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Hong-Ou-Mandel (HOM)干涉是光子的一种非经典效应, 在量子光学中起到重要作用. 偏硼酸钡(β-barium borate, BBO)具有较高的非线性效率, 常被用来产生双光子态, 进而展示HOM干涉. 然而, 在以前的实验中, 人们往往使用带通滤光片对双光子的频谱进行过滤, 所得光谱由带通滤光片直接决定, 而对BBO晶体自身的原始光谱, 特别是泵浦光强聚焦下的原始光谱, 缺乏系统性研究. 本文对泵浦光强聚焦条件下BBO晶体产生的双光子纠缠态光谱分布和HOM干涉进行了深入研究. 理论计算发现, 使用50 mm透镜聚焦的情况和无聚焦情况相比, 下转换光的光谱宽度会增加7.4倍, HOM干涉条纹的宽度会减少为无聚焦情况的1/8, 干涉条纹可见度会从53.0% 提高到98.7%. 实验上使用II型BBO晶体制备了能量-时间纠缠态, 并进行了HOM干涉, 获得了
$(86.6 \pm 1.0) $ % 的干涉可见度. 干涉可见度极大提高的原因在于强聚焦改善了光谱的对称性. 此外, 本文提出的不同入射角获得不同光谱分布的技术方案有望在未来应用于高维量子纠缠态的制备.-
关键词:
- Hong-Ou-Mandel干涉 /
- 偏硼酸钡晶体 /
- 聚束效应 /
- 量子信息
Hong-Ou-Mandel (HOM) interference is a non-classical effect of photons and plays an important role in quantum optics. The β-barium borate (BBO) has a high nonlinear efficiency, and is commonly used to generate biphoton states, thereby exhibiting HOM interference. However, in previous experiments, researchers often used band-pass filters, so the resulting spectrum was directly determined by the band-pass filter. As a result, the original spectrum of the BBO crystal, especially the spectrum under tight focusing, was lack of systematic research. In this paper, the biphoton spectral distribution and HOM interference generated by the BBO crystal under the condition of tight focusing are systematically studied for the first time. Theoretical calculations show that using a lens with 50-mm focusing length, the spectral width of the down-converted photons is increased by 7.9 times that of the non-focused case; the width of the HOM interference fringe is reduced to 1/8, and the visibility of the interference fringe increases from 53.0% to 98.7%. We experimentally prepare the energy-time entanglement state by using type-II BBO crystal and perform HOM interference, thereby obtaining the interference visibility of$(86.6 \pm 1.0)$ %. The increasing of the HOM visibility is due to the improvement of biphoton's spectral symmetry. In addition, the proposed technique by which different spectral distributions are obtained at different incident angles is expected to be applied to the preparation of high-dimensional qudits in the future.-
Keywords:
- Hong-Ou-Mandel interference /
- β-barium borate crystal /
- bunching effect /
- quantum information
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图 1 (a) 泵浦光强聚焦于BBO晶体的示意图; (b)—(d) 入射角分别为42.29°, 41.79°和41.29°时的方案图和联合频谱强度图; (e) 计算泵浦光斑上任意一点p的入射角的立体模型; (f)—(h) 透镜焦距分别为50, 100和200 mm时泵浦光斑的入射角分布
Fig. 1. (a) Schematic diagram of the BBO crystal under the tight focusing; (b)–(d) setups and JSIs with the incident angles of 42.29°, 41.79°, and 41.29°, respectively; (e) three dimensional (3D) model for calculating the incident angle of an arbitrary point p on the pump; (f)–(h) distribution of the incident angle using lenses with the focal lengths of 50, 100, and 200 mm, respectively.
图 2 不同聚焦条件下的JSI分布和边缘投影分布 (a) 无透镜(焦距为
$ \infty $ ); (b)—(d) 透镜焦距分别为200, 50和100 mm; (e) 透镜焦距为100 mm加上带宽为12.1 nm的BPF; (f) BPF的透过率测试图, 图中Δ为半波全宽Fig. 2. Joint spectral intensities and marginal projection under different focusing conditions: (a) No lens; (b)–(d) using lenes with focal lengths of 200, 50, and 100 mm, respectively; (e) focal length of the lens is 100 mm and the BPF with a bandwidth of 12.1 nm; (f) transmittance of the BPF, Δ is FWHM.
图 3 不同焦距透镜聚焦条件下的HOM干涉模拟图 (a) 无透镜聚焦; (b)—(d) 透镜焦距分别为200, 100和50 mm; (e) 透镜焦距为100 mm加上带宽为12 nm的BPF, 图中V为干涉可见度, FWHM为干涉条纹的宽度
Fig. 3. Simulated HOM interference under different focusing conditions: (a) Using no lens; (b)–(d) using lenes with a focal length of 200, 100, and 50 mm respectively; (e) focal length of the lens is 100 mm and a BPF with a bandwidth of 12 nm. In the figure, V is the visibility of interference, and FWHM is the width of the interference fringe.
图 5 (a) 信号光与闲频光的光谱图, 红色为信号光(通道1), 蓝色为闲频光(通道2); (b) 粗略扫描得到的HOM干涉图样; (c) 精细扫描得到的HOM干涉图样
Fig. 5. (a) Spectrogram of the signal and the idler, red is the signal (Channel 1), blue is the idler (Channel 2); (b) HOM interference pattern obtained from rough scanning; (c) HOM interference pattern obtained from precise scanning.
图 6 (a) 透镜焦距f与双光子光谱宽度(Δ为半波全宽)之间的关系图; (b) 透镜焦距f与HOM干涉可见度之间的关系图
Fig. 6. (a) Diagram of the relationship between the lens focal length f and the biphoton spectral width (Δ, the FWHM); (b) diagram of the relationship between lens focal length f and HOM interference visibility.
表 1 不同入射角对应的信号光与闲频光的波长
Table 1. Wavelengths of the signal and idler under different incident angles
θ/(°) $\Delta \theta$/(°) ${\lambda _{{{\rm{s}}_0}}}$/nm ${\lambda _{{{\rm{i}}_0}}}$/nm 40.79 –1.0 777.834 844.941 41.29 –0.5 793.565 827.130 41.79 0 809.897 810.103 42.29 0.5 826.854 793.819 42.79 1.0 844.459 778.243 
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[1] Hong C K, Ou Z Y, Mandel L 1987 Phys. Rev. Lett. 59 2044
Google Scholar
[2] 张越, 候飞雁, 刘涛, 张晓斐, 张首刚, 董瑞芳 2018 67 144204
Google Scholar
Zhang Y, Hou F Y, Liu T, Zhang X F, Zhang S G, Dong R F 2018 Acta Phys. Sin. 67 144204
Google Scholar
[3] 孙涛, 汪垟, 李剑, 王琴 2019 光子学报 48 0427001
Google Scholar
Sun T, Wang Y, Li J, Wang Q 2019 Acta Photon. Sin. 48 0427001
Google Scholar
[4] Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575
Google Scholar
[5] Gisin N, Pironio S, Sangouard N 2010 Phys. Rev. Lett. 105 070501
Google Scholar
[6] Zhong H S, Wang H, Deng Y H, Chen M C, Peng L C, Luo Y H, Qin J, Wu D, Ding X, Hu Y, Hu P, Yang X Y, Zhang W J, Li H, Li Y, Jiang X, Gan L, Yang G, You L, Wang Z, Li L, Liu N L, Lu C Y, Pan J W 2020 Science 370 1460
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[7] Zhang Z, Yuan C, Shen S, Yu H, Zhang R, Wang H, Li H, Wang Y, Deng G, Wang Z, You L, Wang Z, Song H, Guo G, Zhou Q 2021 NPJ Quantum Inf. 7 123
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[8] Fan Y R, Yuan C Z, Zhang R M, Shen S, Wu P, Wang H Q, Li H, Deng G W, Song H Z, You L X, Wang Z, Wang Y, Guo G C, Zhou Q 2021 Photonics Res. 9 1134
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[9] Lyons A, Knee G C, Bolduc E, Roger T, Leach J, Gauger E M, Faccio D 2018 Sci. Adv. 4 eaap9416
Google Scholar
[10] Gerrits T, Marsili F, Verma V B, Shalm L K, Shaw M, Mirin R P, Nam S W 2015 Phys. Rev. A 91 013830
Google Scholar
[11] Jin R B, Gerrits T, Fujiwara M, Wakabayashi R, Yamashita T, Miki S, Terai H, Shimizu R, Takeoka M, Sasaki M 2015 Opt. Express 23 28836
Google Scholar
[12] Jin R B, Shimizu R, Fujiwara M, Takeoka M, Wakabayashi R, Yamashita T, Miki S, Terai H, Gerrits T, Sasaki M 2016 Quantum Sci. Technol. 1 015004
Google Scholar
[13] Jachura M, Chrapkiewicz R 2015 Opt. Lett. 40 1540
Google Scholar
[14] Kobayashi T, Ikuta R, Yasui S, Miki S, Yamashita T, Terai H, Yamamoto T, Koashi M, Imoto N 2016 Nat. Photonics 10 441
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[15] Ono T, Okamoto R, Takeuchi S 2013 Nat. Commun. 4 2426
Google Scholar
[16] 陈创天, 吴柏昌, 江爱栋, 尤桂铭 1984 中国科学 B 14 598
Chen C T, Wu B C, Jiang A D, You G M 1984 Sci. Sin. B 14 598
[17] Kwiat P G, Mattle K, Weinfurter H, Zeilinger A, Sergienko A V, Shih Y 1995 Phys. Rev. Lett. 75 4337
Google Scholar
[18] Kwiat P G, Waks E, White A G, Appelbaum I, Eberhard P H 1999 Phys. Rev. A 6 0
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Google Scholar
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[28] Molina-Terriza G, Minardi S, Deyanova Y, Osorio C I, Hendrych M, Torres J P 2005 Phys. Rev. A 72 065802
Google Scholar
[29] Torres J P, Molina-Terriza G, Torner L 2005 J. Opt. B: Quantum Semiclassical Opt. 7 235
Google Scholar
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Google Scholar
[31] Osorio C I, Valencia A, Torres J P 2008 New J. Phys. 10 113012
Google Scholar
[32] Brambilla E, Caspani L, Lugiato L A, Gatti A 2010 Phys. Rev. A 82 013835
Google Scholar
[33] Kolenderski P, Wasilewski W, Banaszek K 2009 Phys. Rev. A 80 013811
Google Scholar
[34] Bennink R S 2010 Phys. Rev. A 81 053805
Google Scholar
[35] Mosley P J, Lundeen J S, Smith B J, Walmsley I A 2008 New J. Phys. 10 093011
Google Scholar
[36] Raymer M G, Noh J, Banaszek K, Walmsley I A 2005 Phys. Rev. A 72 023825
Google Scholar
[37] 翟艺伟, 董瑞芳, 权润爱, 项晓, 刘涛, 张首刚 2021 70 120302
Google Scholar
Zhai Y W, Dong R F, Quan R A, Xiang X, Liu T, Zhang S G 2021 Acta Phys. Sin. 70 120302
Google Scholar
[38] Jin R B, Shimizu R 2018 Optica 5 93
Google Scholar
[39] Cai N, Cai W H, Wang S, Li F, Shimizu R, Jin R B 2022 J. Opt. Soc. Am. B 39 77
Google Scholar
[40] Smith A "SNLO" http://www.as-photonics.com/snlo[2021-11-22]
[41] Jin R B, Cai W H, Ding c, Mei F, Deng G W, Shimizu R, Zhou Q 2020 Quan. Eng. 2 e38
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