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光学法布里-珀罗(F-P)谐振腔、粒子、微纳机械振子三者结合的复合腔光力学系统在基本物理问题、量子信息、精密测量等方面的研究和应用中越来越引起大家的重视. 本文将纳米光纤置于光学F-P谐振腔的腔模中, 探究了纳米光纤对光学F-P谐振腔精细度的影响, 并通过测量纳米光纤引起的光学F-P谐振腔内腔损耗随纳米光纤位置的关系直接获得光学F-P谐振腔的腰斑半径, 从而进一步实现了对光学F-P谐振腔腔内模场分布的无损表征. 此方法可以用于在纳米光纤表面装载的发光粒子与光学F-P谐振腔耦合的精确控制, 也为集合光子、粒子、声子的复合腔光力学研究提供了良好的平台.The composite cavity optomechanical system combining optical Fabry-Perot (F-P) cavities, particles, and micro/nano mechanical oscillators is becoming more significant in the researches and applications of the fundamental physics, quantum information processing, and precision measurement. Characterizing the mode field distribution of optical F-P cavity is significant prior to the application of optical F-P cavity. In this paper, we propose and demonstrate a method to measure the waist of an optical F-P cavity and to characterize the mode field distribution of the optical F-P cavity by using a nanofiber nondestructively. In experiment, a nanofiber is placed in the mode of the optical F-P cavity with a fineness of around 1500. The optical F-P cavity is composed of two mirrors each with high reflectivity of 99.8%. The radius of curvature of the each mirror is 50 mm. The cavity length is (
$ 80 \pm 4 $ ) mm. The nanofiber is fabricated from a single-mode fiber by the flame-brush method. The nanofiber diameter is around 440 nm. The transmission spectra of the optical F-P cavity are measured by scanning the cavity length. The free spectrum ranges and the inner cavity losses can be obtained from the transmission spectra. First, the influence of the nanofiber on the optical F-P cavity fineness is investigated. The fineness as a function of nanofiber position along the radial direction of the optical F-P cavity is measured. The fineness caused by the nanofiber decreases to a minimum value of about 240. Second, it is investigated that the optical F-P cavity inner loss caused by the nanofiber as a function of the nanofiber position along the radial direction of the optical F-P cavity when the nanofiber is placed at the waist of the optical F-P cavity. The inner loss of the optical F-P cavity caused by the nanofiber is related to the intensity distribution of the optical F-P cavity mode field, which is predicted theoretically. Thus, by making the Gaussian fitting of the optical F-P cavity inner loss as a function of the nanofiber position, we can obtain a waist radius of the optical F-P cavity to be ($ 72 \pm 1 $ ) μm. This is in good agreement with the theoretical calculation. Finally, the mode field distribution of the optical F-P cavity along the cavity axis is characterized. This method can be used for precisely controlling the coupling between the particles on the surface of nanofiber and optical F-P cavity. Besides, this method provides a good platform for studying the hybrid optomechanical system combining cavities, photons and quantum emitters.-
Keywords:
- cavity quantum electrodynamics /
- nanofiber /
- optical Fabry-Perot cavity /
- waist
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图 1 (a) 理论模型结构示意图, 灰色阴影表示高斯光束, 红色阴影表示高斯光束在径向光功率密度分布, 蓝色长棒表示纳米光纤; (b) 光学F-P谐振腔的精细度随纳米光纤在y轴位置的变化关系的模拟结果, 红色三角块为纳米光纤造成光学F-P谐振腔的内腔损耗, 蓝色实线为光学F-P谐振腔腔内高斯光束的强度分布, 橙色圆点为光学F-P谐振腔精细度
Fig. 1. (a) Schematic of the model for numerical simulations. Gray shaded areas represent the Gaussian beams, red shaded areas represent the intensity distribution of Gaussian beams and long blue bars represent the nanofiber. (b) F-P cavity finesse as a function of the nanofiber position along y-axis. The orange circles are the finesse of F-P cavity. The red triangular blocks are the F-P cavity losses and the blue solid line is the intensity distribution of the Gaussian beam in the F-P cavity.
图 2 (a) 实验装置示意图; (b) 纳米光纤的电镜照片
Fig. 2. (a) Schematic of experimental setup; (b) SEM image of the nanofiber.
图 3 光学F-P谐振腔的精细度随纳米光纤在y轴位置的变化关系
Fig. 3. Finesse of the F-P cavity as a function of nanofiber position along y-axis.
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[1] 张智明 2015 量子光学 (北京: 科学出版社) 第184—193页
Zhang Z M 2015 Quantum Optics (Beijing: Science Press) pp184–193 (in Chinese)
[2] 李刚, 张鹏飞, 杨鹏飞, 王志辉, 张天才 2022 光学学报 42 76
Li G, Zhang P F, Yang P F, Wang Z H, Zhang T C 2022 Acta Opt. Sin. 42 76
[3] Walther H, Varcoe B T H, Englert B-G, Becker T 2006 Rep. Prog. Phys. 69 1325
Google Scholar
[4] 张天才, 毋伟, 杨鹏飞, 李刚, 张鹏飞 2021 光学学报 41 392
Zhang T C, Wu W, Yang P F, Li G, Zhang P F 2021 Acta Opt. Sin. 41 392
[5] Vahala K J 2003 Nature 424 839
Google Scholar
[6] 宋丽军, 张鹏飞, 王鑫, 王晨曦, 李刚, 张天才 2019 物理学报 68 074204
Google Scholar
Song L J, Zhang P F, Wang X, Wang C X, Li G, Zhang T C 2019 Acta Phys. Sin. 68 074204
Google Scholar
[7] McCall S L, Levi A F J, Slusher R E, Pearton S J, Logan R A 1992 Appl. Phys. Lett. 60 289
Google Scholar
[8] Kahl M, Thomay T, Kohnle V, Beha K, Merlein J, Hagner M, Halm A, Ziegler J, Nann T, Fedutik Y, Woggon U, Artemyev M, Pérez-Willard F, Leitenstorfer A, Bratschitsch R 2007 Nano Lett. 7 2897
Google Scholar
[9] Ruddell S K, Webb K E, Herrera I, Parkins A S, Hoogerland M D 2017 Optica 4 576
Google Scholar
[10] Hunger D, Steinmetz T, Colombe Y, Deutsch C, Hänsch T W, Reichel J 2010 New J. Phys. 12 065038
Google Scholar
[11] Zhang Q Q, Fan Z Y, Zhang J P, Zhang F B, Zhang Q, Li Y M 2020 Appl. Opt. 59 8959
Google Scholar
[12] 成凡, 张鹏飞, 王鑫, 张天才 2017 量子光学学报 23 74
Cheng F, Zhang P F, Wang X, Zhang T C 2017 J. Quantum Opt. 23 74
[13] Vučković J, Lončar M, Mabuchi H, Scherer A 2001 Phys. Rev. E 65 016608
Google Scholar
[14] Chen Y T, Szurek M, Hu B L, Hond J D, Braverman B, Vuletic V 2022 Opt. Express 30 37426
[15] Kuhn A, Hennrich M, Rempe G 2002 Phys. Rev. Lett. 89 067901
Google Scholar
[16] Yang P F, Xia X W, He H, Li S K, Han X, Zhang P, Li G, Zhang P F, Xu J P, Yang Y P, Zhang T C 2019 Phys. Rev. Lett. 123 233604
[17] Yang P F, Li M, Han X, He H, Li G, Zou C L, Zhang P F, Zhang T C 2019 arXiv 1911.10300
[18] Chen W L, Beck K M, Bücker R, Gullans M, Lukin M D, Tanji-Suzuki H, Vuletic V 2013 Science 341 768
Google Scholar
[19] Colombe Y, Steinmetz T, Dubois G, Linke F, Hunger D, Reichel J 2007 Nature 450 272
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[20] Haas F, Volz J, Gehr R, Reichel J, Estève J 2014 Science 344 180
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Google Scholar
[22] Takahashi H, Kassa E, Christoforou C, Keller M 2020 Phys. Rev. Lett. 124 013602
Google Scholar
[23] Kobel P, Breyer M, Köhl M 2021 npj Quantum Inf. 7 6
Google Scholar
[24] Kiraz A, Michler P, Becher C, Gayral B, Imamoğlu A, Zhang L D, Hu E 2001 Appl. Phys. Lett. 78 3932
Google Scholar
[25] Lodahl P, Mahmoodian S, Stobbe S 2015 Rev. Mod. Phys. 87 347
Google Scholar
[26] Metcalf H J, Van der Straten P 2003 J. Opt. Soc. Am. B: Opt. Phys. 20 887
Google Scholar
[27] Ye J, Vernooy D W, Kimble H J 1999 Phys. Rev. Lett. 83 4987
Google Scholar
[28] Münstermann P, Fischer T, Pinkse P W H, Rempe G 1999 Opt. Commun. 159 63
Google Scholar
[29] Fortier K M, Kim S Y, Gibbons M J, Ahmadi P, Chapman M S 2007 Phys. Rev. Lett. 98 233601
Google Scholar
[30] Kuhr S, Alt W, Schrader D, Dotsenko I, Miroshnychenko Y, Rosenfeld W, Khudaverdyan M, Gomer V, Rauschenbeutel A, Meschede D 2003 Phys. Rev. Lett. 91 213002
Google Scholar
[31] Zhang Y C, Li G, Zhang P F, Wang J M, Zhang T C 2009 Front. Phys. Chin. 4 190
Google Scholar
[32] Zhu J G, Ozdemir S K, Xiao Y F, Li L, He L, Chen D R, Yang L 2010 Nat. Photonics 4 46
Google Scholar
[33] Wang X, Song L J, Wang C X, Zhang P F, Li G, Zhang T C 2019 Chin. Phys. B 28 073701
[34] Nayak K P, Sadgrove M, Yalla R, Kien F L, Hakuta K 2018 J. Opt. 20 073001
Google Scholar
[35] Vetsch E, Reitz D, Sague’ G, Schmidt R, Dawkins S T, Rauschenbeutel A 2010 Phys. Rev. Lett. 104 203603
Google Scholar
[36] Davanco M I, Srinivasan K A 2009 Opt. Express 17 10542
Google Scholar
[37] Tong L M, Gattass R R, Ashcom J B, He S, Lou J Y, Shen M Y, Maxwell I, Mazur E 2003 Nature 426 816
Google Scholar
[38] Zhang P F, Wang X, Song L J, Wang C X, Li G, Zhang T C 2020 J. Opt. Soc. Am. B: Opt. Phys. 37 1401
Google Scholar
[39] Kien F L, Gupta S D, Balykin V I, Hakuta K 2005 Phys. Rev. A 72 032509
Google Scholar
[40] Fenton E F, Khan A, Solano P, Orozco L A, Fatemi F K 2018 Opt. Lett. 43 1534
Google Scholar
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Google Scholar
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[43] Pennetta R, Xie S, Russel P S 2016 Phys. Rev. Lett. 117 273901
Google Scholar
[44] Bernd W, Thorsten O, Sebastian S, Thomas H, Arno R 2021 Phys. Rev. Appl. 16 064021
Google Scholar
[45] Sakai H, Honda Y, Sasao N, Araki S, Higashi Y, Okugi T, Taniguchi T, Urakawa J, Takano M 2002 Jpn. J. Appl. Phys. 41 6398
Google Scholar
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Google Scholar
[47] Sakaue K, Washio M, Araki S, Fukuda M, Higashi Y, Honda Y, Omori T, Taniguchi T, Terunuma N, Urakawa J, Sasao N 2009 Rev. Sci. Instrum. 80 123304
Google Scholar
[48] Zhang P F, Cheng F, Wang X, Song L J, Zou C L, Li G, Zhang T C 2018 Opt. Express 26 31500
Google Scholar
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