Theoretical calculation of fiber cavity coupling silicon carbide membrance

Zhou Ji-Yang; Li Qiang; Xu Jin-Shi; Li Chuan-Feng; Guo Guang-Can

doi:10.7498/aps.71.20211797

Abstract

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.

Keywords:

Authors and contacts

1.
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
2.
CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
3.
State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China

Corresponding author: Xu Jin-Shi, jsxu@ustc.edu.cn ; Li Chuan-Feng, cfli@ustc.edu.cn ;

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0302700), the National Natural Science Foundation of China (Grants Nos. 61725504, U19A2075, 61905233, 11774335, 11821404, 11975221), the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. ZDRW-XH-2019-1), the Anhui Frontier Program in Quantum Information Technologies, China (Grant Nos. AHY060300, AHY020100), the Fundamental Research Funds for the Central Universities, China (Grants Nos. WK2030380017, WK2470000026), and the China Postdoctoral Science Foundation (Grant Nos. BX20200326, 2021M693099).

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References

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Cited By

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t_m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t_m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t_m为4.19 μm. 图(c)和图(d)左上角的小图是界面场强的放大图

Figure 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 t_m is 4.12 μm; (c) field intensity of the “air-mode” in cavity, where t_m is 4.29 μm; (d) field intensity of the “membrane-mode” in cavity, where t_m is 4.19 μm.

DownLoad: Full-Size Img PowerPoint

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^–3

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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”.

DownLoad: Full-Size Img PowerPoint

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[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
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[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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