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Optical echo memory based on photonic crystal cavities

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

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Optical echo memory based on photonic crystal cavities

Xing Xue-Yan, Li Xia-Xia, Chen Yu-Hui, Zhang Xiang-Dong
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  • 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.
      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 $

    Figure 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

    Figure 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

    Figure 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

    Figure 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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Publishing process
  • Received Date:  12 January 2022
  • Accepted Date:  24 February 2022
  • Available Online:  24 May 2022
  • Published Online:  05 June 2022

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