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半导体材料中的自旋色心是量子信息处理的理想载体, 引起了人们的广泛兴趣. 近几年, 研究发现碳化硅材料中的双空位、硅空位等色心具有与金刚石中的氮-空位色心相似的性质, 而且其荧光处于更有利于光纤传输的红外波段. 然而受限于这类色心的荧光强度和谱线宽度, 它们在量子密钥分发和量子网络构建等方面的实际应用依然面临严峻的挑战. 利用光学腔耦合自旋色心实现荧光增强和滤波将能有效地解决这些难题. 将光纤端面作为腔镜, 并与自旋色心耦合可以实现小模式体积的腔耦合, 而且天然地避免了需要再次将荧光耦合进光纤而造成损耗的缺点. 本文理论计算了耦合碳化硅薄膜的光纤腔的性质和特征. 首先通过优化各项参数包括薄膜表面粗糙度、腔镜反射率等, 理论分析了存在于光纤腔中的不同模式的特点, 以及光纤腔耦合色心的增强效果及相关影响因素. 进一步地研究了对开放腔而言最主要的影响因素—振动对腔性质、色心的增强效果以及耦出效率的影响, 最终得到在不同振动下的最大增强效果以及对应的耦出透射率. 这些结果为今后光纤腔耦合色心的实验设计提供了最直接的理论指导, 为实验的发展和优化指明了方向.Single spin color centers in solid materials are one of the promising candidates for quantum information processing, and attract a great deal of interest. Nowadays, single spin color centers in silicon carbide, such as divacancies and silicon vacancies have been developed rapidly, because they not only have similar properties of the NV centers in diamond, but also possess infrared fluorescence that is more favorable for transmission in optical fiber. However, these centers possess week fluorescence with broad spectrum, which prevents some key technologies from being put into practical application, such as quantum key distribution, photon-spin entanglement, spin-spin entanglement and quantum sensing. Therefore, optical resonator is very suitable for coupling centers to filter their spectrum and enhance the fluorescence by Purcell effect. It is very advantageous to use the fiber end face as cavity mirrors, thereby the fiber can provide small cavity volume corresponding to a large enhancement in spin color centers, and collect the fluorescence in cavity simultaneously, which has no extra loss in comparison with other collection methods. In this work, the properties and performance of fiber Fabry-Perot cavity coupling silicon carbide membrane are mainly studied through theoretical calculation. Firstly, some parameters are optimized such as membrane roughness and mirror reflection by calculating the mode of the fiber cavity and enhancing the color centers coupling into the cavity, then analyzing the properties of different modes in cavity, the enhancement effect on cavity coupling color centers, and other relevant factors affecting the cavity coupling color centers. Next, the influences of dominated factor and vibration on the properties of the cavity, the enhancement and outcoupling of centers coupled into the cavity are investigated, and finally the optimal outcoupling efficiency corresponding to different vibration intensities is obtained. These results give direct guidance for the further experimental design and direction for optimization of the fiber cavity coupling color centers.
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Keywords:
- spin color centers /
- fiber cavity /
- silicon carbide membrane
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图 1 光纤腔示意图以及腔内模场谱图和分布图 (a) 耦合薄膜的光纤腔示意图; (b) 腔内基模频率随腔长的变化关系, 其中薄膜厚度tm为4.12 μm; (c) 处于“空气模”时腔内场强的分布情况, 其中薄膜厚度tm为4.29 μm; (d) 处于“薄膜模”时腔内场强的分布情况, 其中薄膜厚度tm为4.19 μm. 图(c)和图(d)左上角的小图是界面场强的放大图
Fig. 1. FFPC sketch, spectrum and field intensity of cavity, top left insets of (c) and (d) are the enlarged field on the surface: (a) Sketch of FFPC coupling membrane; (b) spectrum of the fundamental mode varying with cavity length, where tm is 4.12 μm; (c) field intensity of the “air-mode” in cavity, where tm is 4.29 μm; (d) field intensity of the “membrane-mode” in cavity, where tm is 4.19 μm.
图 2 β因子随薄膜厚度
$ {t}_{\rm{m}} $ 变化, 不同曲线表示不同的表面粗糙度$ {\sigma }_{\rm{MA}} $ , 虚线与所有曲线相交的点表示在该薄膜厚度$ {t}_{\rm{m}} $ 下腔处于“薄膜模” (a) 高精细度腔的β因子, 其中取$ {{\cal{L}}}_{{\rm{M}}, {\rm{a}}} $ 为0.025 × 10-3,$ {{\cal{L}}}_{{\rm{M}}, {\rm{m}}} $ 为0.03 × 10–3; (b) 低精细度腔的β因子, 其中$ {{\cal{L}}}_{{\rm{M}}, {\rm{a}}} $ 和$ {{\cal{L}}}_{{\rm{M}}, {\rm{m}}} $ 均为4.5 × 10–3Fig. 2. β factor varying with the width and roughness of the membrane. The points of intersection between the curves and dotted line indicate that the cavity is in the membrane mode: (a) β factor of high fineness cavity with
$ {{\cal{L}}}_{{\rm{M}}, {\rm{a}}} $ of 0.025 × 10-3 and$ {{\cal{L}}}_{{\rm{M}}, {\rm{m}}} $ of 0.03 × 10–3; (b) β factor of low fineness cavity with$ {{\cal{L}}}_{{\rm{M}}, {\rm{a}}} $ of 4.5 × 10–3 and$ {{\cal{L}}}_{{\rm{M}}, {\rm{m}}} $ of 4.5 × 10–3.
图 3 存在振动时的
$ {\beta }_{\rm{vib}} $ 因子, 其中选取了四个振动标准差0.01, 0.03, 0.07和0.2 nm进行计算 (a) 腔内为“薄膜模”时的$ {\beta }_{\rm{vib}} $ 因子, 与不存在振动的情况相比, 可见振动对高精细度腔的影响十分明显; (b) 腔内为“空气模”时的$ {\beta }_{\rm{vib}} $ 因子. 与“薄膜模”相比, 振动对“空气模”的影响更大, 尤其是在$ {{\cal{L}}}_{\rm{eff}} $ 较小, 即高精细度的情况下Fig. 3.
$ {\beta }_{\rm{vib}} $ factor varying with vibration, where the four cases with the vibration standard deviation of 0.01, 0.03, 0.07 and 0.2 nm are calculated: (a)$ {\beta }_{\rm{vib}} $ factor when the cavity is on the “membrane-mode”. It’s clear that vibration affects the factor a lot compared with the no vibration case; (b)$ {\beta }_{\rm{vib}} $ factor when the cavity is on the “air-mode”. Vibration affects the factor more than that on the “membrane-mode”, especially when$ {{\cal{L}}}_{\rm{eff}} $ is low, i.e., the finesse is high.
图 4 考虑耦出效率时的
$ {\beta }_{\rm{vib}} $ 因子, 其中选取了四个振动标准差0.01, 0.03, 0.07和0.2 nm进行计算, 可以看出存在极大值使耦出效率$ {\beta }_{\rm{vib}} $ 最佳; 将该极大值提取出来, 可以得到该值与振动标准差$ {\sigma }_{\rm{vib}} $ 的关系, 并得到此时对应的耦出透射率$ {T}_{0} $ (a) 腔内为“薄膜模”时的$ {\beta }_{\rm{vib}} $ 因子; (b) 腔内为“空气模”时的$ {\beta }_{\rm{vib}} $ 因子; (c) 腔内为“薄膜模”时的最佳耦出效率$ {\beta }_{\rm{vib}} $ 以及对应的耦出透射率$ {T}_{0} $ 与振动$ {\sigma }_{\rm{vib}} $ 的关系; (d) 腔内为“空气模”时的最佳耦出效率$ {\beta }_{\rm{vib}} $ 以及对应的耦出透射率$ {T}_{0} $ 与振动$ {\sigma }_{\rm{vib}} $ 的关系Fig. 4.
$ {\beta }_{\rm{vib}} $ factor varying with vibration including outcoupling efficiency, where the four cases with the vibration standard deviation of 0.01, 0.03, 0.07 and 0.2 nm are calculated. It’s clear that there exists a maximum value of the outcoupling efficiency, thereby extracting this maximum value and calculating the relation between the max outcoupling efficiency$ {\beta }_{\rm{vib}} $ , the optimal outcoupling transmissivity$ {T}_{0} $ and vibration RMS$ {\sigma }_{\rm{vib}} $ : (a)$ {\beta }_{\rm{vib}} $ factor when the cavity is on the “membrane-mode”; (b)$ {\beta }_{\rm{vib}} $ factor when the cavity is on the “air-mode”; (c) the relation between the max$ {\beta }_{\rm{vib}} $ , the corresponding$ {T}_{0} $ and vibration RMS$ {\sigma }_{\rm{vib}} $ when the cavity is on the “membrane-mode”; (d) the relation between the max$ {\beta }_{\rm{vib}} $ , the corresponding$ {T}_{0} $ and vibration RMS$ {\sigma }_{\rm{vib}} $ when the cavity is on the “air-mode”. -
[1] Smeltzer B, Childress L, Gali A 2011 New J. Phys. 13 025021
Google Scholar
[2] Dréau A, Maze J R, Lesik M, Roch J F, Jacques V 2012 Phys. Rev. B 85 134107
Google Scholar
[3] Bernien H, Childress L, Robledo L, Markham M, Twitchen D, Hanson R 2012 Phys. Rev. Lett. 108 043604
Google Scholar
[4] Sipahigil A, Jahnke K D, Rogers L J, et al. 2014 Phys. Rev. Lett. 113 113602
Google Scholar
[5] Togan E, Chu Y, Trifonov A S, et al. 2010 Nature 466 730
Google Scholar
[6] Bernien H, Hensen B, Pfaff W, et al. 2013 Nature 497 86
Google Scholar
[7] Hensen B, Bernien H, Dreau A E, et al. 2015 Nature 526 682
Google Scholar
[8] Purcell E M 1995 Confined Electrons and Photons (Berlin: Springer) pp839–839
[9] Barbour R J, Dalgarno P A, Curran A, et al. 2011 J. Appl. Phys. 110 053107
Google Scholar
[10] Albrecht R, Bommer A, Deutsch C, Reichel J, Becher C 2013 Phys. Rev. Lett. 110 243602
Google Scholar
[11] Benedikter J, Kaupp H, Hümmer T, et al. 2017 Phys. Rev. A 7 024031
Google Scholar
[12] Greuter L, Starosielec S, Najer D, et al. 2014 Appl. Phys. Lett. 105 121105
Google Scholar
[13] Dutta H S, Goyal A K, Srivastava V, Pal S 2016 Photonics Nanostruct. Fundam. Appl. 20 41
Google Scholar
[14] Cai M, Painter O, Vahala K J 2000 Phys. Rev. Lett. 85 74
Google Scholar
[15] Johnson S, Dolan P R, Grange T, Trichet A A P, Hornecker G, Chen Y C, Weng L, Hughes G M, Watt A A R, Auffèves A, Smith J M 2015 New J. Phys. 17 122003
Google Scholar
[16] Høy Jensen R, Janitz E, Fontana Y, et al. 2020 Phys. Rev. A 13 064016
Google Scholar
[17] Riedel D, Söllner I, Shields B J, Starosielec S, Appel P, Neu E, Maletinsky P, Warburton R J 2017 Phys. Rev. X 7 031040
[18] Koehl W F, Buckley B B, Heremans F J, Calusine G, Awschalom D D 2011 Nature 479 84
Google Scholar
[19] Falk A L, Buckley B B, Calusine G, Koehl W F, Dobrovitski V V, Politi A, Zorman C A, Feng P X L, Awschalom D D 2013 Nat. Commun. 4 1819
Google Scholar
[20] Christle D J, Falk A L, Andrich P, Klimov P V, Ul Hassan J, Son N T, Janzen E, Ohshima T, Awschalom D D 2015 Nat. Mater. 14 160
Google Scholar
[21] Ivády V, Davidsson J, Delegan N, Falk A L, Klimov P V, Whiteley S J, Hruszkewycz S O, Holt M V, Heremans F J, Son N T 2019 Nat. Commun. 10 1
Google Scholar
[22] Li Q, Wang J F, Yan F F, et al. 2021 Natl. Sci. Rev. DOI: 10.1093/nsr/nwab122
[23] Zhou J Y, Li Q, Hao Z Y, Yan F F, Yang M, Wang J F, Lin W X, Liu Z H, Liu W, Li H, You L X, Xu J S, Li C F, Guo G C 2021 ACS Photonics 8 2384
Google Scholar
[24] Gali A 2011 Phys. Status Solidi B 248 1337
Google Scholar
[25] Son N, Carlsson P, Ul Hassan J, et al. 2006 Phys. Rev. Lett. 96 055501
Google Scholar
[26] Gali Á 2019 Nanophotonics 8 1907
Google Scholar
[27] Christle D J, Klimov P V, Charles F, Szász K, Ivády V, Jokubavicius V, Hassan J U, Syväjärvi M, Koehl W F, Ohshima T 2017 Phys. Rev. X 7 021046
[28] Manson N, Harrison J, Sellars M 2006 Phys. Rev. B 74 104303
Google Scholar
[29] Gruber A, Dräbenstedt A, Tietz C, Fleury L, Wrachtrup J, Von Borczyskowski C 1997 Science 276 2012
Google Scholar
[30] Xu J S, Li C F, Guo G C 2021 Fundamental Research 1 220
Google Scholar
[31] Kaupp H, Deutsch C, Chang H C, Reichel J, Hänsch T W, Hunger D 2013 Phys. Rev. A 88 053812
[32] Janitz E, Ruf M, Dimock M, Bourassa A, Sankey J, Childress L 2015 Phys. Rev. A 92 043844
Google Scholar
[33] Kaupp H, Hümmer T, Mader M, et al. 2016 Phys. Rev. A 6 054010
Google Scholar
[34] Bogdanović S, van Dam S B, Bonato C, Coenen L C, Zwerver A M J, Hensen B, Liddy M S Z, Fink T, Reiserer A, Lončar M, Hanson R 2017 Appl. Phys. Lett. 110 171103
Google Scholar
[35] Häußler S, Benedikter J, Bray K, Regan B, Dietrich A, Twamley J, Aharonovich I, Hunger D, Kubanek A 2019 Phys. Rev. B 99 165310
Google Scholar
[36] Ruf M, Weaver M J, van Dam S B, Hanson R 2021 Phys. Rev. A 15 024049
Google Scholar
[37] Li Q, Wang J F, Yan F F, et al. 2019 Nanoscale 11 20554
Google Scholar
[38] van Dam S B, Ruf M, Hanson R 2018 New J. Phys. 20 115004
Google Scholar
[39] Hunger D, Steinmetz T, Colombe Y, Deutsch C, Hänsch T W, Reichel J 2010 New J. Phys. 12 065038
Google Scholar
[40] Hill P, Gu E, Dawson M D, Strain M J 2018 Diamond Relat. Mater. 88 215
Google Scholar
[41] Faraon A, Barclay P E, Santori C, Fu K-M C, Beausoleil R G 2011 Nat. Photonics 5 301
Google Scholar
[42] Li L, Schröder T, Chen E H, Walsh M, Bayn I, Goldstein J, Gaathon O, Trusheim M E, Lu M, Mower J 2015 Nat. Commun. 6 6173
[43] Ruf M, M I J, van Dam S, de Jong N, van den Berg H, Evers G, Hanson R 2019 Nano Lett. 19 3987
Google Scholar
[44] Heupel J, Pallmann M, Korber J, Merz R, Kopnarski M, Stohr R, Reithmaier J P, Hunger D, Popov C 2020 Micromachines (Basel) 11 1080
Google Scholar
[45] Gallego Fernández J C 2018 Ph. D. Dissertation (North Rhine: Rheinische Friedrich-Wilhelms-Universität Bonn)
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