys. Lett. 118 194001Google Scholar

    [30]

    Yin C, Rancic M, Boo G G, Stavrias N, McCallum J C, Sellars M J, Rogge S 2013 Nature 497 91Google Scholar

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出版历程
  • 收稿日期:  2022-01-12
  • 修回日期:  2022-02-24
  • 上网日期:  2022-05-24
  • 刊出日期:  2022-06-05

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