Hong-Ou-Mandel interference of entangled photons generated under pump-tight-focusing condition

Tian Ying; Cai Wu-Hao; Yang Zi-Xiang; Chen Feng; Jin Rui-Bo; Zhou Qiang

doi:10.7498/aps.71.20211783

Abstract

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:

Authors and contacts

1.
Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan Institute of Technology, Wuhan 430205, China
2.
School of Physics, Shandong University, Jinan 250100, China
3.
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

Corresponding author: Jin Rui-Bo, jrbqyj@foxmail.com ; Zhou Qiang, zhouqiang@uestc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12074299, 91836102, 11704290) and the National Key R&D Program of China (Grant No. 2018YFA0307400)

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References

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Cited By

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 4 HOM干涉实验装置图

Figure 4. Experimental setup of HOM interference.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

DownLoad: CSV

[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 物理学报 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 Google Scholar
[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 Google Scholar
[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 Google Scholar
[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 Google Scholar
[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
[19]	Niu X L, Huang Y F, Xiang G Y, Guo G C, Ou Z Y 2008 Opt. Lett. 33 968 Google Scholar
[20]	Takeuchi S 2001 Opt. Lett. 26 843 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
[30]	Bennink R S, Liu Y, Earl D D, Grice W P 2006 Phys. Rev. A 74 023802 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 物理学报 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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